Transcript of Electrochemical Corrosion Measurements · 2 • We need to somehow measure the current due to the...
Electrochemical Corrosion Rate Measurement ndash A Comparison
Dr David LovedayGamry Instrumentswwwgamrycom
Overviewbull Corrosion Testing Theorybull Polarization Resistance (LPR)bull Electrochemical Frequency Modulation
(EFM)bull EISbull Comparison
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Overviewbull Corrosion Testing Theorybull Polarization Resistance (LPR)bull Electrochemical Frequency Modulation
(EFM)bull EISbull Comparison
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
Chart1
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
22966792909
-23704047221
229699298
-21423517997
22976259397
-20378522094
22984232175
-20166484582
22990909867
-20709071618
22997046964
-22196729596
23000227162
-24652208443
23008280774
-28716798728
23011458045
-3405842011
23016832479
-4109775349
23023195134
-49816264977
23033689666
-61892190417
2305227748
-76971064803
2307738488
-9571145688
2311436461
-118684808519
23169813607
-147793187339
23266993127
-182360078708
23403930151
-223544730168
23600814906
-272222871934
23883494315
-32549990886
2426200205
-382872712393
24753593172
-439926020742
25353156981
-493561293044
26052509612
-540219594231
26830378716
-577515135083
27669669044
-603395000341
28536575756
-616854435848
29418116987
-617878098514
30287499395
-606491667235
31130022579
-58281489506
31918867641
-54740751829
32633660435
-501988292287
33250010423
-449330990757
33763871035
-391489775991
34150641107
-33564065985
34455050245
-279549571603
34667315656
-229465956169
34806389184
-187920019037
34904140404
-150979711484
34968508202
-121045388297
35009084842
-97434033292
35036425595
-77265590178
35053013742
-61854451326
350648884
-49060894261
35070249852
-39086553209
35074269913
-31244214759
35077118125
-24747212738
35078534645
-19952148875
35080878341
-15770351196
35081031432
-12639148203
35075791475
-09987970382
35075777286
-08060287558
35076581182
-06292911249
35077573834
-05146308149
35076158821
-04068395941
35077617171
-03256031105
350758985
-02400052396
35077588905
-02070997607
35075838423
-01672944336
35076113455
-01238103434
35075032422
-01156289084
35075701548
-00684893168
35075634245
-00704331603
35074431041
-00465436604
35078182783
-00511393151
35075996781
-0046449791
35077655111
-00147450227
35078505257
-00272220592
35077088546
-00176151618
35075847138
-00188814922
35075563677
-00172568591
35076467698
00070099542
3507324198
-00289634001
3507534848
-00379425424
35073930177
-00126773837
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
50000303995
50000303995
50000303995
50000303995
49000042456
49000042456
49000042456
49000042456
48000672121
48000672121
48000672121
48000672121
4700043122
4700043122
4700043122
4700043122
46000052684
46000052684
46000052684
46000052684
45001554832
45001554832
45001554832
45001554832
44000835989
44000835989
44000835989
44000835989
43000386737
43000386737
43000386737
43000386737
42001087201
42001087201
42001087201
42001087201
40999291328
40999291328
40999291328
40999291328
399992182
399992182
399992182
399992182
38999626914
38999626914
38999626914
38999626914
38001050617
38001050617
38001050617
38001050617
36999400027
36999400027
36999400027
36999400027
35999845411
35999845411
35999845411
35999845411
3500053879
3500053879
3500053879
3500053879
33998743849
33998743849
33998743849
33998743849
33000234384
33000234384
33000234384
33000234384
31998895026
31998895026
31998895026
31998895026
3100039528
3100039528
3100039528
3100039528
29999782847
29999782847
29999782847
29999782847
28999096494
28999096494
28999096494
28999096494
28000183469
28000183469
28000183469
28000183469
27001003036
27001003036
27001003036
27001003036
26001110714
26001110714
26001110714
26001110714
24998423564
24998423564
24998423564
24998423564
23999937011
23999937011
23999937011
23999937011
22999320153
22999320153
22999320153
22999320153
22001196781
22001196781
22001196781
22001196781
21000636732
21000636732
21000636732
