Impedance Spectroscopy - Old Technique

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Fakultät Maschinenwesen | Institut für Energietechnik | Professur für Technische Thermodynamik

Lecture Series at Fritz-Haber-Institute Berlin

„Modern Methods in Heterogeneous Catalysis“

7.12.2012

Impedance Spectroscopy

Old Technique – New Applications

Cornelia Breitkopf

For personal use only!

http://tu-dresden.de/die_tu_dresden/fakultaeten/fakultaet_maschinenwesen/iet/vws

Outline

o Why old technique?

o What mathematics necessary?

o What measurement principle?

o Which applications in general and in heterogeneous catalysis?

Papers and citations

concept of electrical impedance was first introduced by HEAVYSIDE in the 1880s

pressure

detection

volume

modulation

Transient methods – general approach

Black Box analysis disturbance

TAP …temporal analysis of products

Porous solid

concentration

pulse

MS detection = f(t) of reactants and

products

FR …frequency response

Porous solid

EIS …electrical impedance spectroscopy

sine-wave

voltage modulation

Porous solid

see former lectures at FHI

change in

shape of pulse

Electrochemical impedance spectroscopy (EIS) …

…. is now established as a powerful tool

o for investigating the mechanisms of electrochemical reactions

o for measuring the dielectric and transport properties of materials

o for exploring the properties of porous electrodes

o for investigating passive surfaces

Reflections on the history of electrochemical impedance spectroscopy. D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.

Electrochemical impedance spectroscopy (EIS)

The power of the technique arises from:

o it is a linear technique and results are interpreted in terms of Linaer Systems Theory

o if measured of an infinite frequency range, the impedance delivers all information

from a system by linear electrical pertubation/response techniques

o high experimental efficiency

o validation of data is quite easy via integral transform techniques (Kramers-Kronig)

that are independent of the physical processes

Reflections on the history of electrochmical impedance spectroscopy. D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.

…however, EIS data interpretation requires a high level of mathematical skills

Mathematics behind….

…. some examples

Electrochemistry basics behind….

…. some examples

Introduction to impedance

o EIS - Electrochemical Impedance Spectroscopy

o measures dielectric properties of a medium as a function of frequency

o permittivity: interaction of an external field with the electric dipole moment of the

sample

o characterization of electrochemical systems

o impedance…complex electrical resistance

Principle – Representation of Complex Impedance

o Impedance …ability to resist the flow of electric current without limitations of

Ohm´s law

o Electrochemical impedance measurement

applying an AC potential to an electrochemical cell

measure then the current through the cell

analyze via Fourier series

o General principle similar to TAP, Frequency response (see lectures for

diffusion)

Black Box

Sinusoidal Excitation

Response Analysis


o electrical resistance – ability of a circuit element to resist the flow of electrical

current

o Ohm´s law R =E

I R resistance

E voltage I current

• ideal resistor

valid at all E, I levels

R independent of frequency

AC current and voltage are in phase

• ideal capacitor

AC current and voltage are completely out of phase, current follows voltage


o ideal resistor 𝑅 = 𝑑

𝐴

R resistance [] electrical resistivity [ cm] d distance [cm] A area [cm2] conductivity 1/

o ideal capacitor 𝐶 =

0 𝐴

𝑑

C capacitance [F] 0 electrical permittivity of vacuum (8.85 *10-14 F/cm) relative electrical permittivity of material [-]

water = 80,1 polymers = 2…8

vacuum = 1


o replace the simple concept of resistance/capacitance by impedance

o impedance is a more general circuit parameter

o it takes the phase differences between input voltage and output current into account

Impedance can be defined

…as a complex resistance

…realized when a current flows through a circuit

…composed of various resistors, capacitors or inductors.

…it is valid for direct current (DC) and alternating current (AC).

Linearity of electrochemical systems

o systems can be viewed as linear and non-linear systems

o impedance analysis of linear circuits is much easier

o definition of linear systems (by Oppenheim and Willsky in Signals and Systems):

…A linear system ….is one that possesses the important property of

superposition: if the input consists of the weighted sum of several signals, then

the output is simply the superposition (weighted sum) of the responses of the

system to each of the signals

in case of an electrochemical cell: input is potential, output is current

o electrochemical cells are not linear (doubling voltage = double the current)

