- Electrochemical impedance spectroscopy (EIS) measures the impedance of electrical circuits and chemical systems as a function of frequency. It provides more detailed information than DC techniques alone. - Impedance replaces resistance as a more general parameter that accounts for frequency-dependent behavior of circuit elements like capacitors and inductors. It is defined as the ratio of voltage to current. - EIS experiments involve applying a small AC potential over a range of frequencies and measuring the current response. The impedance is calculated from these measurements and plotted on Nyquist and Bode plots for analysis. - Equivalent circuit models consisting of electrical components like resistors and capacitors are used to model electrochemical systems and interpret EIS data

1. Basics of Electrochemical Impedance
Spectroscopy
Islam Mosa
11/14/2017

2. Definition of Resistance and
Impedance
• Resistance is the ability of a circuit element to resist the flow of electrical
current.
• Ohm's law defines resistance in terms of the ratio between voltage, E, and
current, I.
 While this is a well known relationship, its use is limited to only one circuit
element -- the ideal resistor.
 An ideal resistor has several simplifying properties:
• It follows Ohm's Law at all current and voltage levels.
• Its resistance value is independent of frequency.
• AC current and voltage signals though a resistor are in phase with each
other.

3. Definition of Resistance and
Impedance
• Most real applications contain more complex circuit
elements and more complex behavior.
• Impedance replaces resistance as a more general circuit
parameter.
• Impedance is a measure of the ability of a circuit to
resist the flow of electrical current
• Unlike resistance, it is not limited by the simplifying
properties mentioned earlier.

4. Direct current (Dc) vs. alternating current (Ac)
Hz = cycles/sec
Voltage
Time
Voltage
1 Cycle
• Alternating Current is when charges flow back
and forth from a source.
• Frequency is the number of cycles per second
in Hertz. In US, the Ac frequency is 50-60 Hz.
• Applies a small AC wave of changing frequency.
• The frequency dependence allows the
separation of contribution of the signal
• Is the one way flow of electrical charge from a
positive to a negative charge.
• Batteries produce direct current.
• Applies a potential that may change the
system irreversibly.
• The current collected is the sum of all events
that happens at the electrode.
• At open circuit potential: No net current flow.
• Applying DC or AC results in a shift to the system equilibrium
DC current AC current
Time

5. AC and DC
• DC techniques: We can simply apply Ohm’s law
V = i R
• AC techniques: V = i Z
We replace the resistance “R” with impedance “Z”
Impedance “Z” is much more general term as it includes all
reasons of resisting the current flow:
Resistance (R), Capacitance (C) Inductance (L)Diffusion of
reactants to the electrode surface (W).
𝑍 𝑗ѡ =
𝑉(𝑗ѡ)
𝐼(𝑗ѡ)
j = imaginary component, ѡ = frequency;

6. Phase shift in AC
p/w 2p/w
t
e
or
i
p/w 2p/w
t
e
or
i
f
Ė
İ
w
p/2
p
-p/2
0
Ė = İ R
Resistor
İ
Ė = –j XC İ
Capacitor
𝑗 = −1 XC = 1/wC
Xc is the impedance of the capacitor
w is the angular frequency = 2 π f
C is the capacitance of the capacitor
i leads or lags E
In phase Out of phase
Phase angle

7. Phase shift and impedance
-Where Et is the potential at time t, E0 is the amplitude of the signal, and ω is the radial
frequency. The relationship between radial frequency ω (expressed in radians/second)
and frequency f (expressed in hertz) is:
The excitation signal, expressed as a
function of time, has the form
The response signal, It, is shifted in phase
(Φ) and has a different amplitude than I0.
An expression analogous to Ohm's Law allows us to calculate the impedance of the
system as:
The impedance is therefore expressed in terms of a magnitude, Zo, and a phase shift,
Φ as a function of ѡ

8. Making EIS Measurements
• Apply a small sinusoidal potential (or current)
of fixed value.
• Measure the response and compute the
impedance at each frequency.
Zw = Ew/Iw
• Ew = Frequency-dependent potential
• Iw = Frequency-dependent current
• Run the test for a wide range of frequencies
• Plot and analyze

