ANINTRODUCTION

TOELECTROANAL YSIS

byRobert J. Joyce

ANINTRODUCTION

TOELECTROANALYSIS

byRobert J. Joyce

SECTION 1

SECTION 2

SECTION 3

SECTION 4

SECTION 5

SECTION 6

•

CONTENTS

INTRODUCTIONPrimary Sources of Information

Page 1

INSTRUMENTATION PRINCIPLES Page 3

Page 5ELECTROANALYTICAL PRINCIPLESVoltammetry at Zero CurrentVoltammetry at Finite Current

ELECTROANALYTICAL TECHNIQUESPotentiometryPolarographySolid Electrode VoltammetryChronoamperometryPotential Sweep Chronoamperometry and

Cyclic VoltammetryControlled Potential CoulometryChronopotentiometryControlled Current CoulometryElectrodeposition and Separation

Page 13

SUMMARY OF ELECTROANALYTICALMETHODS Page 27

INDEX OF SYMBOLS Page 31

BIBLIOGRAPHY . Page 33

ANINTRODUCTION

TOELECTROANALYSIS

In recent years there has been considerable progressmade ei the field of electrochemistry. Many new electro-analytical techniques have been developed, as have theadvanced instruments required to accomplish them. Theseactivities reflect resurgent interest in a relatively old fieldwhich is outlined historically on the inside cover.The purpose of this booklet is to summarize the moreimportant electroanalytical techniques in use today withregard to their principIes, instrumentation, and applica-tion. The following references can be considered asprimary sources for nearly all phases of this field. Inaddition, a detailed bibliography is carried at the end ofthis booklet. It includes a list of references specific toeach of the techniques described in the booklet. Theywill be useful for more intensive study of each technique.

PRIMARY SOURCES OF INFORMATION

1. Delahay, P., New Instrumental Methods in Electrochemistry.New York: Interscience, 1954.

2. Hampel, C. A., The Encyclopedia 01 Electrochemistry. NewYork: Reinhold, 1964.

3. Kolthoff, I. M. and P. J. Elving, Treatise on Analytical Chem-istry, Part l. Vol. 4, Seco D-2, Ch. 42-52. New York: Inter-science, 1963.

4. Lingane, J. J., Electroanalytical Chemistry, 2nd Ed. New York:Interscience, 1958.

5. Meites, L., Handbook 01 Analytical Chemistry, Seco 5. NewYork: McGraw-HilI, 1963.

SECTION 1... INSTRUMENTATION PRINCIPLES

The Electroscan 30'· Electroanalytical System was devel-oped to carry out a variety of current-voltage measure-ments for electrochemical analysis. With the proper cellsand electrodes, the Electroscan 30 can be used for atleast fifteen electrometric analytical techniques. Thesevarious measurements are achieved by using the systemas (a) a pH meter (b) a galvanostat, and (e) a potentio-stat. The recording function is accomplished by a high-impedance, fast-response, potentiometric recorder whichis built into the system. These basic capabilities of theElectroscan 30 are briefly described here. A more detailedinstrument description is available in Bulletin 7076,Becfman Electroscan 30 Electroanalytical System.

pHMODEAs a pH meter, the system provides a means for pote n-tiometric measurement. Operation in this mode is ilIus-trated in Figure 1. In solution, the glass and referenceelectrodes produce the net voltage (Ej ,') which is sensedat the summing point of the amplifier (AMP) and gen-erates a current (ir) in the feedback loop. This currentgives a voltage drop (ieRr) which is opposite in polarityto Ein' As a resuIt, the voltage around the summing loopis zero and ir continues to flow at a constant rate propor-tional to Ein' The current through the recorder resistor(R,') provides a voItage drop also proportional to E, n andread out on the potentiometric recorder.

a::...•ea::ou...•a::

SUMMINGPOINT

SUMMINGLOOP

Rf

FEEDBACKLOOP

Figure 1. pH System.

GALVANOSTAT MODEThe Electroscan 30, used to create the controlled currentfor electrolysis, is shown in Figure 2. In this case, Einis not generated by the electrodes but by a variable volt-age source. The electrodes now are in the feedback loop.Again, E,; in the summing loop causes the amplifiersystem (AMP) to generate the current ir in the feedbackloop and the voltage drop, i.R, which is equal and oppo-site to Ein' Since the cell is in the feedback loop, ir alsoflows through it. Furtherrnore, as long as Ein and R, areconstant, ir is constant, and a constant current passesthrough the cell. This electrolysis current can be changedin size and polarity by changing E, , or Re. Finally, thecurrent wilI not be affected by the cell resistance, Re,provided that the product ie(Re + Re) does not exceedthe power capabilities of the amplifier (30 volts). The

3

voltage at the surface of the working electrode is moni-tored by placing a reference electrode close to its surfaceand connecting both to the potentiometric recorder.

SUMMINGPOINT

SUMMINGLOOP

FEEDBACKLOOP

WORKING

Figure 2. Galvanostat System.

POTENTIOSTAT MODEIn the potentiostat mode of operation, controlled poten-ti al techniques may be used. Three electrodes areemployed as shown in Figure 3. The reference electrodeis in the summing loop, the working electro de is located atthe point of R¡ in Figures 1 and 2, and the auxiliary elec-trode is in the feedback loop. For versatility, Ein is com-posed of three voltage sources. These are E¿ which is setat a fixed value; Es, which can be varied linearly with

•

time; and ER' the reference electrode voltage. An externalvoltage, Em can also be applied. These voltages, E¡, Es,ER and E.x are additive in the summing loop.

SUMMINGLOOP FEEDBACK

LOOP

Figure 3. Potentiostat System.

In operation, the selected voltage, Ein, is sensed at thesumming point of the amplifier. The amplifier then gen-erates current, i¿ in the feedback loop through the cellby means of the working and auxiliary electrodes so thevoltage at the working electro de surface is equal andopposite to E in. Thus, the potential at the surface of theworking electrode is selected by adjusting Ein and iscontrolled by the amplifier system independent of cellresistance provided the product i.R, does not exceed thepower capabilities of the amplifier (30 volts). The cur-rent i¡ through the recorder resistor R" produces a volt-age proportional to i, which is read out on the recorder.

4

SECTION 2 ... ELECTROANALYTICAL PRINCIPLES

Electroanalytical techniques can be grouped into twomain categories. These are voltammetry at zero current~potentiometry) and voltammetry at finite current (volt-ammetJ;y). In potentiometry, potentials are measured-while no significant amount of current is allowed to flow.In voltammetry, current is permitted to flow and elec-trolysis takes place in the electrochemical cell.

VOLTAMMETRY AT ZERO CURRENT(POTENTIOMETRY)

A fundamental consideration in p~entiometry is theoxidation-reduction relationship existing between twospecies as described by:

O REDUCTION R dx + ne" ••••• e (1)OXIDATION

where Ox and Red are the oxidized and reduced forms,respectively, and n is the number of electrons, e, involvedin the reaction. In the oxidation process, electrons arelost, and the species becomes more electropositive. Inreduction, the reverse is true. For example, tripositiveiron is reduced to the lower oxidation state when it gainsan electron and is oxidized [rom the lower state by losingan electro n :

REDUCTIONFe+3 + e- ••••Fe+2

OXIDATION(2)

in which case n is one. In such systems, the oxidized and

reduced forms constitute a redox couple, and, since theycan undergo an electron transfer reaction, are said to beelectroactive.

The Nernst Equation

When an electrode is brought into contact with a solutioncontaining electroactive species, there is a tendency forthe electrode to exchange electrons with the redox cou-pies present. This tendency is a function of the electronicfree energy of the electrode and the ions. It can be relatedthermodynamically to the solution composition. Thus,the electrical potential of an indicating electrode surface,relative to a reference voltage when no current is flowing,can be related to ionic activities by the Nernst Equation:

E = EO + RT In aox (3)nF aRen

where E is the electrical potential at the indicating elec-trode surface, E ° is the potential at the indicating elec-trode under standard conditions, R is the gas constant,T is absolute temperature, n is the number of electronsinvolved in the electrochemical reaction, F is Faraday'sConstant, and aox and aRedare the activities of the oxi-dized and reduced forms of the electro active speciespresent, respectively. Since most potentiometric measure-ments are made at 25°C and since most people are morefamiliar with logarithms to the base ten, a more con-venient form of the Nernst Equation is:

5

E = EO + 0.059 log aox

n aRed

Finally, the activity (a) of an ion in solutionrelated to its concentration (C) as follows:

a= fC

can be

where f, the activity coefficient, is a measure of interactionbetween species in solution. As the concentration of theelectro active species approaches zero, f approaches unity.

The Indicating ElectrodeAs shown in Equation 3, the actrvity, and thereby theconcentration, of a substance is determined from thepotential at the indicating electrode surface. Several typesof electrodes are used as indicating electrodes.

FIRST-CLASS ELECTRODE

A metal electro de in contact with a solution of its ownions will establish the foIlowing equilibrium:

M+n + ne- ~ MO (6)

The electrode is part of the redox couple and has anactivity of unity. For example a silver electrode will givethe reaction:

Ag+ + e- ~ AgO (7)

The potential at the silver electrode surface is:

E E" + 0.059 1 += Ag/~g+ -1- og aAg (8)

If E is plotted versus log aAg+as in Figure 4, a straightline is obtained which has a slope of 0.059 volts and anintercept at log aAg+ = O (aAg+= 1) of E °Ag/Ag+.

SLOPE = 2.303 ~nF= 0.059 VOL TS

@ 25'C

Figure 4. Plot 01 Potential Versus Log a.tu+.

SECOND-CLASSELECTRODE

A metal electro de in contact with one of its slightly sol-uble or slightly dissociated salts and the anion of thatsalt is sensitive to the activity of the anion. For example,silver in contact with AgCI and Cl- gives the electrontransfer reaction:

(4)Agt + e-~AgO

and the precipitation reaction:Ag- + Cl: ~ AgCl

The potential at the electro deequation:

E - EO + + 0.059 l +- Ag/Ag --1- og aAg (11)

(9)

(10)

surface 1S given by the(5)

However, since the silver ion activity is related to chlorideion activity through the relationship:

Ka + - spAg - aCI- (12)

where Ksp is the solubility product constant of AgCl, thepotential can be related to chloride ion activity by theequation:

E = EOAg/AgCI+ 0.059 log _1_acl- (13)

A plot of E versus log (l/acl-), or -log acl-, will givethe straight-line relationship shown in Figure 5. Thus,second-class electrodes can be used to determine theactivity of anions of slightly soluble salts such as:

Electrode AnionAg/AgCIAg/Ag2SHg/Hg2Cl2Bi/BiF3

Cl-S= (and mercaptans)Cl-F-

SLOPE = 2.303 RTnF= 0.059 VOL TS

@2"C

- LOG .c,-

Figure 5. Plot 01 Potential Versus=-Log ac,-·

REDOX ELECTRODES

A relatively inert electrode in contact with a redox couplecan give rise to an electron transfer reaction involvingthe couple. For example, a Pt electrode in a solution con-taining the Fe+3, Fe+2 couple yields the reaction:

Fe+3 + e- ~ Fe+2 (14)

The potential at the electrode is given by the equation:

E - EO +3 +2+ 0.059 1 aFe+3 (15)- Fe /Fe 1 og +2

aFe

6

A plot of E versus log aFe-s / aFe+2gives a straight line asshown in Figure 6.

