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Autolab Application Note EI

Electrochemical ImpePart 1 Basic Princip

Keywords

Electrochemical impedance spectrosc

response analysis; Nyquist and Bode prese

Summary

Electrochemical Impedance Spectroscop

powerful technique for the charelectrochemical systems. The promise of

single experimental procedure encompass

broad range of frequencies, the influence

physical and chemical phenomena may

distinguished at a given applied potential.

In recent years, EIS has found widesprea

the field of characterization of materials. It

in the characterization of coatings, batterie

corrosion phenomena. It has also been us

a tool for investigating mechanisms in elelectrodissolution, passivity, and corrosi

gaining popularity in the investigation of

across membranes and in the study o

interfaces.

Principles of EIS measurements

The fundamental approach of all impedan

apply a small amplitude sinusoidal excitat

system under investigation and measur

(current or voltage or another signal of i

following figure, a non-linear i-V curve

electrochemical system is shown in Figure

1 This signal is typically voltage or current but casignal of interest, e.g. in the case of Electrohydro

impedance spectroscopy, the signal is rotation

01

dance Spectroscopy (EIS)les

py; frequency

ntations

y or EIS is a

acterization ofIS is that, with a

ing a sufficiently

of the governing

be isolated and

d applications in

is routinely used

s, fuel cells, and

d extensively as

ectrodeposition,n studies. It is

diffusion of ions

f semiconductor

e methods is to

ion signal to the

e the response

interest1). In the

for a theoretical

.

n be any otherdynamic (EHD)

peed.

Figure 1 - Potential and curren

impedance measurement

A low amplitude sinewave

frequency , is superimpo

voltage E0. This results in a c

superimposed on the DC cur

response is shifted with respe

Figure 2).

Figure 2 Time domain plots of t

and response

The Taylor series expansion f

0,0 12

220,0

If the magnitude of the pertu

the response can be consider

The higher order terms in theto be negligible.

t modulation recorded during an

Esin(t), of a particulared on the DC polarization

rrent response of a sine wave

rent i

sin(t+) . The current

ct to the applied potential (see

e low amplitude AC moduleation

r the current is given by:

2

rbing signal E is small, then

ed linear in first approximation.

Taylor series can be assumed

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The impedance of the system can then be

Ohms law as:

This ratio is called impedance, , of thecomplex quantity with a magnitude and a

depends on the frequency of the sign

varying the frequency of the applied signal

impedance of the system as a functio

Typically in electrochemistry, a frequency r

0.1 Hz is used.

The impedance, , as mentioned aboquantity and can be represented in Cart

polar coordinates.

In polar coordinates the impedance

represented by:

||

Where ||is the magnitude of the impthe phase shift.

In Cartesian coordinates the impedance is

"

where Z'() is the real part of the impeda

the imaginary part and 1.

Data presentation

The plot of the real part of impedance agaipart gives a Nyquist Plot, as shown i

advantage of Nyquist representation is tha

overview of the data and one can make

interpretations. While plotting data in the N

real axis must be equal to the imaginary

distort the shape of the curve. The shap

important in making qualitative interpretati

The disadvantage of the Nyquist represen

loses the frequency dimension of the d

overcoming this problem is by labeling th

the curve.

The absolute value of impedance and the

plotted as a function of frequency in tw

Autolab Application Note EIS01

Electrochemical Impedance Sp

Part 1 Basic Principles

calculated using

system and is a

hase shift which

l. Therefore by

one can get the

n of frequency.

ange of 100 kHz

ve is a complex

sian as well as

f the data is

edance and is

iven by:

nce and Z"() is

nst the imaginaryFigure 3. The

t it gives a quick

some qualitative

yquist format the

xis so as not to

of the curve is

ons of the data.

ation is that one

ta. One way of

frequencies on

phase shifts are

o different plots

giving a Bode plot, as shown

complete way of presenting th

Figure 3 A typical Nyquist plot

Figure 4 A typical Bode plot

A third data presentation

available. In this presentation

components are plotted on t

and the logarithm of the freq

(see Figure 5).

The relationship between the

data is given by:

||"!#"$

Alternatively, the real and imaobtained from:

$|| %&' " || '(#

ctroscopy (EIS)

Page 2 of 3

in Figure 4. This is the more

e data.

ode involving a 3D plot, is

mode the real and imaginary

he X and Y axis, respectively

uency is plotted on the Z axis

two ways of representing the

ginary components can be

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Autolab Application Note EIS01

Electrochemical Impedance Spectroscopy (EIS)

Part 1 Basic Principles

Page 3 of 3

Figure 5 3D projection plot

Date

1 July 2011