9. Summary of the concept of impedance
• The term impedance refers to the frequency
dependent resistance to current flow of a circuit
element (resistor, capacitor, inductor, etc.)
• Impedance assumes an AC current of a specific
frequency in Hertz (cycles/s).
• Impedance: Zw = Ew/Iw
• Ew = Frequency-dependent potential
• Iw = Frequency-dependent current
• Ohm’s Law: R = E/I
R = impedance at the
limit of zero frequency

10. Reasons To Run EIS
• EIS is theoretically complex – why bother?
– The information content of EIS is much higher than DC
techniques or single frequency measurements.
– EIS may be able to distinguish between two or more
electrochemical reactions taking place.
– EIS can identify diffusion-limited reactions, e.g., diffusion
through a passive film.
– EIS provides information on the capacitive behavior of the
system.
– EIS can test components within an assembled device using
the device’s own electrodes.
– EIS can provide information about the electron transfer rate
of reaction

11. Applications of EIS
• Study corrosion of metals.
• Study adsorption and desorption to electrode
surface
• Study the electrochemical synthesis of materials.
• Study the catalytic reaction kinetics.
• Label free detection sensors.
• Study the ions mobility in energy storage
devices such as batteries and supercapacitors.

12. Real and imaginary impedance
REAL
𝑍′
= 𝑅𝑠 +
𝑅𝑐𝑡
1 + ѡ2𝑅𝑐𝑡
2
𝐶𝑑𝑙
2
IMAGINARY
𝑍′′ =
𝑅𝑐𝑡
2
𝐶𝑑𝑙ѡ
1 + ѡ2𝑅𝑐𝑡
2
𝐶𝑑𝑙
2
where Z’ and Z’’ are the observed impedance due to the real and
imaginary parts, respectively, Rs is solution resistance, Rct is
charge transfer resistance, ѡ is the angular frequency and
Cdl is the double layer capacitance.

13. Nyquist Plot
ZIm
ZRe
w = 1/RctCd
Kinetic control Mass-transfer
control
ZIm
ZRe
RW RW + Rct
If system is kinetically slow,
large Rct results, and the mass
transfer become significant. If
Rct is small then the system is
kinetically facile.
w = 1/RctCd
ZIm
ZRe
RW RW + Rct
Mass-transfer
control

14. Bode plots
0
10
20
30
40
50
60
70
80
90
100
-3 -2 -1 0 1 2 3 4 5 6 7
f
log f
-
Phase
angle,
0
10
20
30
40
50
60
70
80
90
100
-3 -2 -1 0 1 2 3 4 5 6 7
f
log f
-2
-1
0
1
2
3
-3 -2 -1 0 1 2 3 4 5 6 7
log|Z|
log f

15. Bode Plot
• Individual charge
transfer processes are
resolvable.
• Frequency is explicit.
• Small impedances in
presence of large
impedances can be
identified easily.
Nyquist Plot
• Individual charge
transfer processes are
resolvable.
• Frequency is not
obvious.
• Small impedances can
be swamped by large
impedances.
Nyquist vs. Bode Plot

16. Analyzing EIS: Modeling
• Electrochemical cells can be modeled as a
network of passive electrical circuit elements.
• A network is called an “equivalent circuit”.
• The EIS response of an equivalent circuit can
be calculated and compared to the actual EIS
response of the electrochemical cell.

17. Frequency Response of Electrical
Circuit Elements
Resistor Capacitor Inductor
Z = R (Ohms) Z = -j/wC (Farads) Z = jwL (Henrys)
0° Phase Shift -90° Phase Shift 90° Phase Shift
• j = -1
• w radial frequency = 2pf radians/s, f = frequency (Hz or
cycles/s)
• A real response is in-phase (0°) with the excitation. An
imaginary response is ± 90° out-of-phase.