21000636732
20000390847
20000390847
20000390847
20000390847
18998658986
18998658986
18998658986
18998658986
18000093991
18000093991
18000093991
18000093991
16990420912
16990420912
16990420912
16990420912
1602124045
1602124045
1602124045
1602124045
1499402499
1499402499
1499402499
1499402499
13977853723
13977853723
13977853723
13977853723
13010538812
13010538812
13010538812
13010538812
11984756349
11984756349
11984756349
11984756349
10969169617
10969169617
10969169617
10969169617
0999943538
0999943538
0999943538
0999943538
08972910703
08972910703
08972910703
08972910703
08004579361
08004579361
08004579361
08004579361
06987510647
06987510647
06987510647
06987510647
05991207513
05991207513
05991207513
05991207513
0499299343
0499299343
0499299343
0499299343
03998207684
03998207684
03998207684
03998207684
02999189533
02999189533
02999189533
02999189533
01995494967
01995494967
01995494967
01995494967
00994354614
00994354614
00994354614
00994354614
00000260569
00000260569
00000260569
00000260569
-00998519858
-00998519858
-00998519858
-00998519858
-01999307233
-01999307233
-01999307233
-01999307233
-03000002024
-03000002024
-03000002024
-03000002024
-0399820225
-0399820225
-0399820225
-0399820225
-04999063003
-04999063003
-04999063003
-04999063003
-05999699918
-05999699918
-05999699918
-05999699918
-07001420079
-07001420079
-07001420079
-07001420079
-07998994986
-07998994986
-07998994986
-07998994986
-09000708672
-09000708672
-09000708672
-09000708672
-10000260585
-10000260585
-10000260585
-10000260585
-10999115648
-10999115648
-10999115648
-10999115648
-11999499933
-11999499933
-11999499933
-11999499933
-12998676433
-12998676433
-12998676433
-12998676433
-14000187317
-14000187317
-14000187317
-14000187317
-14999557334
-14999557334
-14999557334
-14999557334
-16000495256
-16000495256
-16000495256
-16000495256
-16999700321
-16999700321
-16999700321
-16999700321
-17998885404
-17998885404
-17998885404
-17998885404
-18998707966
-18998707966
-18998707966
-18998707966
-19999565727
-19999565727
-19999565727
-19999565727
-21000154375
-21000154375
-21000154375
-21000154375
-22000394726
-22000394726
-22000394726
-22000394726
-22999889377
-22999889377
-22999889377
-22999889377
-23998987443
-23998987443
-23998987443
-23998987443
EISCURVE
Pstat pc4Start Frequency 100000 HzEnd Frequency 0001 HzEOC 0000048359 VDC Pot 0 VAC Pot 10 mV(rms)Area 1 cm2Electrode 787 gmcm3 2792 gequivConditioning OFFDelay ON s
Notes
Results
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
DataFileName
Copeland_EIS_DummyDTA
PointCount
75
Title
Potentiostatic EIS
Date
1291999
Time
104155
ChartTitle
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ModelName
ModelParamCount
ModelLabels
ModelParams
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
1000E+00
ModelError
ModelLock
NumberOfIterations
30
AnalCurveFlag
PlotType
1
PlotImmittance
1
YLog
AspectRatio
Disp1ChartName
Chart 9
Disp1EnablePointsFlag
Disp1AxisRange
-3
6
22
36
-70
10
Disp1FitAxisRange
Disp1Labels
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Disp1MatchToList
Modulus
Phase
Disp2ChartName
Chart 10
Disp2EnablePointsFlag
Disp2AxisRange
-3
6
0
3500
-200
1600
Disp2FitAxisRange
Disp2Labels
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Disp2MatchToList
Real
Imaginary
Disp3ChartName
Chart 11
Disp3EnablePointsFlag
Disp3AxisRange
0
3500
-200
1600
Disp3FitAxisRange
Disp3Labels
Real (Ohm)
-Imag (Ohm)
Disp3MatchToList
Nyquist
CurveFreq
CurveReal
CurveImag
CurveMod
CurvePhz
CurveSigma
FitCurveReal
FitCurveImag
FitCurveMod
FitCurvePhz
DispFreqData
DispRealData
DispImagData
DispModData
DispPhzData
DispSigmaData
AnalRealData
AnalImagData
AnalModData
AnalPhzData
Display1PointStatus
Display2PointStatus
Display3PointStatus
PtTog
DataTable
100007
197837
-818946
1980064287444
-23704047221
1
500
198E+02
819E+00
230
-237
794336
198011
-74073
1981494996569
-21423517997
1
490
198E+02
741E+00
230
-214
631055
198313
-705642
1984385018897
-20378522094
1
480
198E+02
706E+00
230
-204
501237
19868
-699586
1988031298977