Pseudo-linearity of electrochemical systems

o at small AC signals (1 – 10 mV), electrochemical cells become pseudo-linear

o linear systems do not produce any harmonics of the excitation frequency

o thus, presence and absence of significant harmonic responses can be used to

check for linearity

Conditions for measurement

o systems being measured must be at steady state

o systems which change with time may cause problems in standard EIS

measurements

o reasons for being not at steady state

o adsorption of solution impurities

o growth of an oxide layer

o build up of reaction products

o coating degradation

o temperature changes

…however, these problems may be solved by faster

detection techniques (see applications) and thus open

opportunity to follow such phenomena


o for small excitations a pseudo-linear response results with characteristic phase shifts

o excitation signal as function of time


o excitation as f(t) Et potential at time t E0 amplitude radial frequency = 2p f f frequency

o response signal It = Io sin(t + ) It response at time t I0 amplitude phase

Et = Eo sin(t)


o expression similar to Ohm´s law

o E(t) on x-axis, response I(t) on y-axis Lissajous figure

sin( ) sin( )

sin( ) sin( )

t oo

t o

E E t tZ Z

I I t t

Z impedance Z0 magnitude


o EULER relationship

o representation of impedance as a complex function

exp(j) = cos+ j sin

Et = Eo exp(jt) It = Io exp(jt - i)

Z () =𝐸

𝑡

𝐼𝑡

Re Im

.exp( )( ) (cos sin )

.exp( )

t oo

t o

E E j tZ Z j Z jZ

I I j t


Z () = Z0 (cos + j sin)

o Z() is composed of a real and an imaginary part

o plot on x-axis real part

o plot on y-axis imaginary part Nyquist plot

Principle – Nyquist plot

negative!

Each point on the Nyquist plot is the impedance at one frequency

high frequencies low frequencies

impedance is represented as

vector with length IZI

angle between vector and x-axis is

phase angle

Principle – Nyquist plot

Nyquist plots ….. are based on …….. equivalent circuits

o semicircle is characteristic of a single time constant

Principle – Bode plot

log frequency

BODE plot as another presentation opportunity. It shows frequency information.

log frequency

absolute value of IZI

phase shift

Models and analogs interpretation

tools to

interprete

impedance data

physical models analogs

o analogs which always take the form of electrical equivilant circuits

o simply reproduce the properties

o do not pretend to describe physico-electrochemical properties of the system

o aim to reproduce the phenomena of interest

o account for the mechanism of the processes in terms of valid concepts

Electrical circuit elements

o Equivilant circuits serve as analysis/evaluation tool for EIS data

o EIS data are fitted to a model representing an equivilant circuit

o common circuit elements: resistors, capacitors, inductors*

o properties of basic models determine the dependency of frequency

* Basics of EIS. www.gamry.com

Physical Electrochemistry – Electrolyte resistance

o solution resistance is a significant factor

o resistance in ionic solution is determined by ionic concentration, type of ion,

temperature, area of cell

o k as conductivity of solution (see standard textbooks and tables for data)

o problem: uniformity of current through an electrolyte area

Basics of EIS. www.gamry.com

Physical Electrochemistry – Double layer capacitance

o existance of electrical double layer on the interface between an electrode and its

surrounding electrolyte

o double layer forms by "sticking" ions on the electrode surface charged electrode

is separated from charged ions formation of a capacitor

o value of double layer capacitance depends on electrode potential, temperature,

ionic concentrations, type of ions, oxide layers, electrode roughness, adsorption of

impurities….


Physical Electrochemistry – Polarization/charge transfer

o polarization occurs via electrochemical reactions at electrode surface

o mixed potentials

o amount of current depends on kinetics of reaction and diffusion of reactants

towards and away from electrode

o example: corrosion

o single kinetically controlled reaction causes a charge transfer resistance

o no mixed potentials

o example: metal substrate in an electrolyte

o charge transfer speed depends on kind of reaction, temperature, concentration of

reaction products, applied potential


Physical Electrochemistry – Examples

…for combination of electrolyte resistance R1, charge transfer resistance R2,

double layer cpacitance C

R1

R2

C

demonstration examples

Physical Electrochemistry – Examples

…for diffusion and kinetic controlled electrochemical reactions

(dependencies between rate constant k0, transfer coefficient a, bulk solution

concentration cbulk, diffusion coefficient D)

o reaction control by kinetics or by diffusion


Physical Electrochemistry - Diffusion

o diffusion creates an impedance which is called WARBURG impedance

o impdedance depends on pertubation frequency

at high frequency a small Warburg impedance results

at low frequency a higher Warburg impedance is generated

Warburg impedance appears in

Nyquist plot as diagonal line

with slope of 45 °

Example for mixed kinetic and diffusion control

o Warburg impedance is the diffusional impedance for the diffusion layer of infinite

thickness which is characterized for the macroelectrode

o W is given by

with l as relative parameter of charge transfer k and diffusion coefficient D

with kf and kb heterogeneous kinetics on electrodes and D as diffusion coefficient

o RANDLES cell: equivalent circuit with mixed kinetic and charge transfer/diffusion control