RTSLOPE = 2.303 nF

= 0.059 VOL TS@ 25°C

-2 -1 oLOG ( •••• +./ ••.• +2)

2

Figure 6. Plot 01 Potential Versus Log aF.+3/aF.+2•

MEMBRANE ELECTRODES

In the presence of certain ions, some membranes developsurface potentials which can be used to measure ionicactivities. The best known of these are glasses whichrespond to hydronium ion (HaO+) activities and are usedas pH electrodes. Others respond favorably to sodium,potassium, silver, and other ions and are used as pNaelectrodes, pCation electrodes, etc.

For pH measurements, the potential of the electrodesurface can be related to HaO+ activity by the followingequations:

H20 + H+ = HaO' (16)

aH30+E = e + 0.05910g -' - (17)

aH20

In aqueous solutions, aH20 is a constant so the potentialcan be related to log aHaO+.However, HaO+ activitiesusually are less than one, and, therefore, log aHaO+is usu-ally negative. Accordingly, it is convenient to considerthe negative of the log of aH30+which is nfore commonlyknown as pH. Thus, Equation 17 becomes:

E = e' -0.059 pH (18)

where e' is a constant similar to E o. Its value is a functionof several factors including treatment of the membraneduring fabrication. Because of this, e' cannot be calcu-lated reliably, and the relationship between E andlog aHaO+ must be determined experimentally as by cali-bration against a pH buffer standard.

The configuration of a pH measuring system is shown inFigure 7. Rl (Ag-AgCl reference electro de) and a con-stant pH solution are enclosed within the glass membraneto form a convenient probe. R2 can be one of severalreference electrodes which is usually connected to theunknown pH solution through a liquid junction.

R1 R2

R2

J

M

Figure 7. Schematic (a) and Physical Configuration (b) 01 pHMeasuring System. R1 = Reference Electrode No. 1; R2 = Rej-erence Electrode No. 2; S = Constant pH Solution; X = UnknownpH Solution; M = Glass Membrane; J = Liquid Junction.

The Reference ElectrodeIn order to measure the potential at an indicating elec-trode, the electrode is connected to one input of a volt-meter while the solution is, in some way, connected tothe other, thus completing the measuring circuito AI-though the solution connection could be made by a simplewire, this is not satisfactory because the solution-wireinterface would develop uncertain potentials which wouldvary from one test to another. Therefore, the contact ismade through a system which will produce an invariantpotential regardless of time or solution composition.This is the function of a practical reference electro dewhich should have a repeatable and stable electro de sur-face which produces a known potential when in contactwith an appropriate solution (filling solution); a fi1lingsolution containing proper ions to produce a stable poten-tial when in contact with the reference electrode surface;and a restricted passage which allows the filling solutionto make a good stable-potentíal contact with the samplesolution without diluting or being diluted excessively bythe sample solution. This is the liquid junction.

Among the many reference systems available, the mostuseful are the saturated calomel electrode (SCE) andthe silver, silver chloride electrode (Ag,AgCl). Both aresecond-class electrodes.

In the SCE, the electro de surface is mercury coated withHg2Cl2, while in the Ag,AgCI electrode, it is silver coatedwith AgCI-Ag. The filling solution in contact with theelectro de is a saturated solution of KCI (SCE) or KCl +AgCl (Ag,AgCl). The restricted junction is often madethrough an asbestos fiber or cerarnic plug.

7

These electro des are actually secondary standards forproviding reference potentials. The primary standard isthe normal hydrogen electrode (NHE) which is a first-class electrode. By convention, the value for EO in theNHE is 0.00 volts regardless of temperature. Whilethe NHE is very reproducible, it is less convenient thanthe SCE and Ag, AgCI electrodes and, therefore, is usedmainly to establish the potential of these secondarystandards. Thus, at 25°C the potentials of the SCE andAg, AgCI electro des relative to the NHE are +0.244volts and +0.200 volts, respectively.

VOLTAMMETRY AT FINITE CURRENT(VOL T AMMETRY)

Electrolysis simply refers to the process whereby solutioncomponents are converted from one oxidation state toanother by means of a current fiow at an electrode-solu-tion surface:

Fe+3 + e- ~ Fe+2 (19)

H20 + e- ~ 1h H2 + OH- (20)

It should be noted that these reactions are different fromthe equilibrium systems involved in potentiometry (seeEquation 1) in that an external driving force is applied.

Faraday's LawThe quantity of matter con verted during electrolysis isrelated to the quantity of electricity passed through thesolution. This relationship, discovered by Faraday, maybe written:

Q = FEq (21)

where Q is the quantity of electricity in coulombs, F isFaraday's Constant (96,490 coulombs/equivalent), andEq is the number of equivalent ~ights of the electro-active species converted. The value of Q can be deter-mined from the total current during electrolysis, '

Q = ) ot i dt (22)

where i is the electrolysis current in amperes and t istime in seconds. If the electrolysis current is constantwith time, Q is obtained simply by the equation,

Q = i (Llt) (23)

where Llt is the total time of electrolysis.

Cathode-Anode ConsiderationsIn an electrolysis system the electrode which receiveselectrons from the external driving force and transmitsthese electrons to the reactant in solution, is denoted asthe cathode. Its surface is where reduction occurs. Theother electrode, the anode, receives electrons from solu-tion and is the site of oxidation. Typical reactions at theseelectrodes are as follows:

CATHODEREDUCTIONCu+2 + e- ••.Cu+1 (24)

ANODE 2 H20 OXIDATIO~ O

2+ 2H+ + 2e-

(25)

Electron Transfer ProcessWhen an electro de surface is in equilibrium with a solu-tion, it exhibits a potential (Ee) which is thermodynam-,ically related to the concentration of electro active speciespresent. The over-all electro de reaction: .

Reduction (ic)Ox + ne .•. Red

Oxidation (ia)(26)

proceeds at arate governed by (1) the rate at whichelectrons are transferred between the electrode and elec-troactive species, and (2) the rate of movement of electro-active material (mass transport) to the electrode surface.The over-all current (i) at an electrode is given by:

i = ic + i, (27)

where i., which is (+), is the current due to the reduc-tion reaction and ia, which is (-), is the current due tothe oxidation reaction. At (Eeq) i, equals ia, and no netcurrent fiows.

When a voltage (Eapp) is applied to the electrode whichis different from Eeq, electrolysis takes place. As elec-trolysis proceeds, the composition of the electro de-solution interface approaches a new equilibrium condi-tion. However, before a substance can undergo such achemical transformation, an energy barrier must be over-come. Furthermore, the magnitude of this barrier deter-mines the rate of transformation, and, therefore, theamount of current during an electrochemical reaction.The driving force necessary to overcome the energy bar-rier is the applied voltage. In this case, the standard rateconstant (k.) for the electro n transfer process is com-posed of a cathodic rate constant (k.) and an anodic rateconstant (k.}:

ksCathodic (k.)

Ce+4 + e- ••. Ce+3 (28)Anodic (ka)

If the mass transport rate is sufficientIy fast, i will beindependent of time and limited by the electron transfer .rate and:

i, = nf'C"Ox k, (29)

i, = nf'C"Redk, (30)

where COOX and CORed are the concentrations of theoxidized and reduced species at the electrode surface.These rate constants are in turn given by:

k, = k, ° exp [-anF (Eapp)/RT] (31)

k, = k, ° exp [(1-a)nF(Eapp)/RT] (32)

where k, ° and k, ° are the formal rate constants atEapp = O and a is that fraction of Eapp which enhances

8

the rate of the cathodic reaction over that of the anodicreaction. AIso:

k, o Ikao = exp (nF Eeq o IR T) (33)

where Eeq o is the standard equilibrium potential understandard conditions (i.e., COx = CRed). AIso, when:

andEapp = Eeq o

k, °/ka o = 1,k,0= k,0= k,

(34)

(35)

(36)

For very fast electron transfer rates, k. is large, and theelectrode process is said to be reversible. On the otherhand, very smalI values of k, are indicative of an irre-versible process.

+

uso:z:!eu

Ox4--:t~-

Ox--t-+RED

(a)

usozo(

o~---------~~~~~------

+

uso:z:

5

Ox--+

(b)

o~-----~~~~-~------ui5ozo(

'"4--;'--RED

+

ui5o:z:

5 o~----------~~~~~.-----------uaozo(

POSITIVE "4"'-- Ea•• VS E ••• ---t.~NEGATIVE

Figure 8.1dea/ized i-E Curve where (a) k. is Large, (b) k. is Small,and (e) k, is Very Small.

IDEALIZED CURRENT-VOLTAGE CURVES

When a voltage is applied to a pair of inert electrodes,specific relationships exist between current and voltagewhich depend upon the electro active species present insolution. Idealized curves for these are given in Figure 8.As shown, voltages which polarize the electrode morenegatively (better electron donor) are plotted withincreased values to the right, while those which polarizethe electrode more positively increase to the left. Thecurrent which flows during reduction (positive current)is plotted upward while the oxidation current (negativecurrent) is plotted downward.

When the electro active species is present only in theoxidized form and the applied voltage is sufficientlynegative, reduction occurs at the electrode surface andcathodic current flows. This corresponds to the curvein Figure 8a.

As voltage becomes more negative, more current flows.This increase in positive current is very steep if k, is verylarge. If only the reduced form is present, the reversecurrent wiII flow as Eapp is scanned from negative topositive. If both forms are present, the current wilI changevery rapidly from positive to negative, or vice versa, asEapp is scanned through Eeq. Similar relationships existwhen current is applied and voltage is measured. If theelectro n transfer mechanism is slow (i.e., small k.); theslope of the i-E curve is not as steep and becomes evenshalIower for very smalI values of k.. These effects areshown in Figures 8b and 8c.

Mass Transport MechanismsDuring electrolysis, the decrease of reactant concentra-tion at the electro de surface affects both electrode poten-tial and electrolysis current. Therefore, the mass transportrate (rate at which reactants move from the bulk of thesolution to the electrode surface) is an important factorin all electrochemical reactions involving electrolysis.There are three basic mechanisms by which mass transferis achieved; migration, diffusion, and convection.

Migration

Migration involves ionic movement due to electricalgradients whereby ions are attracted by the electrode ofopposite charge. This is i1Iustrated in Figure 9 for a ferricchloride solution.

C~~

.--. C'THOOE = I:=-:~1: ANOOE -..-- .••. r.+· ~ +

CI

Figure 9. Migration 01 lons in So/ution.

9

It is usually desirable to eliminate migration in volt-ammetry. This can be done by adding a supportingelectrolyte which is (a) electrochemically more inertand (b) more abundant than the electro active species sothat it accounts for nearly all migration. For example, ifKCl at 100 times greater concentration were added tothe FeC13 solution, the Fe+3 migration would be reducedto about 1% of its previous value.