-20166484582
1
470
199E+02
700E+00
230
-202
398112
198979
-719506
1991090438162
-20709071618
1
460
199E+02
720E+00
230
-207
316341
199241
-772258
1993906074088
-22196729596
1
450
199E+02
772E+00
230
-222
251237
199352
-858266
1995366682008
-24652208443
1
440
199E+02
858E+00
230
-247
199544
199656
-100152
1999070348113
-28716798728
1
430
200E+02
100E+01
230
-287
158529
1997
-118848
200053339065
-3405842011
1
420
200E+02
119E+01
230
-341
125872
199786
-143551
200301060137
-4109775349
1
410
200E+02
144E+01
230
-411
99982
199837
-174189
2005947273639
-49816264977
1
400
200E+02
174E+01
230
-498
79426
199908
-216789
2010800416979
-61892190417
1
390
200E+02
217E+01
230
-619
63111
200123
-270474
2019425090855
-76971064803
1
380
200E+02
270E+01
231
-770
501118
200286
-337721
203113358828
-9571145688
1
370
200E+02
338E+01
231
-957
398093
200471
-421307
2048502324223
-118684808519
1
360
200E+02
421E+01
231
-1187
316267
200618
-529281
207482446712
-147793187339
1
350
201E+02
529E+01
232
-1478
251116
201521
-663971
2121774925137
-182360078708
1
340
202E+02
664E+01
233
-1824
199537
202518
-832837
2189742336662
-223544730168
1
330
203E+02
833E+01
234
-2235
158449
203751
-104814
2291297549359
-272222871934
1
320
204E+02
105E+02
236
-2722
125904
206128
-131571
2445397317922
-32549990886
1
310
206E+02
132E+02
239
-3255
99995
209422
-165316
2668088340741
-382872712393
1
300
209E+02
165E+02
243
-3829
794163
214955
-207526
2987853622603
-439926020742
1
290
215E+02
208E+02
248
-4399
630984
223426
-260272
3430170425212
-493561293044
1
280
223E+02
260E+02
254
-4936
501303
236723
-326084
4029498154671
-540219594231
1
270
237E+02
326E+02
261
-5402
398209
257186
-407639
48198982657
-577515135083
1
260
257E+02
408E+02
268
-5775
316113
289367
-508128
5847455216357
-603395000341
1
250
289E+02
508E+02
277
-6034
251185
338627
-628516
7139331953236
-616854435848
1
240
339E+02
629E+02
285
-6169
199495
413459
-770704
8746044822072
-617878098514
1
230
413E+02
771E+02
294
-6179
158533
523702
-931289
10684395099045
-606491667235
1
220
524E+02
931E+02
303
-6065
125911
681991
-110344
12971860150653
-58281489506
1
210
682E+02
110E+03
311
-5828
100009
897989
-127019
15555599892711
-54740751829
1
200
898E+02
127E+03
319
-5474
794083
11739
-14089
18338594329992
-501988292287
1
190
117E+03
141E+03
326
-5020
630971
149621
-149272
21134941122464
-449330990757
1
180
150E+03
149E+03
333
-4493
500083
18449
-150193
23789598010265
-391489775991
1
170
184E+03
150E+03
338
-3915
400059
216695
-143776
26005434278435
-33564065985
1
160
217E+03
144E+03
342
-3356
315793
246389
-130759
27893629273008
-279549571603
1
150
246E+03
131E+03
345
-2795
249911
26973
-114197
29290822403784
-229465956169
1
140
270E+03
114E+03
347
-2295
200011
286318
-97426
30243978342804
-187920019037
1
130
286E+03
974E+02
348
-1879
157934
298647
-805698
30932430114855
-150979711484
1
120
299E+03
806E+02
349
-1510
125002
306963
-658326
31394301169442
-121045388297
1
110
307E+03
658E+02
350
-1210
99987
312319
-536292
31688996332109
-97434033292
1
100
312E+03
536E+02
350
-974
789389
315996
-428735
31889121815793
-77265590178
1
090
316E+03
429E+02
350
-773
631623
318248
-34491
32011157208855
-61854451326
1
080
318E+03
345E+02
351
-619
499748
319812
-274518
32098803196886
-49060894261
1
070
320E+03
275E+02
351
-491
397302
320637
-219075
32138454276031
-39086553209
1
060
321E+03
219E+02
351
-391
315718
321204
-175331
32168217111243
-31244214759
1
050
321E+03
175E+02
351
-312
251085
321593
-138989
32189320755525
-24747212738
1
040
322E+03
139E+02
351
-247
199489
321803
-112107
32199821521786
-19952148875
1
030
322E+03
112E+02
351
-200
158325
32205
-886649
32217203035788
-15770351196
1
020
322E+03
887E+01
351
-158
125729
322105
-710662
32218338733216
-12639148203
1
010
322E+03
711E+01
351
-126
100006
321746
-560934
32179489307824
-09987970382
1
000
322E+03
561E+01
351
-100
0794599
321762
-45268
32179384170963
-08060287558
1
-010
322E+03
453E+01
351
-081
0631058
321834
-353491
32185341251058
-06292911249
1
-020
322E+03
353E+01
351