18. Electrochemistry as a Circuit
• Double Layer
Capacitance
• Electron
Transfer
Resistance
• Uncompensated
(electrolyte)
Resistance Randles Cell
(Simplified)

19. Other Modeling Elements
• Warburg Impedance: General impedance which
represents a resistance to mass transfer, i.e.,
diffusion control. A Warburg typically exhibits a
45° phase shift.
• Constant Phase Element: A very general
element used to model “imperfect” capacitors.
CPE’s normally exhibit a 80-89° phase shift.

20. Complex Plane (Nyquist) Plot
-2.00E+02
3.00E+02
8.00E+02
1.30E+03
1.80E+03
2.30E+03
0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03
Real (Ohm)
-Imag
(Ohm)
Rs Rs + Rct
High Freq Low Freq
Rs
Rct
CDL
Rct = RT/Fio
Io ⍺ ko
sh

21. E. P. Randviir, C. Banks, Anal. Methods, 2013, 5, 1098

22. Bode Plot
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00
Log Freq (Hz)
Log
Modulus
(Ohm)
-70.00
-60.00
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
10.00
Phase
(Degree)
Phase Angle
Impedance
Rs
Rs + Rct
Rs
Rct
CDL

23. Nyquist Plot with Fit
-2.00E+02
3.00E+02
8.00E+02
1.30E+03
1.80E+03
2.30E+03
0.00E+00 5.00E+02 1.00E+03 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03
Real (Ohm)
-Imag
(Ohm)
Results
Rct = 3.019E+03 ±
1.2E+01
Rs = 1.995E+02 ±
1.1E+00
Cdl = 9.61E-07 ± 7E-09

24. EIS Modeling
• Complex systems may require complex
models.
• Each element in the equivalent circuit should
correspond to some specific activity in the
electrochemical cell.
• It is not acceptable to simply add elements
until a good fit is obtained.
• Use the simplest model that fits the data.

25. Electrolyte Resistance
• Solution resistance is often a significant factor in the impedance of an electrochemical cell. A modern
three electrode potentiostat compensates for the solution resistance between the counter and
reference electrodes. However, any solution resistance between the reference electrode and the
working electrode must be considered when you model your cell.
• The resistance of an ionic solution depends on the ionic concentration, type of ions, temperature, and
the geometry of the area in which current is carried. In a bounded area with area, A, and length, l,
carrying a uniform current, the resistance is defined as,
• ρ is the solution resistivity. The reciprocal of ρ (κ) is more commonly used. κ is called the conductivity
of the solution and its relationship with solution resistance is:
Parameters measured by EIS
• Unfortunately, most electrochemical cells do not have uniform current distribution
through a definite electrolyte area. Therefore, calculating the solution resistance
from the solution conductivity will not be accurate. Solution resistance is often
calculated from the EIS spectra.

26. Double Layer Capacitance
• An electrical double layer exists on the interface between an electrode and its
surrounding electrolyte.
• This double layer is formed as ions from the solution adsorb onto the electrode surface.
The charged electrode is separated from the charged ions by an insulating space, often
on the order of angstroms.
• Charges separated by an insulator form a capacitor so a bare metal immersed in an
electrolyte will be have like a capacitor.
• You can estimate that there will be 20 to 60 μF of capacitance for every 1 cm2 of
electrode area though the value of the double layer capacitance depends on many
variables. Electrode potential, temperature, ionic concentrations, types of ions, oxide
layers, electrode roughness, impurity adsorption, etc. are all factors.
XC = 1/wC
XC = 1/2πfC
XC is the capacitor impedance

27. Parameters measured by EIS
Charge Transfer Resistance
Resistance in this example is formed by a single, kinetically-controlled
electrochemical reaction. In this case we do not have a mixed potential, but rather a
single reaction at equilibrium.
Consider the following reversible reaction
• This charge transfer reaction has a certain speed. The speed depends on the kind
of reaction, the temperature, the concentration of the reaction products and the
potential.
Rct =
RT
F2ko
sh C∗
o