DiffusionDiffusion is the movement caused by concentrationgradients. During electrolysis, the concentrations of somespecies are decreased at the electrode surface whileothers are increased. Concentration gradients are createdwhich cause ions and molecules to diffuse. The thicknessof the diffusion layer (o) increases with time and neverreaches a limiting value even when the concentration ofthe diffusing species at the electrode surface becomeszero. When some other means of mass transfer is opera-tive, such as reproducible stirring, (o) reaches a steadylimiting value. Compared to mechanical stirring, diffu-sion is relatively slow.Each ion or molecule has a characteristic diffusion ratewhich depends upon its own properties as well as thoseof the solvent. The rate is practically independent ofother electrolytes surrounding it. This rate is expressedas the diffusion coefficient (D) in cm=/sec. The limitingcurrent, ilim, which can flow during electrolysis is relatedto the diffusion coefficient in the equation:

¡lim = nFDCbAo (37)

where C, is the concentration of the diffusing species inthe bulk of the solution and A is the area of the electrodesurface.

Convection •Convection is the movement caused by mechanical orthermal agitation. Mechanical stirring increases the masstransport rate and reduces and stabilizes the diffusionlayer. This results in an increase in limiting current.Therefore, the rate of stirring must be controlled if aconstant current is to be obtained. Control may beachieved either at zero rate (quiescent solution) or atsome finite rateo However, quiet solutions are difficult tomaintain over periods longer than 100-200 secondsbecause of thermal convections.

EFFECT OF MASS TRANSPORT ON

CURRENT-VOLTAGE CURVES

The i-E curves in Figure 8 apply to solutions in whichthe mass transport rate (MTR) approaches infinity, butthis is not achieved in practice. Accordingly, the curvesin Figure 10 are more realistic. Examples of cathodiccurrent reactions are given here. Curves for anodic cur-rent reactions are similar.

J-ZWa:a:::lo

J-ZWa:a:::lo

J-ZWa:a:::lo

,_--- FAST

SLOW

o

VERY SLOW

FAST

_----- SLOW

o E.pp -EO

Figure 10. ldealized i-E Curves Modified by MTR with (a) Fast,(b) Slow, and (e) Very Slow Eleetron Transjer Rates.

As shown in these curves, current increases as the appliedvoltage becomes more negative. In the early stages, theMTR is sufficient to replace those species lost at theelectrode, and the electrochemical kinetics, or electrontransfer rate (ETR) , limits the current flow. However,as Eappbecomes more negative, k, increases and even-tually the ETR exceeds the MTR. At this point currentno longer increases with Eappand is now limited by theMTR. Thus, a fast MTR gives a high limiting currentand a slow MTR gives a low limiting current.If the MTR is very slow, as in a quiet solution wherediffusion is the sole factor, a peaked curve usually

10

results. The current rises abruptly at first as the electro-active species at or near the surface are electrolyzed,then decays because the MTR is not sufficient to supportthe current flow.As seen in the progression given in Figures lOa, 10b,and 10c, the ETR also affects the slope of the curves.However, as long as sufficient potential is applied, thesame limiting current is reached in each case for thesame MTR.

Significance of Current-Voltage Curves

HALF-WAVE POTENTIAL

The potential at which the current is half its limitingvalue is known as the half-wave potential (E'h)' one ofthe most useful properties of an electro active substance.When fast electro n transfer rates are involved, E'h isequal to EOof the Nernst Equation. For slow rates, morevoltage than predicted by the Nernst Equation is requiredto reach the E'h point. These differing conditions areshown in Figures l l a and l lb, respectively. For thesecond case, the additional voltage required is the over-voltage (-l')).

EVa = EO

(a) •1

EVa

EVa (MEAS.) =EVa (CALC.) +'1

EVa (CALC.) = EO

,,-IIJ'~4t---'1 -~~

11/1

(b)

EVa (CALC.) EVa (MEAS.)

Figure 11. Hali-Wave Potential Curves [or (a) Fast ETR and(b) Slow ETR.

OTHER FEATURES OF CURRENT-VOLTAGE CURVES

In Equation 37 it is seen that the limiting current, ilim,

actually depends upon several factors including n, thenumber of electrons involved in the reaction, and Cb,

the concentration of the electro active species. These areillustrated in Figure 12.

n = 3

n = 2

n = 1

Figure 12. Effect 01 (a) n and (b) C. on the Limiting Current(other [actors being constant) .

MUL TICOMPONENT SYSTEM

When more than one electro active species is present,each one is e1ectrolyzed at the Eappsufficient to overcomeits particular energy barrier. Accordingly, these cornpo-nents can be electrolyzed sequentially if their E 'h values

SOLVENTELECTROLYSIS

ZnH~_.......,~_ ....• Zn0

CU:..:H~-I-__ ...•. CuO

E

Figure 13. Current- Voltage Curves [or a Multicomponent System.

11

are significantly different and they are more electro activethan the solvento Usually, about 0.2 V is necessary forgood resolution. These conditions are illustrated inFigure 13.

Solvent Electrode LimitationsBoth solvent condition and electrode material affect the

electrochemical kinetics, and, therefore, E Yl for a givenelectrolysis depends upon experimental conditions. Fur-thermore, each solvent-electrode system limits the usefulpotential range since the solvent itself will eventually beelectrolyzed. In Figure 14 useful ranges for varioussolvent-electrode combinations are indicated.

SOLVENT

WATER

LIQUIDAMMONIA

(-36·C)

DIMETHYLFORMAMIDE

FORMAMIDEACETAMIDE

ETHYLENEDIAMINE

ACETO-NITRILE

FUSEDEUTECl'lC

Li 03-NaN03-KN03 (160·C)

FUSEDEUTECTICLiCI-KCl(450·C)

ELECTRODE

{

MerCUry

Platinum

{ Mercury

{ Mercury

{ Mercury

{ Mercury

Mercury

Platinum

1 Oxida/ion §I . Cr01 mercury § -Ag--Cu--Pb-Cd--Zn-NI-Co-Fe-Mn-AI-Ba-Rb-

1 Oxida/ion ~ Reduction01 water -- -Hg-Ag--Cu--Pb- n-I~ 01 water

<---+ -500mV

'I~Reductiona-Sr-K-Ca-LI-~ 01 water

{ Mercury

{

Platinum

Graphite

----TI--Cu---Cs-Rb-K-Na--Li----

{Oxido/ion =1 . Rb K . @ .Reduction 01

I = --Cu---NI-Zn-Co-B -N -Sr-Ca-LI-- indifferent elec-O mercury = a a - trolyte (R4N+)

{Oxido/ion al,ª, 1 § Red,,;c/ion 01

mercury 'ª' -TI-Pb Zn---K---------------- § indifferent•• electrolyte

{Oxido/ion 01=1 C B Reduction 01 in-== --TI-Cd---Pb--Zn- Sa- Ma -Ag-- ---different electrolyte

mercury = r g or solvent?

{ .. =f-- . M Na Rb· @Reduc/ionolOXida/Ion 01 § Ag--NI-Cu-Cd-Co-Zn-Fe-Cr-Mn-AI-Be-Ba- g ; C - K -LI--------- indifferentMercury = Sr a electrolyte

{Oxida/ion al'ª' 1 ~ Reduction 01- - Hg---Ag--Cu-Cd--Zn Li--------- indifferent

acetonitrile 'ª' <---+ - electrolyte2v

{O .dati =1 - ReductionXI auon ol§ --Ni-Pb-Cd-Zn--I'ª' 01

mercury == == Nitrates

1Oxida/ion o/~I--Bi-Hg-ln-Ga-Sn-Co-Pb-Cu-Cd-TI-Zn-Cr-AI---~ Reduction 01 salven/platinum = § (deposition 01 K-L/)

1Oxida/ion 01 ~ Pt Pb~ Reduction 01chlorides 3 ~ so/ven/

1 vol!

Figure 14. Ranges [or Solvent-Electrode Combinations,'

'G. Charlot,J. Badoz-Larnbling,B. Tremillon,Electrochemical Reactions, NewYork: Elsevier,1962,p. 354.

12

SECTION 3 ... ELECTROANALYTICAL TECHNIQUES

POTENTIOMETRYDefinitionPotentiometry involves measurement of the electricalpotential or the electro motive force (EMF) at an elec-trode surface (indicating electrode) relative to a refer-ence voItage (reference electrode). In zero currentpotentiometry, no net electrochemical reaction occurs atthe indicating electrode, and the measurement is inde-pendent of mass transport. In constant current potenti-ometry, a small current ftows through the indicatingelectrode. In a stirred solution, the current is sufficientlysmall that a stable potential is achieved due to diffusionof the electro active species presentoImportant applications of potentiometry include directdetermination of ionic activity (direct potentiometry,e.g., pH, pNa, pCI), and end point detection for volu-metric titrations (potentiometric titrations).

InstrumentationFor pH and other potentiometric measurements requir-ing a high-impedance amplifier, the pH mode of theElectroscan 30 Electroanalytical System is used. Forthis, the indicating electrode is connected to the glasselectrode terminal as shown in Figure 15a. Low-impedance electrodes can also be used this way or alter-nately with the electrolysis display mode. In this case,the indicating electrode is connected to the working

13

electrode terminal. Either zero current or a constantpositive or negative current is applied to it. If current isapplied, an auxiliary electrode must also be added asshown in Figure 15b.

REF

(a)GLASS

REF

(b) INDICATING

AUX.

Figure 15. Instrumental Configuration [or (a) High-Impedanceand (b) Constant Current Potentiometric Measurements.

PrincipIe

The principIes of this technique are covered under voIt-ammetry. (See VOLTAMMETRYATZEROCURRENT,page5) .

ApplicationsDirect potentiometry has been applied most successfulIyto pH and chloride ion measurements, although it hasbeen used for direct measurement of Nat, S;, Agt, andseveral other ions. It has also been used for redox poten-tial measurements. Unfortunately, there are only a fewion-specific membrane and second-class electrodes avail-able. Redox electro des lack specificity for general analyt-ical use, and most first-class electrodes (e.g., Pb+2/PbO)also lack specificity. However, use of these electrodes asend point indicators broadens their usefulness consider-ably since the titrant supplies the specificity required.

Advantages and LimitationsPotentiometry is a continuous measurement offeringsimplicity in both technique and instrumentation. It pro-vides speed with most indicating electrodes reachingequilibrium in 10 seconds. With use of glass electrodesfor pH and second-class electrodes, such as Ag, AgCI forCl- and Ag, Ag2S for sulfides and mercaptans, the tech-nique has good selectivity. LastIy, potentiometry has adynamic range where reliable measurements can be madeover several decades of concentration.On the other hand, accuracy is limited by two major fac-tors in direct potentiometric work: (1) variations in liquidjunction potential of the reference electrode, which cangive errors of 2-3 % and (2) uncertainties in activitycoefficients which are needed to convert activities(measured) into concentrations (desired). These prob-lems are eliminated when potentiometry is used as anend point detector in a volumetric titration. Additionally,interferences are also a limitation because specific indi-cating electrodes are not available for all types of ions.

