Electrochemical Impedance Spectroscopy (EIS)

Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
Electrochemical Impedance Spectroscopy (EIS)
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
1. Introduction
Today in chemistry different technique exist to work on new materials, oxido-reduction reaction,
catalytic activity… Electrochemical impedance spectrometry (EIS) is one really interesting
method to study chemical system and analysis of complex processes1 2 3 .Using EIS with one cheap
and easy experimental set up different materials (solid, liquid) and different processes (diffusion,
electrode processes, kinetic) could be studied.
The introduction of the impedance into the electrical engineering in the end of the XIX century by
Olivier Heaviside is the beginning of the impedance spectroscopy.4 Soon, vector diagrams and
complex representations were integrated. In 1899, Emil Warburg applied the impedance concept
to electrochemical systems and his work about diffusional transport (cf Warburg impedance) was
one of the first electrochemical impedance spectroscopy (EIS) publication. With the invention of
new instruments and potentiostats in the 1940s, frequency response analyzers (FRAs) in the 1970s
and increasing of their performances, EIS has developed quickly. Today, many researchers are
working with EIS on different electrochemical processes and reactions including hydrogen
evolution reaction (HER), oxygen reduction reaction (ORR), metal dissolution, porous electrodes,
corrosion…
2. Impedance spectroscopy: definition and fundamental
Definition
The electrochemical impedance spectroscopy (EIS) is a general term used for all the techniques
based on the small signal measurement of the linear electrical response of one material (including
electrode processes) and the analysis of the response to obtain information about the physicochemical properties of the system. To realize one EIS measurement, one small perturbation is
applied to the system and the response is collected.
Three principal stimuli (perturbation) methods are used:
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Measurement with a step function of voltage [V(t) = 0 for t < 0, V(t) = V0 for t > 0] is applied
at t = 0 to the system and the resulting time-varying current
i(t) is measured. The ratio V0 /i(t) called indicial impedance (or timevarying resistor), measures the impedance coming from the perturbation. This quantity is
not the usual impedance referred to in EIS. It is necessary to convert the time varying
results into frequency domain, via Fourier or Laplace Transform to frequency-dependent
impedance. This technique is easily done and the voltage controls the reaction rate at the
interface. But transformations of the results are necessary and the signal-to-noise ratio
differs between frequencies, so the impedance could be not well measured over all the
frequency range
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
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Impedance Spectroscopy
The second technique, called white noise, a V(t) random signal is applied to the interface and
the resulting current, i(t) is measured. Again, to pass into the frequency domain and obtain
impedance, a Fourier Transform of results is needed. The advantages are a fast data
collection; only one signal is applied for a short time. The disadvantages are to require a
Fourier analysis and the true white noise.
The third method, and the most used, is the application of one single-frequency voltage or
current and to measure the real and imaginary parts or the phase shift and amplitude of the
resulting current at that frequency using frequency response analyzer (FRA).
Today standard FRA could measure impedance in a frequency range of 1.10-4 to 1.10-6 Hz
and the analysis of results is done with computers. Before the FRA, the impedance
measurements were done using Lissajous figures. This method is easy to use and a good
signal-noise ratio could be obtained in a large frequency range.
There are other methods, like AC polarography, a combination of the first and the third
technique, with a simultaneous application of a linearly varying unipolar transient signal and
a much smaller single-frequency sinusoidal signal (Smith and al. 1966).
3. Fundamentals
A - Response to one perturbation
One perturbation, a sinusoidal potential V (t ) = Vm cos(ωt ) of one angular frequency (or pulsation)
ω is applied to the system (Figure 1).
The resulting current is i (t ) = I m cos(ωt − φ ) with I m = I m (ω ) and φ = φ (ω )
Figure 1: Sinusoidal potential, V(t), applied, resulting current, i(t), and phase shift φ
The tension V (t ) could be associated to the complex number V = Vm .e jωt and the current i(t) to
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
the complex number i = I m .e j (ωt −φ ) .
V
V
The impedance is defined as Z = with a modulus |Z | = m and argZ =
i
I m (ω )
(ω) .