Physical Electrochemistry - Diffusion

o Randles cell – equivalent circuit

o electrolyte resistance Re (4700), charge transfer resistance Rct (44000), double

layer cpacitance Cdl (5*e-9), l =7

graph with Warburg impedance according to values


History – some important theories and names

o concept of electrical impedance was first introduced by HEAVYSIDE in the 1880s

o improvement by KENNELLY and STEINMETZ via use of vector diagrams and

complex numbers representation

o Warburg (1899) determined impedance of diffusional transport of an electroactive

species to an electrode surface


from: Reflections on the history of electrochemical impedance spectroscopy. D. D. Macdonald. Electrochimica Acta 51 (2006) 1376-1388.

o Kramers-Kronig transforms (1920s)

o validate data consistency

o independent check for validity

o originally to treat optical data

o based on Cauchy theorem which

provides theoretical basis for

causality


o introduction of double-layer theory by FRUMKIN and GRAHAM resulted in use of

equivalent circuit modeling approach by RANDLES (1947)



o coupling of electrochemical reactions with diffusion by GERISHER and adsorption

by EPPELBOIN

o important electrochemical processes and reactions could be described for the first

time

hydrogen and electrode reactions

metal dissolution

passivity

corrosion



o effects of porous surfaces on electrochemical kinetics theory of porous

electrodes developed by de LEVIE in the 1960s



o de LEVIE



o data analysis improved by further development of mathematical methods

o improvement of computer and measurements techniques in last 40 years

o new applications: dielectric spectroscopy analysis of conduction in bulk polymers

or cell suspensions, surface corrosion kinetics, analysis of state of biomedical

implants

Example: gas diffusion in porous systems

Matysik, S.; Schulze, K.-D.; Breitkopf, C.; Papp.H: Impedance spectroscopy on solid sulfated zirconia catalysts Computer and Experimental Simulations in Engineering and Science CESES. 4 (2009) 145.

…possible to describe also gas diffusion ?



0,10 0,15 0,20 0,25

15

20

25

30

Ethan

Propan

Methan373 K

3*1014

Moleküle/Puls

1.5*1014

Moleküle/Puls

Neon

ButanDeff [

cm

2/s

]

1/(M0.5

)

…and comparison to TAP results ?

Knudsen diffusion of gases over corund determined by TAP (C. Breitkopf)



o comparison of surface modified samples

o modification with pyridine

o loading of sample with n-butane

o remeasure properties as time resolved responses

example: gas diffusion in porous systems


o equivilant circuit

Literature example: The rate of hydrogen and iodine adsorption at Platinum

R. Oelgeklaus, J. Rose, H. Baltruschat. Journal of Electroanalytical Chemistry, 376 (1994) 127-133

o aim of study:

evaluation of adsorption rate of hydrogen in presence of iodine in solution

on the surface of crystal Pt(111) and polycrystalline Pt by EIS

o why interesting?:

- former investigation of adsorption of hydrogen on Pt, Rh in acid solution

- using iodine can increase adsorption of hydrogen on the surface

Literature example: The rate of hydrogen and iodine adsorption at Platinum (experiment)


Sample

- single-crystall Pt(111) and polycrstalline Pt with 10mm in diameter

- electrolyte: alkaline: KOH addition KI with pH= 13; 14

Set up of experiment

- carrying out in standard electrochemical cell

- using 3 electrodes: counter- (Pt sheet), working (Pt or Pt (111))-, and reference electrode

Method

- cyclic voltammetry (CV): check the surface orientation

- electrochemical impedance: evaluation of hydrogen and iodine adsorption

Standard electrochemical cell

Literature example: The rate of hydrogen and iodine adsorption on Platinum (equivalent circuit)


o for reversible adsorption (Langmuir) and irreversible adsorption (Frumkin)

• equivalent circuit for adsorption control: (Fig. 1)

CD- double-layer capacitance

RadH, Cad

H- resistance and capacitance of

hydrogen adsorption

Re-solution resistance Figure 1

Literature example: The rate of hydrogen and iodine adsorption at Platinum (results and discussion)


1. Single-crystal Pt(111)

- evaluation of several series and parallel equivilant circuits

- adsorption of iodine is very fast (Fig.3)

- adsorption of hydrogen is slow (Fig.3)

The rate of hydrogen and iodine adsorption at Platinum (results and discussion)


- rate of iodine adsorption in polycrystalline Pt < Pt(111)

- structure-activity relations with respect to water dissiciation

2. Polycrystalline Pt

Literature example: Impedance spectroscopy on porous materials: A general model of lithium-ion batteries

Fabio La Mantia, Jens Vetter, Petr Novak. Electrochimica Acta 53 (2008) 4109–4121

Aim of study

- general model to fit electrochemical impedance spectra experimental data considering

adsorption of species at the electrode’s surface of lithium-ion batteries

Reasons

- essential information about processes at graphite electrodes from electrochemical

impedance: charge transfer at interface, diffusion inside, adsorption at the interface,

geometric limitation.