POLAROGRAPHY

DefinitionPolarography is a controlled potential technique in whichthe electrolysis of an analyte occurs at a dropping mer-cury electrode (DME), where the potential of the DMEis constant or varied linearly with time. Convective diffu-sion of the analyte is the only means of mass transport.The electrolysis current is displayed against the controlledpotential of the DME.

InstrumentationThe Electroscan 30 Electroanalytical System, and an

appropriate electrolysis cell, can be used for controlledpotential polarographic analysis. With the arrangementshown in Figure 16, the potentiostat controls the DMEpotential versus the potential of the reference electrode.This potential can then be held constant or scannedlinearly with time.

REF (SeE)

~:'.

WORKING (OME)

AUX.N,PURGE

~

Figure 16. Instrumental Configuration [or Polarography.

The DME consists of a length of marine barometer tubingwith afine capillary and a head of mercury above it. Themercury head is usually adjusted to give a drop time of2-5 seconds. The auxiliary electrode is isolated from thetest solution by a sintered glass disk and an agar plug inorder to reduce contamination of the test solution by itsproducts. The reference electrode is usually a saturatedcalomel electrode. The test solution must be purged withhigh-purity nitrogen to remove oxygen interference.

PrincipIeTYPICALCURRENT-POTENTIALCuRVEA typical (i-E) curve or polarogram is shown in Figure17. Curve (a) is that of a lF HCI solution while Curve(b) is that of 1 x 1O-3FCd+' in lF HC!.

"- •..••••(e)

I '\IVV'1,\ I'-/

10

DECOMPOSITIONPOTENTIAL

8

~ 6~zw 4a:a:i3 2

O' -0.3 -0.6

IEVa

Edme VS Erer

-0.9 -1.2

Figure 17. Polarogram 01 Cd+ in lF HCI.

14

In this example, the potential at the DME (Edme) isscanned in the negative direction. At first, the current inCurve (a) is zero, then rises gradually due to trace im-purities and charging of the double-layer capacitance atthe mercury-solution interface. This current is called theresidial current (ir). Finally, the decomposition potentialof hydrogen is reached and the current rises sharply. InCurve (b), the current rises sharply frorn that producedby the solvent when the decomposition potential of Cd+is reached:

Cd+++Hg +2e- Cd(Hg) (38)

As the current starts to rise, it is controlled by diffusionof Cd++(or by the kinetics of the electron transfer reactionfor irreversible cases) and eventually becomes lirnitedby the net rate at which Cd+ diffuses to the electrode.This limitation produces a current plateau which con-tinues until a potential sufficient to electrolyze anotherelectro active species is reached. The net current pro-duced by the diffusion of the electrolyzed species in theplateau regio n is called the diffusion current (id). Thetotal current in the plateau region, including ir and id, iscalIed the limiting current (i, im).The oscillations seen in these curves are due to the growthand fall of the mercury drops. As shown in the Inset (e),the current increases as the drop grows, and then dropssharply when the mercury drop detaches itself and falIs.

The value of id during the drop life is given by the IlkovicEquation:

(id)max= 708 nm% tJ.i Dlh C, at 25° (39)

where (irt)maxequals the diffusion current (ua) at t, nequals the number of electrons in the electron transferreaction, m equals the average Hg flow rate (mg/sec.),t equals the drop life (sec.), D equals the diffusion coeffi-cient of the electro active species (cm- / sec), and C,equals the concentration (mM) of the analyte in thebulk of the solution.When a fast recording system is used (i.e., < 1 secondfull scale response), the peaks of the oscillations equal(id)max.When the recording system is damped, the aver-age diffusion current (id)ave ¡" determined from theaverage of the recorded oscillations. (id)maxcan be calcu-lated from the relationship:

(id)max= % (id) ave (40)

CURRENT-POTENTIALRELATIONSHIPThe potential where i is Yz of i, is calIed the half -wavepotential. If the electro n transfer reaction is fast (i.e.,reversible), then at 25°C:

0.059 i - (id)aEdme= El!: - -- log (i ). (41)

2 n ldc-1

and Ey, = EO' - 0.059 log DDox (42)n Red

where Edme equals the potential of the DME, EO, equals

the formal potential of the half reaction, n equals thenumber of electrons in the electro n transfer reaction,i equals the electrolysis current, (id)a equals the anodicdiffusion current, (id)Cequals the cathodic diffusion cur-rent, Dox equals the diffusion coefficient of the oxidizedform, and DRed equals the diffusion coefficient of thereduced formo Since DoxlDRed is usualIy close to 1, E l/2

equals EO'.

If the electron transfer reaction is very slow (i.e., irre-versible), then for a cathodic wave:

E E _ 0.054 log _..L,dme= l/2 (43)ana Id - 1

where a equals the transfer coefficient and k, equals therate constant for the cathodic reaction.

From the Equation 44, it is obvious that for irreversiblesystems, Ey, is strongly influenced by the kinetic Iactorsk, and a.

MAXIMA

Polarograms often exhibit current maximum as shownin Figure 18.

MAXIMUM

1-ZL¿Ja::a::~o

0+------

Figure 18. Polarogram Exhibiting Maximum,

These are due to the streaming of solutions past themercury surface at certain potentials. These maxirnumcan often obscure the wave of interest. Often, they canbe elirninated by adding a small amount (:::::0.003 %) ofsurface-active material, such as gelatin.

ApplicationsQUALITATIVEANALYSIS

Extensive tables (see PRIMARY SOURCES OF INFORMA-TION, page 1) exist for the Ey, of electroactive sub-stances in a variety of solvent-supporting electrolytemedia. Thus, an Ey, value from the polarograrn of anunknown sample can be indicative of a relatively smallnumber of possible substances. Polarographing the

15

unknown in various media may then provide sufficientdifferentiation for final identification. This is possible,because the media often have different effects upon thekinetics of the electro n transfer reaction.The reason that various media change the relative E Yi

values of certain substances is that they affect the therrno-dynamics or kinetics of the electron transfer reaction(e.g., complex formation, overvoItage, and reversibility).For example, EYi for both Cu" and Bi+ is - 0.01 voItsversus SCE in 1F HNOs. However, in O.lF potassiumbiphthalate, their EYivalues are - 0.1O volts and - 0.23volts versus SCE, respectively.

DIRECT QUANTITATIVE ANALYSIS

Quantitative work depends upon the relationship betweenthe id and concentration.

SensitivityQuantitative polarography has been most successfuIIyapplied in the 10-2 to 10-5 formal region. At higher con-centrations, solubility factors at the surface of the mer-cury drop often give spurious resuIts. At concentrationslower than 10-4F, the residual current is often as largeas the diffusion current. Thus, the problem of trying tomeasure a small change in a large signal resuIts, whichseverely limits precision.

SelectivityThe current waves or steps occur in the order of the EYivalues of the species in solution. The first species to beelectrolyzed can be determined with the greatest reliabil-ity. The selectivity depends greatIy upon the solvent usedas pointed out under Qualitative Analysis. When ana-lyzing a muIticomponent system, species with E Yi valuesdiffering by 150 mv or greater can usually be resolved.

AccuracyBy rearranging Equation 39, we can see that:

Cs = (ict)max/708nDIh m% tV6 (45)

For a given substance in a given medium, the diffusioncurrent constant 708n D1h (sometimes tabulated as I),is constant, and the capillary constants (m% t1A;) can bemeasured. Once these constants have been deterrnined,this equation can be used to estímate C, directIy from ameasurement of (id) maxwithout the need of calibrationstandards. In practice, this procedure gives resuIts whichhave an error in the order of -+- 5% .For additional accuracy, standards can be polarographedto determine the proportionality constant k in:

C, = k (ict)max (46)

This procedure can yield accuracies in the order of 1-2%.

QUANTITATIVE ANALYSIS BY TrTRATION

(AMPEROMETRIC TITRATION)

A polarized DME can function as an indicator electrodein a titration. The potential at the DME is set so as toelectrolyze the reactant, titrant, and/or products of thetitration. The potential is selected so as to give thesharpest end point indication and the electrolysis currentis plotted against titrant volume.

SensitivityAmperometric titrations have about the same sensitivitylimits as direct polarography.

SelectivityThe selectivity of the titrant combined with the abilityto choose the electrolysis potential often makes ampero-metric titrations more selective than potentiometrictitrations.

AccuracyLike most titration techniques, the accuracy of theamperometric technique is often better than 1% .

KINETIC STUDIES

The kinetic parameters a and k can be evaluated from apolarogram using Equations 43 and 44.A plot of log (i/id - i) versus Edmegives a straight linewith a slope equal to 0.054/ ana, from which a can becalculated. Once a is known, the rate constant k, canthen be calculated from Equation 44.

Advantages and LimitationsPolarography shares the same advantages possessed byall voItammetric techniques in that the recorded tracescontain qualitative, quantitative, and kinetic information.It can also be applied to an extremely broad range ofinorganic cations, anions, and organic functional groups.The DME offers three additional advantages over othervoItammetric techniques. These are controlled and re-peatable stirring caused by the growth and fall of themercury drop; new, uncontaminated electrode surfacewith each new drop; and large hydrogen overvoItagewhich extends its range of application in the negativeregion.The disadvantages of the technique include the occa-sional fouling of the capillary tip as welI as the timerequirement for running a good polarogram, which takesseveral minutes. The presence of maxima is another lim-iting factor. Furthermore, 'polarography is limited topotentials more negative than 0.5 volts versus SCE dueto the oxidation of mercury. With anions, which formslightIy soluble or ionized mercury saIts, this potentialis limited further.

16

SOLID ELECTRODE VOLTAMMETRY

DefinitionSolid electrode voltammetry is a technique in which theelectrolysis of an analyte occurs at the surface of a fixed-area electrode in a stirred solution. The surface potentialis either constant or varied linearly with time. Diffusionand convection due to constant rapid stirring are themeans of mass transport. Electrolysis current is displayedagainst the controlled potential. Typical working elec-trodes used are platinum, gold, boron carbide, pyrolyticgraphite, and carbon paste. To a large extent, the appli-cations of this technique are the same as those ofpolarography.

InstrumentationThe instrumental configuration for this technique isshown in Figure 19. The potentiostat control s the work-ing electrode potential versus the potential of the refer-ence electrode. This potential can then be held constantor scanned linearly with time. As in polarography, theworking electrode is moved relative to the solution. Thisis most often accomplished by mounting the electrode ina chuck, which is rotated at a constant rate by a syn-chronous motor. The essential features of such an elec-trode arrangement are shown in Figure 20.

REF (SCE)

RPE

AUX.N,PURGE

:.l

¡;

Figure 19. Instrumental Configuration [or Solid Electrode Volt-ammetry.

TO WORKING ELECTROOETERMINAL

CHUCK

PLATINUM OROTHER

SUITABLE MATERIALSEALEO INTO ENO OF

THE TUBE

Figure 20. Rotating Electrode Assembly.