Z is one complex number, Z = Z'+jZ' ' and |Z | = Z' 2 +Z' ' 2 where j = − 1 . In the complex plan, the
impedance corresponds to one vector of length |Z | making one angle with the real axis. The
 Z' ' 
relation φ = arctan
 with the phase angle φ is verified.
 Z' 
The complex impedance could be also expressed as: Z = |Z |.e jφ (ω ) .
The impedance Z is in ohm, (Ω). The angular frequency (or pulsation), ω = 2πf is in radians .s-1
and the frequency, f, in hertz (Hz).
B - The immittances
There are different quantities measured or derived from impedance which could be really useful in
EIS: the immitances.
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The admittance, symbolized Y, is the inverse of the impedance: Y =
•
The capacitance C =
Є=
•
1
, in Siemens (S)
Z
Y
and complex dielectric constant or dielectric permittivity Є
jω
Y
C
with C0 the capacitance of the empty measuring cell.
=
jωC0 C0
The modulus, M, is the inverse of the dielectric constant M =
1
and also equal to
C
M = j ωt
All the immittances are complexes number. The immittances could help to study one system,
changing the representation from impedance to admittance…
C - Impedance representation
Impedance (and immittance) data are commonly presented as diagrams (Figure 2) with different
information:
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
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Impedance spectra, Nyquist or complex plane plot: -Z'' vs Z'. Very popular, it could permit
one visual identification of the electrical equivalent circuit which could be used to model
the system. The evolution of the frequencies (high to low) indicated by an arrow could be
really useful for the analysis.
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Bode diagrams: Bode plot log (⌡Z⌡) vs log (ω) for the magnitude response and Bode phase
plot Ф vs log (ω) for the phase shift.
Figure 2: Nyquist and Bode diagram
D - Electrical equivalent circuit
The analysis of data after electrochemical impedance spectroscopy is done using electric
equivalent circuit composed by ideal resistor (R), capacitor (C) and inductor (L) to represent the
theoretical physico-chemical processes model. The electrical components are arranged in serial or
parallel and the experimental data are fitted with the electrical equivalent circuit. It could permit
to have relaxation time, dielectric properties, corrosion information…
E - Basic impedances, ideal circuit elements
For one AC voltage, we can calculate the impedance of the basic electrical components:
- The resistor (R)
With the Ohm Law, vr (t ) = ir (t ) ∗ R and considering the voltage signal as v(t ) = V p sin (ωt ) , we have
R=
vr V p sin (ωt )
=
ir I p sin (ωt )
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
so Z r = R and Yr =
Impedance Spectroscopy
1
R
- The capacitor (C)
The charge stored in one capacitor Q = C ∗ V and the current is: I =
For one AC voltage, V (t ) = V0 .e jωt and I (t ) = C
The impedance Z c =
dQ
dV
=C
dt
dt
dV0 .e jωt
= jω.C.V0 .e jωt ,
dt
1
and the admittance is Yc = jωC
j ωC
- The inductor (L)
For the inductor L, the is the relation: vL (t ) = L
i (t ) = i0 .e jωt so L.
dI L (t )
and an AC current signal
dt
dI L (t )
= L.i0 . j.ω.e ( j .ωt ) = ν(t )
dt
ν
1
The impedance Z L = = j.ω.L and the admittance YL =
i
j ωL
A linear arrangement of impedance can be added: Ztot= Z1+Z2+Z3
A ladder arrangement of admittance can be added in the admittance plan: Ytot= Y1+Y2+Y3
4. Impedance spectrometry: advantages and limitations
The EIS is really interesting for researchers, easy to use and cheap, this method permits to have
information about physico-chemical properties and processes like electrode phenomena, diffusion,
charge transfer, capacitance, mass transport. After the EIS measurement, the equivalent circuit and
the fitting of experimental results, kinetic constants, relaxation time, diffusion and more could be
obtained. But the experimentalist has to be careful choosing his equivalent circuit. It has to
correspond to one plausible theoretical model of process and not only fitting the experimental
data. The interpretation of data could be ambiguous and one equivalent circuit is not unique.
