An Introduction to Impedance Spectroscopy and · PDF fileAn Introduction to Impedance Spectroscopy and Conductivity Damilola Daramola and Ramasamy Palaniappan Center for Electrochemical

An Introduction to

Impedance Spectroscopy

and Conductivity

Damilola Daramola and Ramasamy

Palaniappan

Center for Electrochemical Engineering

Research

ABC’s of Electrochemistry

August 9, 2011

2

Introduction

• “Impedance spectroscopy is classified as the small-

signal measurement of linear electrical response . .

. and the subsequent analysis of the response”

• Most commonly performed in the frequency domain

but can also be performed in the time domain and

then Fourier transformed into the frequency

domain.

Center for Electrochemical Engineering Research, Ohio University

J. R. Macdonald Annals of Biomedical Engineering 20, pp 289 - 305

3

Impedance

• “To impede” means “to hinder”

– Resistance is a type of impedance

• Represented with the symbol Z

• Stimulus and response is frequency dependent i.e.

sinusoidal

• A complex term i.e. Z = Z' + jZ''

– Re (Z) = Z'

– Im (Z) = Z''

– j (usually expressed as i) =


1Impedance spectroscopy : emphasizing solid materials and systems / edited by J. Ross Macdonald; Wiley: New York :, 1987.

4

Elements in an Electrical Circuit


dt

tdVC

dt

tdV

tdV

tdq

dt

tdqtI

dt

tdILtV

tRItV

)()(

)(

)()()(

)()(

)()(

Orazem, M. E. Electrochemical impedance spectroscopy / Mark E. Orazem, Bernard Tribollet; Wiley: Hoboken, N.J. :, 2008

5

Stimulus and Response in Electrical Circuits

• For a sinusoidal potential

• The current response is

• Based on complex algebra:


)cos()( tVtV

)cos()( tItI

ω is frequency

φ is phase change

|ΔV| and |ΔI| are amplitudes

jbja

baj

jbjajbjabaj

ja

ee

eba

eeee

ajae

Re

Re)cos(

)sin()cos(

)(

)(

VV

eII

IeeeItI

eVtV

j

tjtjj

tj

where

ReRe)(

Re)(

Therefore


6

• For f, a continuous function of t

• Therefore,

• And Resistance, Inductance and Capacitance responses are

• Based on complex algebra:


dt

tdftf

dt

d )(Re)(Re

tj

tj

Vejdt

tdVtV

dt

d

Iejdt

tdItI

dt

d

Re)(

Re)(Re

Re)(

Re)(Re

tjtj

tjtj

tjtj

VejCIe

IejLVe

IeRVe

ReRe

ReRe

ReRe

dt

tdVCtI

dt

tdILtV

tRItV

)()(

)()(

)()(

jjeee

bjbeeee

jj

ajbajba

)sin()cos(

)sin()cos(

22

0022

22

22

ReReRe

ReReRe

ReRe

tjjtjtj

tjjtjtj

tjtj

VeCeVeCIe

IeLeIeLVe

IeRVe

Therefore


Stimulus and Response in Electrical Circuits

7

Impedance in Electrical Circuits

• In addition,

• Consequently

• Since impedance is defined as


tjtjtj

tjtjtj

tjtjtj

VeCjVejCIe

IeLjIejLVe

IeRIeRVe

ReReRe

ReReRe

ReReRe

VCjI

ILjV

IRV

I

VZ

CjZ

LjZ

RZ

capacitor

inductor

resistor

1


8

Impedance in a simple circuit


11

1

1

1

11

1

11

1

11

CRj

R

CjRZZ

Z

CR

parallel

11

10

1 CRj

RRZtotal

parallelRtotal ZZZ 0

0

10

;

;0

RZ

RRZ

total

total

9

Representation of Impedance

• Nyquist Plots: (Real Impedance vs Imaginary Impedance)

• Bode Plots: (Magnitude of Impedance or Phase Angle vs frequency)


J. R. Macdonald Annals of Biomedical Engineering 20, pp 289 – 305

http://www.che.ufl.edu/orazem/pdf-files/Orazem%20EIS%20Spring%202008.pdf

http://www.che.ufl.edu/orazem/pdf-files/Orazem EIS Spring 2008.pdf



10

Nyquist Plot of simple circuit


http://www.che.ufl.edu/orazem/pdf-files/Orazem%20EIS%20Spring%202008.pdf

11

10

1 CRj

RRZtotal





11

But . . .