PrincipIeTYPICAL VOLTAMMOGRAM

A typical voltammogram is shown in Fi re 21.

o E•• VS E.of

Figure 21. Typical Voltammogram.

As in the case of polarography, (a) is the i-E curve forthe solvent-supporting electrolyte system and (b) is thecurve for the same system with an electro active analyteadded.

INTERPRETATION OF LIMITING CURRENT

The over-all interpretation of these curves is the same asthat for the polarographic curves. However, oscillationsin the recorded curves are rather erratic and are causedby turbulence at the rotating electrode surface.In solid electrode voltammetry, the electrolysis current isdue to both diffusion and convection. The current in theplateau region is called the limiting current (ilinJ and itis estimated from the average of the current oscillations.The equation for this current is:

nFADCbilim = a (47)

which was defined earlier (Equation 37).Since the stirring rate affects the thickness of the diffu-sion layer (8), Equation 47 can be rewritten as follows:

ilim = Mrot nFADCb (48)

where Mrot is the mass transport coefficient for therotating electrode. Unfortunately, Mrot is a function ofmany factors, including electrode and cell designo Con-sequently, it cannot be rigorously defined except in certainspecial cases. However, when a certain electrode and celldesign is consistently used, Ml'ot is a repeatable propor-tionality constant. Equation 48 can be used for quanti-tative analysis by experimentalIy determining Mrot withstandard solutions.

AppIicationsIn general, the discussion of qualitative and quantitativeapplications presented for polarography are applicableto solid electrode voltammetry. This technique has been

17

extensively used for amperometric titrations. The studyof kinetic factors is similarly applicable.

Advantages and LimitationsThere are two basic reasons for using a rotated, fixed-surface electrode in preference to a DME. These areincreased signal and greater usable potential range. Theincrease in signal results from the enhanced mass trans-port caused by rapid stirring. At typical stirring rates of600rpm, there is about a five-fold increase of signal-to-background ratio, as compared to polarography.The potential range in volts (versus SCE) of platinumin aqueous media at various pH values is illustrated inFigure 22.

pH17

13

Positive Negative-0.3-0.6-1.0

+ 1.1+0.8+0.4

Figure 22. Table 01 Voltage Ranges 01 Platinum at Various pHValues.

The potential range of gold varies from that of platinumto as much as 0.5 volt more positive or negative, depend-ing upon the supporting electrolyte used. The presenceof chloride ions severely decreases the potential range ofboth platinum and gold electrodes. Boron carbide (B4C)has a potential range of +0.9 to -1.3 volts versus SCEin 1M H2S04 and slightly less in other media. The variousgraphite electrodes (e.g., pyrolytic, wax impregnated,and mineral oil paste electrodes) have a potential rangesimilar to gold, and can be used in strong chloride media.There are two fundamental limitations of fixed-surfaceelectrodes compared to the DME. These are less repeat-able mass transport, and surface contamination. AIthoughthe mass transport due to rotation is repeatable, it is notas precise as with the DME. AIso, the surfaces of fixed-surface electrodes become contaminated with adsorbedand electrodeposited materials. Thus, unlike the DME,they must be cleaned often. However, despite these lim-itations, fixed-surface electrodes have been successfullyused in many applications, especially in the positiveregion, where mercury cannot be used. It is in this regionwhere many organic oxidations take place.

CHRONOAMPEROMETRYDefinitionChronoamperometry is a controlled potential techniquein which the electrolysis of an analyte occurs at a sta-tionary electrode in a quiescent solution. The electro depotential is suddenly stepped to some fixed value and theelectrolysis current is displayed against time. Diffusionis the sole mode of mass transport.

InstrumentationThe instrument configuration for this technique is shownin Figure 23. The working electro de material may beany material which can be held stationary during theelectrolysis. Since the solution must remain quiet, thecell should be mounted on a vibration-free support.

REf (SCE)

WORKING

N,AUX. PURGE

J

Figure 23. Instrumental Configuration [or Chronoamperometry.

Principle

CURRENT TIME CURVE

r.

o~--~~------------------------------o t (SEC)

Figure 24. Typical Chronoamperogram.

A typical (i-t) curve is shown in Figure 24.

When time (t ) equals zero, the potential of the workingelectrode in a quiet solution is suddenly stepped to somefixed value (Eapp). If E is sufficient to cause electrolysis,the current suddenly increases from zero to some finitevalue (io)' The current then decays as the electro activespecies in the vicinity of the electrode is consumed.

INTERPRETA TION OF CURRENT- TIME RELA TIONSHIP

The electrolysis current is governed by the diffusion rateof the electrolyzed component and the electron transferrate of the electro de reaction. If the applied potential issufficiently large so that the rate constant k, (or ka) is

18

large (i.e., the electrolysis is diffusion controlled), thenthe resulting current is given by the Cottrell Equation:

nFAD'hid = 7T~~tlh C, (49)

The only new term in this equation is t, which is the time(in seconds) after the controlled potential has beenapplied to the working electrode. In the case of a veryreversible system, any applied potential greater than thedecomposition potential of the system is sufficient tosatisfy the above conditions. If the electrode potential isnot sufficiently large to make the electrolysis current dif-fusion controlled, which is often the case with an irre-versible system, the resulting current is given by:

i = i, [7T'hAexp (Ay erfc (A)] (50)

tlhA = k, Dlh

erfc(A) = 1- ~¡ ( A71"1'2 , o

where (51)

e-Z' dzand (52)

ApplicationsDIRECT QUANTITATIVE ANALYSIS

As can be seen from Equation 49, id is proportional toCb. Accordingly, C, can be ca\culated by selecting fromthe chronoamperogram a value (id) x corresponding toa value (t)x and substituting these in Equation 49.

KINETIC STUDIES

As can be seen from Equation 50, by selecting current-time values from the recorded trace and substituting theminto this equation, k, (or ka) can be ca\culated for anyapplied potential.

Advantages and LimitationsFor quantitative analysis as well as kinetic studies, chrono-amperometry offers speed and simplicity. However, itdoes require a prior knowledge of the current-voltagecharacteristics of the electrochemical system. In the caseof quantitative analysis, a potential must be chosen atwhich i will be diffusion controlled. On the other hand,when determining k, (or ka), potentials must be usednear the foot of the i-E curve where i is not diffusioncontrolled.

/ POTENTIAL SWEEPCHRONOAMPEROMETRY AND

CYCLIC VOLTAMMETRY

DefinitionPotential sweep chronoamperometry is a controlledpotential technique in which the electrolysis of an ana-lyte occurs at a stationary electro de in a quiescent solu-tion. In contrast to solid electrode voltammetry, diffu-

sion is the sole mode of mass transport and the workingelectro de potential is scanned linearly at a rapid rate(several mv / seco to several hundred mv / sec.) .

Cyc1ic voltammetry is an extension of the potential sweeptechnique in which the potential is swept back and forthover the same regio n several times.

InstrumentationThe instrumental configuration of this technique is shownin Figure 25. It is identical to that shown for chrono-amperometry.

REF (SCE)

WORKING

AUX,

N,PURGE

J

Figure 25. Instrumental Configuration [or Potential Sweep Chro-noamperometry and Cyclic Voltammetry.

PrincipleTYPICAL CURRENT-POTENTIAL CURVE

A typical i-E curve is shown in Figure 26.

1-ZWa:a::1o

o

E.

E.•. VS Er ••

Figure 26. Typical i-E Curve.

If the working electrode potential is swept negatively,a current peak due to reduction results. Positive sweepsresult in oxidation peaks. During the first part of thesweep, no current fiows until the decomposition potentialof the analyte is reached. Once this point is passed, thecurrent rises rapidly as the analyte is consumed at theelectrode surface. Since the solution is uñstirred, the ana-lyte concentration at the electrode surface is soon de-pleted, and the current begins to drop. This process isrepeated when the potential is sufficient to electrolyzethe next electroactive species.

19

CURRENT-POTENTIAL RELATIONSHIPS

If the electrode reaction is fast (reversible) and thereactants and products are soluble, then:

ip = 2.72 X l O? n'Y!ADlh C, V~2 at 25°C (53)

where ip is in amps and v is the potential sean rate involts/sec. If the electrolysis resuIts in the deposition ofan insoluble substance, the numerical constant in Equa-tion 53 is 3.67 X 105• The relative position of the peakpotential is:

E, = El!2 - 0.028/n (54)

where E'h is the voItammetric half-wave potential. Ifthe electro de reaction is slow (irreversible), then:

ip = 3.01 X 105n(ana)lhAD'hCbv%at25°C(55)

where n, is the number of electrons in the rate-controllingstep and a is the transfer coefficient. Consequently, theheight of the current peak is affected by the electrodereaction rateoDuring the initial current rise (up to 10% of ip) thecurrent is almost totally controlled by the kinetics of theelectron transfer mechanism. In this region, the currentis defined by:

i = nFAC,ks exp [(anaF/RT) (Eapp - E¡)] (56)

where E¡ equals the potential at the start of the sweep andEapp equals the potential of the working electrode at anygiven point in the potential sweep.

CYCLIC VOLTAMMETRY

If, at the end of one potential sweep, the sweep directionis reversed, electrolysis of the products of the forwardsweep takes place. This technique is illustrated in Fig-ure 27.¡--------

•...zwa:a::::>u 1___________1

o-+-,~--.....

Figure 27. Cyclic Voltammogram.

For a reversible system:(ip)c = (ip)a

and the separation of these peaks are:(Ep)c - (Ep)a = AEp = 60/n (mv)

(57)

(58)

For an irreversible system, the peak separation AEp is

related to '" as shown in the following table where:

(59)(

nFVD)'h'1' = k, 7T __RT

assuming Dox ~ DRed

'1'20

76543210.75

(60)

n (AEp)

61 mv6364656668728492

Figure 28. Variation 01 6.Ep with .p. (See BIBLIOGRAPHY FORPOTENTIAL SWEEP CHRONOAMPEROMETRY AND CYCLIC VOLTAM-METRY, page 34, rejerence 10.)

Applications

QUALITATIVE ANALYSIS

Since E, is closely related to the Ell2 of polarography,it has the same qualitative usefulness.

DIRECT QUANTITA TIVE ANAL YSIS

For a given electro active species in a particular solvent,Equation 53 or 55 can be reduced to:

ip = ic; (61)

where k is the constant of proportionality which can beevaluated with standard solutions.

SensitivityFor a reversible system, this technique is in the order of10 times more sensitive than polarography. Often, dis-tinct peaks can be detected at concentrations as low as10-6 M. While the improvement for irreversible systemsis less, there is a 5 to 10-fold improvement over polarog-raphy.

SelectivityIn general, the selectivity of this technique is the same asfor polarography except for improved resolution. Specieswith El!2 values, differing by 100 mv, can usually beresolved.

AccuracyThe accuracy of this technique is approximately the sameas for polarography. That is, about 5% if Bquation 53is used or 1-2% if careful standardization is used withEquation 61.