There are different circuits with the same impedance. We have also to remember that the real
system could have a distribution of his properties in the space. One equivalent circuit could be
tested with different experimental conditions (ex: different electrolyte concentrations). The circuits
with ideal components (R, L, C) could not be sufficient to fit experimental data. New elements like
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
the constant phase element (CPE), used to represent non ideal capacitor and the Warburg
Impedance (WG or RW) used to model diffusion are existing. It is also really useful to change the
representation, using the immittances: on the Nyquist diagram, one characteristic shape of one
equivalent circuit not visible with impedance could be recognized with the admittance.
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
5. Impedance spectroscopy: experimental part
6. Measurement setup
The impedance could be measured in galvanostatic or potentiostatic mode with the impedance
frequency response analyzer (FRA) and potentiostat Autolab PT204 (all in one machine). One
continuous (DC) potential could be applied during the impedance measurement. To measure, one
sinusoidal wave generated by the FRA is applied to the sample and the AC signal is superimposed
to the DC signal. The signal is coming back to the FRA and the response signal, the impedance of
the sample, is analyzed.
The Autolab is controlled with NOVA software. With this software, you could choose the type of
experiment, set all the experimental parameters, analyze your data and also fit your experimental
results for the impedance measurements (after the definition of the equivalent circuit).
Material
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Autolab PGSTAT204 with FR32 impedance module: FRA-potentiostat
electrical cables
electrical plate to plot components
resistors
capacitors
inductors
variable resistor
empty boxes
Sodium Chloride (NaCl) aqueous solution (0,1 mol.l-1)
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
7. Experiments
1. Measure the impedance in potentiometric mode at 1V DC of one resistor for one frequency
range 1.105 – 1 Hz and one amplitude of 10 mV AC. Observe the shape of the impedance and
admittance on the Nyquist diagram. Do the same for one capacitor.
2. Combine one resistor and one capacitor in series and another circuit with one resistor and
one capacitor connected in parallel. Set impedance measurement in galvanostatic mode with
one frequency range 1.105 – 0.1 Hz and one amplitude of 0.1 mA AC. Do the same in
potentiostatic mode (1.5V DC) with the same frequency range and one amplitude of 10mV
AC. What could you conclude about impedance spectra in galvanostatic and potentiostatic
mode in these conditions?
3. Plug the electrical components to mount the three electrical circuits of the figure 3 and
measure the impedance for both circuits (frequency range: 1.105 – 0.05 Hz, potentiostatic
mode, 1.5V DC, amplitude 10mV AC )
Figure 3: Electrical circuits to compare impedance spectra
Compare the Nyquist diagrams of all the electrical circuits. What is the problem? How could
you find one solution?
4. Using the theorical values of impedance for capacitors, resistors and the combination of
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
impedance in serie or parallel, calculate the impedance of the circuit a).
Determination of unknown resistance with Nyquist diagram and relaxation time
Applying one sinusoidal wave to the studied system, the impedance measurement is
inducing one local polarization in the medium. The response, called Debye relaxation
corresponds to the dielectric relaxation response of one medium of non-interacting dipoles
to an alternating external electric field. It could be expressed in the complex permittivity ε
of a medium as a function of frequency of the electric field ω :
with ε∞ limit of permittivity at high frequency, Δε = εs − ε∞ with εs is the
static permittivity at low frequency and τ is the characteristic relaxation time of the medium.
There are more complex relaxation model using equations like Cole-Cole, David Cole,
Havriliak–Negami relaxation. The relaxation time is really interesting in electrochemical
impedance spectroscopy. With the hypothesis of only linear processes occurring during our
measurements, we could see the relaxation time corresponding to different phenomena on
Nyquist diagram.
For one electrical circuit made with series resistor and capacitor, τ = RC
1
1
with ω0 =
at the top of the half circle on the
and for one ladder R,C circuit, τ 0 =
RC
τ0
Nyquist diagram.