J. R. Macdonald Annals of Biomedical Engineering 20, pp 289 – 305

• Care should be taken when translating plots to equivalent circuits

as different circuits can be mathematically equivalent.

• Additional tests should be done for intepretation

12

Ionic Conductivity - Theory

13

Ionic Conductivity - Background

j

1

is the flux

is the electrochemical potential of species j

(V) is the electrostatic potential

is the Velocity

D is the diffusion co

ln( )

( . )

j

j j j j j

j j

j

j j j

j

J

J

Z FD C C V

RT

V

J D C

z F RT C

kJ mol

efficient

14

Ionic Conductivity Background

2 2

j

j

j

Migration (linear):

Z.

Z

i =

Einstein-Smaluchowski equation:

Mobility, =

j j

j

j

j j j jj j

F AD C

RT x

FD

RT

E

x l

FA Ei i Z C

l

15

Ionic Conductivity Background

-1

2

is the Conductance (S.cm ),

is the distance between the electrodes (cm),

A is the area of the working electrode (cm )

j j j

j

i AL

E l

F Z C

L

l

16

Ionic Conductivity - Equations

1

Cell Constant

Res

The conductivity of the solution, , is more commonly used in solution resistance calculations.

Its relationship with solution resistance is:

.

1, ( . ) =

( )

lR A

Conductivity s cm

lRA

-1

where

Ris the Resistance ( ) ,

is the solution resistivity ( . ).

istance

l

ACell Constant (cm ) =

cm

17

Equivalent ionic Conductivity and

Dependency on Concentration

-1 -1

= C

is the Equivalent or molal ionic Conductivity (Scm mol )

Warning: Equivalent ionic

conductivity is concentration

dependent and degree of

dissociation. - check Bard and

Faulkner for more on this.

18

Constructing the Conductivity Cell

Experimental Warning: The conductivity Cell must be

calibrated using standard KCl solutions every time prior

to its use.

19

Electrochemical Aspect for Impedance

Spectroscopy

20

Series Resistance – Nyquist Plot

21

Series Resistance – Bode Plot

22

Fitting Equivalent Circuits

Interpreting Impedance Spectra for Electrochemical Systems

Toughest aspect of EIS

Warning: A lot of circuits can be used to fit a single

spectra, still it does not mean it is valid. Equivalent

circuits should match with the electrochemical system in

study.

23

References

• Electrochemical Methods Fundamentals and Applications – Bard

and Faulkner.

• Su-Moon Park et al., Analytical Chemistry, (2003), p. 453A

• J. R. Macdonald Annals of Biomedical Engineering 20, pp 289 –

305

• Impedance spectroscopy : emphasizing solid materials and

systems / edited by J. Ross Macdonald; Wiley: New York :, 1987.

• Orazem, M. E. Electrochemical impedance spectroscopy / Mark E.

Orazem, Bernard Tribollet; Wiley: Hoboken, N.J. :, 2008

• http://www.che.ufl.edu/orazem/pdf-

files/Orazem%20EIS%20Spring%202008.pdf (Mark Orazem

Presentation)







24Center for Electrochemical Engineering Research, Ohio University

Questions

Documents

An Introduction to Impedance Spectroscopy and · PDF fileAn Introduction to Impedance Spectroscopy and Conductivity Damilola Daramola and Ramasamy Palaniappan Center for Electrochemical