KINETIC STUDIES

It can be seen from Equation 56 that a plot of (In i)

20

where i is less than 10% of ip,versus Eapp- E¡ will resultin a line with a slope proportional to ana and an interceptproportional to ka-

In the case of cyclic voltammetry, a sean rate (v) can beselected such that ~Ep is measurably different from 60mv. This ~Ep can then be used to get t/J from the Table(Figure 28) and k, can then be calculated from Equa-tion 59.

Advantages and LimitationsPotential sweep chronoamperometry has a number ofadvantages over polarography. Resolution of substanceswith half-wave potentials lying close to each other can bemore easily distinguished. Sensitivity is 5 to 10 timesbetter. Speed is 10 to 20 seconds versus 10 to 15 minutesper sean. By using stationary electrodes rather than drop-ping electrodes, the technique is simpler than polarog-raphy. The advantages of potential range is the same asthat cited for solid electrode voltammetry.On the other hand, fixed-surface electro des require care-fuI maintenance in order to achieve repeatable results,and quantitative accuracies cited above are applicable toonly the first species electrolyzed in a multicomponentsystem.

t,// CONTROLLED POTENTIALCOULOMETRY

DefinitionIn coulometric analysis, a measurement is made of thequantity of electricity required to electrolyze a substancequantitatively and stoichiometrically at a working elec-trode in a well-stirred solution. In controlled potentialcoulometry, the potential of the working electrode is con-trolled at a constant value, and the electrolysis currentis measured against time. Completion of the electrolysisis signaled by decay of the current to a negligibly smallvalue.

REF (SCE)

INTEGRATOR

N,PURGE

SPINBAR.-L-~;;;;r::,

MAGNETICSTIRRER

b

Figure 29. Instrumental Configuration [or Controlled PotentialCoulometry.

InstrumentationThe instrumental configuration for this technique isshown in Figure 29. Stirring is done either by rotating theelectro de or by stirring the solution. Large-area workingelectrodes are usually used in order to speed up the elec-trolysis.

PrincipIeTHE CURRENT-TIME CURVE

A typical current-time curve for controlled potential cou-lometry is shown in Figure 30.

r,

o~--~--------~~========~o TIME

Figure 30. Typical i-t Curve [or Controlled Potential Coulometry.

Before starting the electrolysis, the working electrodepotential is chosen which will electrolyze the species ofinterest. If this potential is not known beforehand, it canbe determined from a polarogram or voltammogram of astandard solution of the desired analyte.When the electrolysis is begun, the current increases to aninitial high level (i.), It then decays exponentially as theanalyte is consumed. The electrolysis is complete, for allpractical purposes, when the current has decayed to lessthan 0.1 % of the initial current.

INTERPRETATION OF THE CURRENT-TIME CURVE

The current decay in controlled potential coulometry isdescribed by this equation:

i, = iolO-Kl (62)

where i,equals the initial current, i, equals the current attime (t):and K = 25.8 DA/Yol. 8 (63)

The constant K is inversely proportional to the timerequired for the electrolysis to reach any degree of com-pletion. Thus, the electrolysis time can be made small bymaking the electrode are a to solution volume ratio(A/Yol.) large and/or by making the diffusion layer 8small by rapid, efficient stirring.The total amount of electricity (Q) which is required to

21

exhaustively electrolyze a certain species is the current-time integral:

l

O = fa idt (64)

This integral is equal to the are a under the i-t curve inFigure 30. The quantity (O) is in turn related to the orig-inal concentration of the electrolyzed species accordingto Faraday's Law (see FARADAY'SLAW, page 8):

O = nFVCb (65)

where F equals 96,490 coulombs, V equals volume ofsolution (liters), and C, equals bulk concentration of theelectrolyzed analyte (moles/liter).

COULOMETERS

Integration of the i-t curve may be done by graphic,mechanical, electromechanical, or electronic means. Aconcise summary of these various methods of integrationhave been presented (see BIBLIOGRAPHYFORCONTROLLEDPOTENTIAL COULOMETRY, page 34, reference 10).One concise method of accomplishing integration is witha ball and disk integrator. This type of integration isdescribed in detail (see BIBLIOGRAPHYFOR CONTROLLEDPOTENTIAL COULOMETRY, page 34, reference 2). Com-mercially-available units can be attached to the potentio-metric recorder which draws the i-t curve. This type ofintegrator gives a continuous indication of the i-t integral.

ApplicationsDIRECT OUANTITATIVEANALYSIS

The quantitative application of controlled potential cou-lometery depends upon Equation 65, which relates thecurrent-time integral (O) and the bulk concentration.

Sensitivity

Coulometry is particularly suited to the quantitativedetermination of small quantities of electrolyzable mate-rial. For example, a current of l¡;.a flowing for 1 secondis an amount of electricity equivalent to approximately10-11 gram equivalents. Such an amount of electricity canbe measured with reasonable accuracy.

Selectivity

The ability to electrolyze one species in the presence ofanother depends upon the relative position and separationof their half-wave potentials. In every case, it is the mostoxidizable or the most reducible species which is elec-trolyzed selectively. If the most re active species is fol-lowed by one whose half-wave potential is 0.4 volt moreinert, a 99.99% separation can be accomplished. If ilE1/2

is 0.2 volt, a separation of 99.5 % is possible.

Accuracy

When the desired electrolysis proceeds with 100% cur-

rent efficiency (i. e., no side reactions), and adequate cor-rections are made for residual and non-Faradaic currents,the error of this technique approaches 0.1 % .

When attempting to determine electro-kinetic constants,the value of n (the over-all number of electrons exchangedper molecule) must be known. This can be determinedmost reliably by measuring the coulombs necessary toelectrolyze a known concentration of the system beingstudied and calculating n from Equation 65.

Advantages and LimitationsThe combination of high accuracy and sensitivity makescontrolled potential coulometry one of the most reliableand useful analytical techniques. Furthermore, no stand-ard solutions are required, once a given procedure hasbeen demonstrated to proceed with 100% current effi-ciency.

Two limitations of this technique are the need for an inte-grator and the lack of speed. Exhaustive electrolysis oftenrequires several minutes.

CHRONOPOTENTIOMETRY

Definition

Chronopotentiometry is a controlled current technique inwhich the electrolysis oí an analyte occurs at a stationaryelectrode in a quiescent solution. The cell current is sud-denly stepped to some fixed value and the resulting work-ing electro de potential displayed against time.

Reverse current chronopotentiometry is an extension oíthe basic technique. In reverse current chronopotentiom-etry, the polarity of the electrolysis current is reversed,resulting in electrolysis of the species previously pro-duced at the electrode.

InstrumentationThe instrumental configuration is shown in Figure 31.The working electrode material may be any materialwhich can be held stationary during the electrolysis. Since

REF (SCE)

WORKING

Figure 3l. Instrumental Configuration [or Chronopotentiometry.

22

the solution must remain quiet, the cell should bemounted on a vibration-free support.

PrincipIe

POTENTIAL-TIME CURVES

A typical chronopotentiogram for a Fe+3 solution is shownin Figure 32.

----1--1•••141---..,...1-- T ~

1 1I+T/.-.l1I11I1

...Jc( •

~ UJZ VIUJ >....o •o.. UJ

o t (SEC)

Figure 32. Typical Chronopotentiogram o/ the Reduction o/ Fe+3•

At time (t) equals zero, the current through the electroly-sis cell is suddenly stepped from zero to some fixed valuei. Initially, the solution contains only Fe+3 ions. At theinstant that a constant cathodic current is initiated, Fe+2

ions are produced at the electro de surface and the poten-tial changes to a value in the vicinity of the standardpotential for the Fe+3/Fe+2 couple. As the current con-tinues to ftow, more and more Fe+2 ions are producedfrom the Fe+3 ions that difIuse to the electrode. Eventu-ally, the rate of difIusion of Fe+3 to the electro de from thebulk of the solution becomes smaller than the rate of con-sumption of Fe+3 by the electro de reaction, so that theconcentration of Fe+3 at the electrode surface becomesvery small. At this point the electro de potential whichdepends on the ratio of the concentrations of Fe+3 andFe+2 at the electrode surface, abruptly becomes muchmore negative. This rapid potential transition defines atime called the transition time. It is the time required forthe electrode reaction to convert essentially all of theFe+3 at the electro de surface to Fe+2• This same processis repeated for the next electro active species.

INTERPRETATIONOF POTENTIAL TIME-CURVES

The fundamental equation for chronopotentiometry is theSand Equation:

I _ (7T1hF) (A) (nDlh)Th- -2- T -1- Cb (66)

where T, F, A, i, n, D, and C, are the transition time(sec.), the Faraday (96,490), the area of the working elec-trode (cm-), the constant current (}La), the number ofelectrons, the difIusion coefficient of the electro active

species (cm- / sec), and the bulk concentration of thelatter (mF), respectively.

This equation, which is applicable to reversible and irre-versible systems, is derived with the assumption thatsemi-infínite linear difIusion takes place.

A chronopotentiogram of a two-component system willhave two potential transitions. The equation for the sec-ond transition is:

(Tl + T2)~ -TI Yz = (7TY2iA ) (nlD2~) (Cb)2

(67)

where the subscript (2) relates to the second component.

The working electro de potential (Ec) and the transitiontime (T) for a reversible system are related as follows:

RTE; = Er/4 + nF 10 [(T/t)~-I] (68)

where E; equals the potential at the working electro de,Er/4 equals the potential at J,4 of the transition time and:

Er/4 = EO (69)

The potential-time equation for an irreversible system is:

a, = RT In (nFACbkC) + RT In [1 -(t/TY~]cwaF 1 cxnaF

(70)

REVERSE CURRENT CHRONOPOTENTIOMETRY

If the current polarity is reversed during the potentialpause, a chronopotentiogram of the electrolysis productsis obtained. The reverse current chronopotentiogram ispictured in Figure 33.

E

t (SEC)

Figure 33. Current Reversal Chronopotentiometry.

If the electrolysis products are soluble:T[ = V3Tr (71)

If the products are insoluble:T[ = Tr (72)

AppIicationsQUALITATIVEANALYSISSince Er/~ is related to the EO of potentiometry and theE1/2 or polarography, it has the same qualitative use-fulness.

23

DIRECTQUANTITATIVEANALYSISWhen analyzing for a given electro active species, with afixed-area electrode, Equation 66 can be reduced to:

ir'h = kCb (73)

where k is a proportionality constant which can be evalu-ated with standard solutions. The best results are usuallyobtained by changing i as C, changes so as to keep r inthe 5 to 10 second range. Chronopotentiometry has beensuccessfully applied to many organic and inorganicsystems.

SensitivityChronopotentiometry has about the same lower limit ofsensitivity as polarography. This technique can oftenbe used in solutions which are more concentrated thanthose suitable for polarography.

SelectivityThe cornments concerning the selectivity of polarographyapply here as well (see SELECTIVITY,page 16).

AccuracyNumerous workers have demonstrated that this techniqueis more accurate than polarography. Many examples ofaccuracies of better than 1% have been reported.

KINETICSTUDIESThe kinetic factors k, (or ka) and ana can be derived froma chronopotentiogram using Equation 70. A plot of1n [1- (t/T) 'h] versus E; yields a straight line whoseslope is proportioned to ana, and whose E-intercept isproportional to k, (or ka).