28. Real systems: EIS
Study electrochemical behavior of catalysts for fuel cells
J. Fuel Cell Sci. Technol 11(5), 051004 (Jun 10, 2014)
What do you understand from the study of the Pd/c catalyst stability
above?
Rct increases with cycle number, catalyst losing activity

29. Catalytic activity
Oxygen evolution reaction
Mosa, I. M.; Biswas, S.; El-Sawy, A. M.; Botu, V.; Guild, C.; Song, W.; Ramprasad, R.; Rusling, J. F.; Suib, S. L., Tunable mesoporous
manganese oxide for high performance oxygen reduction and evolution reactions. Journal of Materials Chemistry A 2016, 4 (2), 620-631.
Cs-MnOx-450, Ir/C smallest Rct
Largest rate const.

30. Parameters from fitting
oxidation of ethanol
Table 2. The electrochemical active surface area (ECASA) and the fitted equivalent circuit parameters of ethanol oxidation
for the different materials in the films.[a]
Catalysts surf. area (cm2) C (μF) (Rct,), KΩ Rate constant (ko, cm s-1)
AuNCs 2nm 20.1 ± 1.5 0.335 ± 0.03 1.42 ± 0.1 0.0158
AuNCs-MPA 19.1 ± 1.9 0.318 ± 0.03 34.7 ± 3.5 0.0006
AuNCs-DT 18.5 ± 1.9 0.308 ± 0.03 35.1 ± 3.5 0.0006
Au-6nm 14.9 ± 1.2 0.248 ± 0.02 6.0 ± 0.5 0.0037
Au-10nm 12.4 ± 0.9 0.207 ± 0.01 16.2 ± 1.1 0.0014
[a] The capacitance was calculated from the fitted equivalent circuit (assuming a specific capacitance of 60 mF/cm2).
Yao, H.; Liu, B.; Mosa, I. M.; Bist, I.; He, J.; Rusling, J. F., Electrocatalytic Oxidation of Alcohols, Tripropylamine, and DNA
with Ligand-Free Gold Nanoclusters on Nitrided Carbon. ChemElectroChem 2016, 3 (12), 2100-2109.
0 5 10 15 20 25 30 35
0
-5
-10
-15
-20
-25
A
0.0 0.5 1.0 1.5 2.0
0.2
0.0
-0.2
-0.4
-0.6
-0.8
Z''(KW)
Z''(K
W
)
a
e
d
c
b
Z''(k
W
)
Z'(kW)
a

31. Electrochemical capacitors
(Ac line filter)
Miller, J. R.; Outlaw, R. A.; Holloway, B. C., Graphene double-layer capacitor with ac line-filtering performance. Science 2010,
329 (5999), 1637-9.
Near Linear Nyquist plot characteristic of capacitor – mass transport
Graphene DLC capacitor has phase angle close to -90 deg. Up to 10 KHz.

32. Electrochemical Capacitors
Linear Nyquist plot characteristic of capacitor
The LSG-EC capacitor has phase angle closte to -90
deg. Up to 10 Hz.
Maher F. El-Kady et al. Science 2012;335:1326-1330

33. EIS Take Home
• EIS is a versatile technique
– Non-destructive
– High information content
• Running EIS is easy
• EIS modeling analysis is very powerful
– Simplest working model is best
– Complex system analysis is possible.

34. References for EIS
• E. P. Randviir, C. Banks, Anal. Methods, 2013, 5, 1098
• http://www.gamry.com/application-notes/EIS/basics-of-
electrochemical-impedance-spectroscopy/
• Electrochemical Impedance and Noise, R. Cottis and S.
Turgoose, NACE International, 1999. ISBN 1-57590-093-9.
An excellent tutorial that is highly recommended..
• Electrochemical Impedance: Analysis and Interpretation, STP
1188, Edited by Scully, Silverman, and Kendig, ASTM, ISBN 0-
8031-1861-9.
26 papers covering modeling, corrosion, inhibitors, soil,
concrete, and coatings.
• EIS Primer, Gamry Instruments website, www.gamry.com