-063
0501187
321914
-289151
32192698586183
-05146308149
1
-030
322E+03
289E+01
351
-051
0398272
321814
-228514
32182211306997
-04068395941
1
-040
322E+03
229E+01
351
-041
0316296
321925
-182947
32193019831243
-03256031105
1
-050
322E+03
183E+01
351
-033
0251206
3218
-134799
32180282328942
-02400052396
1
-060
322E+03
135E+01
351
-024
0199461
321926
-116363
32192810301491
-02070997607
1
-070
322E+03
116E+01
351
-021
0158526
321797
-939598
32179837173827
-01672944336
1
-080
322E+03
940E+00
351
-017
0125872
321818
-695417
32181875136294
-01238103434
1
-090
322E+03
695E+00
351
-012
0099994
321738
-649302
32173865518008
-01156289084
1
-100
322E+03
649E+00
351
-012
0079449
321788
-384654
32178822990081
-00684893168
1
-110
322E+03
385E+00
351
-007
0063103
321783
-395565
32178324313219
-00704331603
1
-120
322E+03
396E+00
351
-007
0050134
321694
-261325
3216941061424
-00465436604
1
-130
322E+03
261E+00
351
-005
0039809
321972
-287376
32197212824865
-00511393151
1
-140
322E+03
287E+00
351
-005
0031626
32181
-260892
32181010575281
-0046449791
1
-150
322E+03
261E+00
351
-005
0025116
321933
-0828492
32193301066059
-00147450227
1
-160
322E+03
828E-01
351
-001
0019954
321996
-152985
3219960363427
-00272220592
1
-170
322E+03
153E+00
351
-003
0015853
321891
-098963
32189101521272
-00176151618
1
-180
322E+03
990E-01
351
-002
0012593
321799
-106047
32179901747359
-00188814922
1
-190
322E+03
106E+00
351
-002
0010001
321778
-096916
32177801459502
-00172568591
1
-200
322E+03
969E-01
351
-002
0007943
321845
0393767
32184500240881
00070099542
1
-210
322E+03
-394E-01
351
001
0006309
321606
-162574
32160604109112
-00289634001
1
-220
322E+03
163E+00
351
-003
0005012
321762
-213078
3217620705525
-00379425424
1
-230
322E+03
213E+00
351
-004
0003982
321657
-0711705
32165700787367
-00126773837
1
-240
322E+03
712E-01
351
-001
EISCURVE
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
ampF
Page ampP
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Log Freq (Hz)
Log Modulus (Ohm)
Phase (Degree)
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Log Freq (Hz)
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Real (Ohm)
-Imag (Ohm)
Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
Polarization ResistanceCarbon Steel
Calculation of ICORR from RP
I Calculation of Corrosion Rate from ICORR
II Calculation of Corrosion Rate from ICORR
Polarization ResistanceCarbon Steel
Electrochemical Frequency ModulationEFMWhat is it
Theory
More Theory
And then A Miracle Occurs
An Example
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theory
Theory
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
Electrochemistry as a Circuit
Bode Plot
Complex Plane (Nyquist) Plot
Nyquist Plot with Fit
Criteria For Valid EIS
Electrochemistry A Linear System
EIS of Carbon Steel
Combined Results
Thatrsquos all folks
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemical Corrosion Rate Measurement ndash A Comparison
Overview
Why Are Electrochemical Techniques Used for Corrosion Measurement
Electrochemical Techniques are Fast
Electrochemical Techniques Are Sensitive
A Review of Electrochemistry
Redox Reactions (Half-Reactions) in Corrosion
What is Potential
What is Current
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
Electrochemical Techniques
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
The 3-Electrode Electrochemical Cell
Slide Number 15
The Open Circuit Potential
Quantitative Corrosion Rate Measurements
Corrosion Current Icorr
Precision of Electrochemical Corrosion Rate Measurements
Comments on the Precision of Electrochemical Corrosion Measurements
Electrochemical Corrosion Measurements are based on good solid science developed over many yearsSo wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one reduction and one oxidation in an electrochemical reaction
Butler-Volmer Equation
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
Butler-Volmer Equation
Stern-Geary Equation and Polarization Resistance
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