ELECTROCHEMISTRYOFLABILESUBSTANCESCurrent reversal chronopotentiometry offers the chemista unique tool for studying the electrochemical propertiesof labile substances. An otherwise unstable substance canbe generated with a current of one polarity and then elec-trolyzed chronopotentiometrically before it decays byreversing the current polarity. This technique has alsobeen useful in elucidating many reaction mechanisms.

Advantages and LimitationsThe quantitative sensitivity and resolution of this tech-nique is about the same as polarography. However, theadvantages of speed, simplicity, and potential range citedfor potential sweep chronoamperometry also apply here.As in the case of cyc1ic voltammetry, current reversalchronopotentiometry is a very powerful and accurate toolfor studying the electrochemical properties of labile sub-stances.The limitations of this technique are similar to those citedfor potential sweep chronoamperometry. Fixed-surface

electrodes require careful c1eaning, and high quantitativeaccuracy is achieved only with the first species to beelectrolyzed.

/CONTROLLED CURRENTCOULOMETRY (Coulometric Titrations)

DefinitionControlled current coulometry is a technique in which aconstant cell current is used to generate a reagent in awell-stirred solution which will stoichiometrically titratethe substance to be determined. The potential of an indi-cator electrode is measured against time in order to locatethe titration end point.

InstrumentationThe Electroscan 30 Electroanalytical System can be usedfor controlled current coulometric titrations utilizing thearrangement shown in Figure 34. The instrument controlsthe current through the cell to a constant, preset value andpolarity. The potential of the indicating electrode is dis-played against time on the recorder chart.

REFERENCE

INDICATING

WORKING N,PURGE;+-

SPIN,L-=~!::::.I,BARMAGNETlCSTlRRER

Figure 34. Instrumental Configuration [or Controlled CurrentCoulometry.

14

",' -'" I> '""

",- 7

TIME

Figure 35. Coulometric Acid-Base Titration witb Potentiometriclndication,

24

An example of a coulometric acid-base titration with apotentiometric indicating system is shown in Figure 35.The pH of the sample solution is initially high, because ofan excess of OH- ions. After the electrolysis (H+ genera-tion) begins, the pH drops, slowly at first, and then rap-idly, as the titration is completed and an excess of H+ ionsis produced. The end point of the titration is located atthe infiection point in the titration curve, which corres-ponds to time (t) in Figure 35.Both the coulombs (Q) required to cause the titration ofthe sample and the concentration (Cb) of the sample maybe ca1culated from the following equation:

Q = it = nFVCb (74)

where i equals the constant generating current and tequals time (sec.) to reach the end point.

TITRANTGENERATIONBefore the titration is started, three things must be accom-plished. First, an appropriate solvent must be found whichwill provide the components necessary to allow the elec-trochemical generation of the appropriate titrant. Second,the current level must be chosen so that the current den-sity (i/A) at the working electro de surface will be suffi-cientIy low to insure 100% current efficiency. Finally,the current polarity must also be chosen so that the appro-priate titrant will be generated at the working electro desurface. For example, with platinum electrodes in anaqueous solution, a base may be generated by reductionof water at the cathode:

H20 + e- ~ OH- + 112 H2 (75)

or an acid may be generated by oxidation of water at theanode:

112 Hp ~ H+ + lA O2 + e- (76)

If the sample solution contains any substance which ismore easily reduced (when a base is being generated) oroxidized (when an acid is being generated) than the sol-vent, water, then external generation must be employed(see BIBLIOGRAPHYFORCONTROLLEDCURRENTCOULO-METRY,page 34, reference 10).

ENDPOINTDETECTION

Once the preliminary steps outlined above are taken, thecoulometric titration is identical to a classic titrationexcept the buret is replaced by the working electrode. Themethods of end point detection are also identical to thoseused in ordinary titration procedures.

ApplicationsQUANTITATIVEANALYSISBYTITRATIONThis technique has the same high accuracy and sensitivityas described for controlled potential coulometry. Theselectivity of this technique is provided by the selectivityof the titrant generated.

Controlled current coulometry has been successfullyemployed in redox, acid-base, precipitation, and com-plexion titrations. It has also been successfully used todetermine the thickness of metal and metal oxide surfacefilms.

Advantages and LimitationsAs in the case of controlled potential coulometry, accu-racy and sensitivity are two of the outstanding features ofthis technique. Three additional advantages, which thistechnique shares with the controlled potential method, areno standard solutions are required; titrants too unstableto be stored,often may be coulometrically generated (e.g.,C12, Ag+2,Cr+2,etc.); and accurate standard solutions forother analytical techniques may be coulometrically gen-erated.The technique has two advantages over controlled poten-tial coulometry. The 100% current efficiency is easier toachieve due to the selection of an appropriate solvent-electrolyte system, and determination of Q does notrequire an integrator.The technique has two limitations. Not all titrants can begenerated coulometrically, and an effective indicatingsystem must be found in order to determine the titrationend point.

ELECTRODEPOSITION ANDSEPARATION

DefinitionElectrodeposition and separation is a technique in whichan insoluble deposit is formed electrochemically on asolid electrode or amalgamated with a mercury electrode.The complete electrolysis of a depositable species is usu-ally carried out at a large surface area electrode in a well-stirred solution. The electrolysis may be carried out ateither controlled potential or controlled current.

REnSCE)

WORKING

AUX.N,PURGE

SPINBAR

~~L,MAGNETICSTlRRERo

Figure 36. Instrumental Configuration [or Electrodeposition andSeparation.

25

Instrumentation

The instrumental configuration for this technique isshown in Figure 36. Stirring is done either by rotating theelectrode or by stirring the solution. Large area workingelectrodes are usually used in order to speed up the elec-trolysis.

PrincipleSeveral cations (e.g., Fe+3, Co+2, Ni+2, etc.) can be electro-Iytically reduced to their metallic state and deposited ontoor into an electrode. The usual objectives of this techniqueare quantitative determination of a depositable species byweighing the resulting deposit (electrogravimetry); de po-sition to secure a separation of the deposited species fromthe rest of the solution (electroseparation); and electro-lytic deposition for preparative purposes (electroplating).

Co TROLLEDPOTENTIAL ELECTRODEPOSITIO

Before starting the electrolysis, the working electro depotential is set large enough to electrolytically deposit thespecies of interest but not so large as to deposit the nextmost electro active species. If this potential is not knownbeforehand, it can be determined from a polarogram orvoltammogram of a standard solution of the desired spe-cies. The potential is usualIy set 0.1 to 0.2 volt morenegative than the half-wave potential of the species.

This form of electrodeposition is the same as controlledpotential coulometry (CPC) except that the objective issecuring a depositrather than measuring coulombs. As inCPC, the initial current is high as electrolysis is begun, butdecays to zero as the deposition goes to completion. Sev-eral species can be deposited sequentially by advancingthe working electrode potential as each deposition iscompleted.

CONTROLLEDCURRENT ELECTRODEPOSITIONrn this technique a fixed cathodic current is applied to theelectrolysis cell and the plating-out of the most easilydeposited species takes place. When only one depositablespecies is present, this method is faster than the controlledpotential method. However, when there are severaldepositable materials present, special techniques must beused in order to insure selective deposition. In such cases,controlled potential deposition often offers the best com-promise between speed and selectivity.

ApplicationsDIRECT QUANTITATIVEANALYSIS

The amount of a substance in solution may be determinedby weighing the working electrode before and afterexhaustively depositing it from solution.

SEPARATION

Electrodeposition has been used to remove unwantedmaterials from solution prior to electrochemical, spectro-graphic, and spectrophotometric analysis. It has also beenused for separating radioactive isotopes from other ele-ments and as an aid in analyzing exchange rates of radio-active elements.

Advantages and LimitationsA high degree of selectivity and accuracy can be achievedby electrogravimetric analysis if the amount of analytedeposited is sufficient to be weighed accurately. Electro-deposition often results in a 99.9 % separation of thedesired species from solution. This degree of separationis hard to achieve by other separation techniques.

The major limitation of this technique is that it is onlyapplicable to elements which form stable deposits on orin an electrode.

26

SECTION 4 ... SUMMARY

ELECTRO ANAL YTICAL TECHNIQUESWhen using electrochemical techniques for chemicalanalysis, the potential at an electrode surface (Ea) is afunction of the concentration of some analyte (C), thecurrent that may fiow during the measurement (i), a timefunction (t), and any mass transport rate (MTR) that

might exist at the electrode and the area (A) of theelectrode.As illustrated in the following table, electroanalyticaltechniques can be classified according to which terms arecontrolled and which are measured.

27

SUMMARY OF ElECTROANAl YTICAl METHODS

PARAMETER CONTROLLED VARIABLE MEASURED

CONTROLLED CURRENT METHODS

Potentiometry Zero i E

Potentiometric Titration Zero i and titrant addition E vs Vol.

Potentiometric Titration(one or two polarized electrodes)

Constant i and titrant addition E vs Vol.

Controlled Current Coulo-metric Titration, withPotentiometric Indication

Constant i to producetitrant frorn appropriate solvent

E vs t, where t equiv. to titrant

Chronopotentiometry Constant i E vs t

Constant-CurrentElectrogravimetry

Constant i Weight 01 Deposit

CONTROLLED POTENTIAL METHODS

Polarography Constant E or Linear Sweep E i vs E

Voltammetry Constant E or Linear Sweep E i vs E

Amperometric Titration(one or two polarized electrodes)

Constant E and titrant addition i vs Vol.

A.C. Polarography Linear Sweep E + Sinusoidal E(small amplitude)

Chronoamperometry Constant E i vs t

Potential Sweep Chronoamperometry Linear Sweep E i vs E

Cyclic Voltammetry Triangular Sweep E i vs E

Controlled E Electrogravimetry Constant E Weight 01 Deposit

Controlled E Coulometry Constant E i vs t

28

MASS TRANSPORT RATE ANAL YTICAL SIGNIFICANCE TYPICAL TRACE

IncidentalRT aox

E= Eo+-In-nF aRedMeter or recorder deflection

Fast (stirred solution) ,~VPL.

Fast (stirred solution)~E POLARIZ';~O

E ,,-~RIZED

VOL.

Fast (stirred solution)

Slow (diffusion controlled) lti', ,:"--T

E i \t

Fast (stirred solution) Wt a Cb (Vol.) None

Controlled by diffusion and DME 'LmEFast (rotating electrode) 'ld

E

Fast (stirred solution) '1;:>VOL.

Controlled by diffusion and DME

Slow (diffusion controlled)

Slow (diffusion controlled) ,~E

Slow (diffusion controlled) ,~E

Fast (stirred solution) NoneWt a Cb (Vol.)