Mount the circuit of the figure 4 and make three impedance measurements for three
different resistance values using the variable resistor (frequency range: 1.105 – 0.05 Hz,
potentiostatic mode, 1.5V DC, amplitude 10mV AC).
Figure 4: Electrical circuit with variable resistor (R2)
After all your measurements, plot your Nyquist diagram and determine the value of the
resistance for each measurement using the relaxation time. You could verify your value by
one simple impedance measurement of the variable resistor.
5. See the electrical circuit corresponding to the scheme of the figure 5. This circuit is used as
equivalent circuit by S. Hern Seo and C. Sik Lee to analyze their EIS results for a DMFC working
in different chemical conditions5. Here we will use he equivalent circuit used for the oxidation
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
of methanol at the anode (left part on figure 5). To improve methanol oxidation, researchers
are working on new catalysts and the EIS is measured at different potentials to characterize
the system and to have information about chemical processes.
Figure 5: Equivalent circuit for DFMC modeling (5)
Make the left part of the electrical circuit of the figure 5.
Set EIS measurement with 10 mV amplitude, frequency range 1.105 – 0.01 Hz and do
impedance measurement in potentiostatic mode at 0.2 V DC. On Nova, define the same
equivalent circuit and compare the values obtained by fitting with the values of the electrical
components.
6. Measurement with chemical solution: to work with real system, we will use one aqueous
solution of NaCl connected to one classical electrical circuit.
Mount the electrical components on the plate and fill the little plastic box (linked to one
metallic support) with the NaCl 0,1 M solution until the two metallic piece of the top are in
contact with the solution when the box is closed. Be careful, not to spill solution on electric
components! Define one impedance measurement in potentiostatic mode at 0.4V DC with a
frequency range 1.105 – 0.01 Hz and 10 mV amplitude AC. Do one measurement with
one unknown resistance and don´t touch the variable resistor.
Figure 6: Scheme of the circuit with NaCl aqueous solution
On Nova software, you could define your equivalent circuit, considering NaCl like a ladder
circuit with one non ideal capacitor, defined as constant phase element in impedance
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
spectroscopy and one resistor and your 0,47µF capacitor with the resistor (see scheme figure
7). Fit your curve after the definition of the equivalent circuit. Is it a really nice fitting?
Figure 7: Equivalent circuit for the system with NaCl solution
7. Make one impedance measurement with the same parameters only for the variable resistor
and compare the value of resistance found by curve fitting after definition of equivalent
circuit and the value of the impedance measurement for the variable resistor alone. Do this
again (variable resistor in electrical circuit with NaCl and only variable resistor) two time to
have more results for the comparison.
8. References and sources
1. Yuan, X., Wang, H., Colin Sun, J. & Zhang, J. AC impedance technique in PEM fuel cell diagnosis—
A review. Int. J. Hydrog. Energy 32, 4365–4380 (2007).
2. Zhuang, Q.C. ,QiuX. Y.,Diagnosisof_electrochemical impedance spectroscopy in lithium ion
batteries, www.interchopen.com
3. Harrington, D. A. & van den Driessche, P. Mechanism and equivalent circuits in electrochemical
impedance spectroscopy. Electrochimica Acta 56, 8005–8013 (2011).
4. Macdonald, D. D. Reflections on the history of electrochemical impedance spectroscopy.
Electrochimica Acta 51, 1376–1388 (2006).
5. Seo, S. H. & Lee, C. S. Impedance Characteristics of the Direct Methanol Fuel Cell under Various
Operating Conditions. Energy Fuels 22, 1204–1211 (2008).
- Barsoukov , E., Macdonald, J.R (editors), Impedance Spectroscopy , Theory, Experiment, and
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Institut für Technische Chemie und Umweltchemie (ITUC) der FSU Jena
Experiment 6
Impedance Spectroscopy
Applications, 2nd edition, Wiley, ISBN-13: 978-0471-64749-2 (2005)
- Llvovich, V.F Impedance Spectroscopy Applications to Electrochemical and Dielectric Phenomena,
Wiley, ISBN 978-0470-62778-5 (2015)
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