- understanding of limitations in order to obtain maximum performance of electro-active

materials

Literature example: Impedance spectroscopy on porous materials: A general model of lithium-ion batteries (experiment)

1. Structure of cell (Fig.4)

- working electrode: prepared from graphite powder

mixture with binder

- reference electrode: lithium

- current collector: titanium wire

- counter electrode: lithium

- electrolyte: ethylene carbonate (EC) mixture dimethyl

carbonate (DMC) in 1M LiPF6

2. Approach

EIS: using a Potentiostatic/Galvanostat by Princeton

Applied Reseach at 25oC, DC potential of 1.5V,

frequency 100kHz down to 10mHz, amplitude 2mV

Cyclic voltammetry: potential between 1.5V and 0.9V

at sweep rate of 0.2mVs-1

3. Materials (Table 1)

Table 1


Literature example: Impedance spectroscopy on porous materials: A general model of lithium-ion batteries (results)

o Figs. represent the modulus of impedance

spectra with different graphite materials in

Bode plot

impedance correlates with

irreversible charge consumption on

SEI layer (solid electrolyte interface).

(processes cannot be analyzed from

these diagrams)

o influence of the BET on impedance

impedance of KS sample at low

frequencies significantly different

Modulus of the electrochemical impedance of a GN44

electrode in EC:DMC at 1.5V vs. Li/Li+

Modulus of specific the electrochemical impedance for

different graphite samples in EC:DMC at 1.5V vs. Li/Li+


Literature example: Impedance spectroscopy on porous materials: A general model of lithium-ion batteries (expressions of model)

A general model interpretation of EIS experimental data:

• Based on resistivity of both electrolyte solution and

electrode, eq (6):

• Describing the behavior of a porous electrode, mass

transport equations, electrochemical reaction at the

surface, eqs (19,20)

with

ln(1 2 ) (6)

.

p w S E

S p

d A RT Ct

x dx x FC x a A

0, 0,

ln(1 2 ) (19)

ln2 (1 ) (20)

p S E

w

S

p

x x x x

d A RTt C j

x dx x FC a

d ACD t

t x dx x

• Eqs(19,20) be used for AC response of porous electrodes with assumption in time-

domain and steady-state by eq (45)

cosh( )( ) (45)

sinh( ) 2T

p

l lZ

NA l l

k

k k

2 2

2 2

2 .;S E S E

S E S E

Electrical equivalent circuit representing the

current lines and reacting sites in porous electrode


Literature example: Impedance spectroscopy on porous materials: A general model of lithium-ion batteries (Fitting experimental data with model)

o equation (45) used for fitting experimental impedance spectra

o impedance spectra were analyzed using Kramer-Kronig transformation

Nyquist plot of electrochemial impedance of GN44

electrode in EC:DMC at 1.5V vs. Li/Li+


Applications of EIS (current and future)

o impedance of electroactive polymer films with respect to their special properties

such as flexible solution and melt processability manufacturing, blendability with

commodity polymers, ambient stability, unconventional electrical and optical

properties

new materials in value-added industrial and consumer products as

electroactive inks, paints, coatings, and adhesives

electrochromic smart windows

electrically conductive transparent and corrosion-protective films

supercapacitive materials

conductive high-performance fibers

electrochemical sensors, enzyme-modified conductive polymers

from: Impedance spectroscopy – applications to electrochemical and dielectric

phenomena. Vadim F. Lvovich. Wiley 2012.

o impedance of industrial colloids and lubricants

reduction of friction processes in industry and automobiles

opportunity by EIS to resolve a complicated lubricant system both spatially

and chemically to analyze specific parts of that system

o cell suspensions, protein adsorption, and implantable biomedical devices

o insulating films and coatings

o electro-rheological fluids

o impedance of metal-oxide films and alloys

o corrosion monitoring



Applications of EIS (current and future)

Modifications of EIS (current and future)

o AC voltammetry

o potentiodynamic and (fast) Fourier-transform impedance spectroscopy

o non-linear higher-harmonics impedance analysis

o local EIS

o scanning photo-induced impedance microscopy (SPIM)



Thanks for the attention !

Questions please send to:

[email protected]

Impedance Spectroscopy - Old Technique

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