Fast (stirred solution) Q =ft i dt a Cb (Vol.)o

29

SECTION 5 ... INDEX OF SYMBOLS

A Area (cm') (id)., (id)'a Activity (id)av e

Ag,AgCI Silver, Silver chloride electrode (id)",ux

AMP Amplifier 1,

a Transfer coefficient i1im

C Concentration inCb Bulk concentration ioCOOx, CORed Concentration of oxidized and reduced species at (ir)', (ip),

the electrode surface i,D Diffusion coefficient (cm'Jsec) i,Dox, DRod Diffusion coefficient of oxidized and reduced k

species k" k,DME Dropping mercury electrode kOa, k" ('8 Thickness of diffusion layer (cm) k,E Electrical potential KEO Electrical potential under standard conditions x.,EO. Standard equilibrium potential In xEO' Formal standard potential log x

A constant similar to EO Me- Electron MrotEapp Applied voltage MTREll.! Half-wave potential n&me Dropping rnercury electrode potentialEe(1 Equilibrium potential n,EEX External voltageE, Potential at the start of a potential sean '7E," Input voltage Oxerfc(x) Error function compliment of x pCIEl' Peak potential (volts) pH(Ep)" (Ep)c Anodic and cathodic peak potential pNaEq Number of chemical equivalents 7T

E, Reference voltage RE, Sean voltage R.E".!. Chronopotentiometric quarter-wave potential RedETR Electron transfer rate R,Ew Working electrode potential R,exp(x) eX SCEL'>Eo Peak potential separation Qf Activity coefficient TF Faraday's Constant (96,490 coulombs/equivalent) t

Current (amp or Ilamp) ti, Current due to anodic (oxidation) reaction 7"

i, Current due to cathodic (reduction) reaction Tt, r-id Diffusion current v

Diffusion current constant Vol, V

31

Anodic and cathodic diffusion currentAverage diffusion current at DMEDiffusion current at maximum drop lifeFeedback currentLimiting currentNet current at an electrodeInitial currentAnodic and cathodic peak currentResidual currentCurrent at time (t)Proportionality constantRate constant for anodic and cathodic reactionFormal anodic and cathodic rate constantsStandard rate constantMass transport constantSolubility product constantLogarithm of x to the base eLogarithm of x to the base 10Average mercury fiow rate (mg/sec)Mass transport coefficient for a rotating electrodeMass transport rateNumber of electrons exchanged per molecule ofthe electro active speciesNumber of electrons exchanged in therate-controlling stepOvervoltageOxidized formInverse logarithrn of the chloride ion activityInverse logarithm of the hydrogen ion activitylnverse logarithm of the sodium ion activity3.1416Gas constantCell resistanceReduced formFeedback resistorRecorder resistorSaturated calomel electrodeCoulombs (amp-sec)Temperature in °ATime (sec)Drop time (sec)Chronopotentiometric transition time (sec)Forward and reverse transition timesPotential sean rate (volts/sec)Volume of solution being electrolyzed

SECTION 6 ... BIBLIOGRAPHY

The following bibliography provides specific and detailedinformation for more intensive study within each of theelectroanalytical techniques discussed. For your conveni-ence, they have been grouped according to technique.

POTENTIOMETRY1. Bates, R. G., Determination 01 pH, Theory and Practice. New

York: Wiley, 1964.2. Delahay, P., Instrumental Analysis. New York: MacMillan

Co., 1957, pp. 9-63.3. Dole, M., The Glass Electrode. New York: Wiley, 1941.4. Furrnan, N. H., Anal. Chem. (Review), 1950, Vol. 22, p. 33;

1951, Vol. 23, p. 21; 1954, Vol. 26, p. 84.5. Kolthoff. 1. M. and P. J. Elving, Treatise on Analytical Chem-

istry, New York: Interscience, 1963, Part 1, Vol. 4, Seco D-2,pp. 2166-2170, 2181-2187, and 2270-2300.

6. Kolthoff, 1. M. and N. H. Furman, Potentiometric Titrations(2nd Edition). New York: Wiley, 1932.

7. Lingane, 1. J., Electroanalytical Chemistry (2nd Edition). NewYork: Interscience, 1958, pp. 36-168.

8. Reilley, C. N., Anal. Chem. (Review), 1956, Vol. 28, p. 671;1958, Vol. 30, p. 765; 1960, Vol. 32, p. 185R.

9. Reilley, C. N. and R. W. Murray, Anal. Chem. (Review), 1962,Vol. 34, p. 313R; 1964, Vol. 36, p. 370R.

POLAROGRAPHY1. Delahay, P., New Instrumental Methods in Electrochemistry ,

New York: Interscience, 1954.2. Kolthoff, 1. M. and J. J. Lingane, Polarography (2nd Edition).

New York: Interscience, 1952.3. Kolthoff, 1. M. and P. J. Elving, Treatise on A nalytical Chem-

istry, New York: Interscience, 1963, Part 1, Vol. 4, Seco D-2,Ch. 46.

4. Lingane, J. J., Electroanalytical Chemistry (2nd Edition). NewYork: Interscience, 1958, p. 234.

5. Meites, L., Polarographic Techniques (2nd edition). NewYork: Wiley, 1965.

6. Milner, G. W. C., The Principies and Applications 01 Polar-ography and Other Electroanalytical Processes. Longmans,Green, New York, 1957.

7. Milner, G. W. C. and L. J. Slee,lnd. Chemist., 1957, Vol. 33,p.494.

8. Nurnberg, H. W. and M. J. von Stackelberg, J. Electroanal.Chem., 1961, Vol. 2, pp. 181-350; 1962, Vol. 4, p.!.

9. Schmidt, H. and M. J. von Stackelberg, Modern Polaro-graphic Methods. New York: Academic Press, 1963.

10. Weissberger, A., Techniques 01 Organic Chemistry: PhysicalMethods (3rd Edition). New York: Interscience, 1960, Vol. 1,p.3155.

11. Zuman, P. and 1. M. Kolthoff, Progress in Polarography, NewYork: Interscience, 1962, Vols. 1 and 2.

SOLID ELECTRODE VOLTAMMETRY1. Kolthoff, 1. M. and P. J. Elving, Treatise on Analytical Chem-

istry . New York: Interscience, 1963, Part 1, Vol. 4, Seco D-2,Ch. 47.

2. Kolthoff, 1. M. and J. Jordan, J. Am. Chem. Soc., 1954, Vol.76, p. 3843.

3. Laitinen, H. A. and 1. M. Kolthoff, J. Phys. Chem., 1941, Vol.45, pp. 1061-1079.

4. Zuman, P. and 1. M. Kolthoff, Progress in Polarography. NewYork: Interscience, 1962, Vol. 2, p. 503.

CHRONOAMPEROMETRY1. Delahay, P., New Instrumental Methods in Electrochemistry .

New York: Interscience, 1954, Ch. 8.2. Kolthoff, 1. M. and P. 1. Elving, Treatise on Analytical Chem-

istry . New York: Interscience, Part 1, Vol. 4, Seco D-2, Ch. 44.3. Lingane, J. J., Anal. Chem., 1964, Vol. 36, p. 1723.4. Murray, R. W. and C. N. Reilley, J. Electroanal. Chem., 1962,

Vol. 3, pp. 64 and 182.

33

POTENTIAL SWEEP CHRONOAMPEROMETRY ANOCYCLIC VOLTAMMETRY

1. Kolthoff, 1. M. and P. J. Elving, Treatise on Analytical Chem-istry . New York: lnterscience, 1963, Part 1, Vol. 4, Sec. 0-2,Ch. 47.

2. Manning, o. L., J. Electroanal. Chem., 1964, Vol. 7, pp.302-306.

3. Miller, F. J. and H. E. Zittel, J. Electroanal. Chem., 1964,Vol. 7, pp. 116-122.

4. Nicholson, R. S. and 1. Shain, Anal. Chem., 1964, Vol. 36.5. Nicholson, R. S., Anal. Chem., 1965, Vol. 37, p. 1353.6. Ross, J. W., R. O. DeMars, and 1. Shain, Anal. Chem., 1956,

Vol. 28, p. 1768.7. Saveant, J. M. and E. Vianello, Electrochemica Acta., 1965,

Vol. lO, p. 905.8. Streuli, C. A. and W. o. Cooke, Anal. Chem., 1953, Vol. 25,

p. 1691; 1954, Vol. 26, p. 963.9. Zuman, P. and 1. M. Kolthoff, Progress in Polarography.

New York: lnterscience, 1962, Vol. 2, p. 429.10. Nicholson, R. S., Anal. Chem., 1965, Vol. 37, p. 1353.

CONTROLLEO POTENTlAL COULOMETRY1. Jones, A. G., Analytical Chemistry: Some New Techniques.

New York: Academic Press, 1959.2. Kies, H. L., J. Electroanal. Chem., 1962, Vol. 4, p. 257.3. Kolthoff, 1. M. and P. J. Elving, Treatise on Analytical Chem-

istry, New York: lnterscience, 1963, Part 1, Vol. 4, Seco 0-2,Ch. 49.

4. Lewis, o. T., Analyst, 1961, Vol. 86, p. 494.5. Lingane, J. J., Electroanalytical Chemistry (2nd Edition), New

York: lnterscience, 1958, Ch. 19-21.6. Page, J. A., J. A. Maxwell, and R. P. Graham, Analyst, 1962,

Vol. 87, p. 245.

7. Rechnitz, G. A., Controlled Potential Analysis. London: Per-gamon, 1963.

8. Reilley, C. N., Proc. Intern. Symposium Microchem., Bir-mingham University, Birmingham, Alabama, 1958.

9. Weissberger, A., Technique oi Organic Chemistry: PhysicalMethods. New York: lnterscience, 1960, Vol. 1, Part 4,Ch. 49.

10. Yoe, J. H. and H. J. Koch, Trace Analysis. New York: Wiley,1957.

CHRONOPOTENTlOMETRY1. Kolthoff, 1. M. and P. J. Elving, Treatise on A nalytical Chem-

istry, New York: lnterscience, 1963, Part 1, Vol. 4, Seco 0-2,Ch. 44.

2. Lingane, J. J., "Analytical Aspects of Chronopotentiornetry,'Analyst, 1966, Vol. 91, pp. 1-9.

3. Lingane, J. J., Electroanalytical Chemistry (2nd Edition), NewYork: lnterscience, 1958, Ch. 22.

CONTROLLEO CURRENT COULOMETRYSee bibliography for Controlled Potential Coulometry, above.

ELECTROOEPOSlTlON ANO SEPARA TlON1. Alfonsi, B., Anal. Chim. Acta., 1958, Vol. 19, pp, 276-283,

389-394,569-575; 1959, Vol. 20, pp. 277-282.2. Herringshaw, J. E. and Z. M. Kassir, Analyst, 1962, Vol. 87,

p.923.3. Kolthoff, l. M. and P. J. Elving, Treatise on Analytical Chem-

istry. New York: Interscience, 1963, Part 1, Vol. 4, Seco 0-2,Ch. 48.

4. Lingane, J. J., J. Electroanal. Chem. (2nd Edition). New York:Interscience, 1958, Ch. 14-16.

5. Meites, L., Handbook oi Analytical Chemistry. New York:McGraw-Hill, 1963, Sec. 5, p. 170.

34

PRINTEO IN U.S.A.