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## Impedance Spectroscopy

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### Impedance Spectroscopy (Or, how a sinusoidally varying voltage is used ... Constant phase element (a fudge factor) Virtual inductor (adsorption?) And... l. A ... – PowerPoint PPT presentation

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Title: Impedance Spectroscopy

1
Impedance Spectroscopy
(Or, how a sinusoidally varying voltage is
usedto probe multiple electrical properties of
materials)
Yun-Ju (Alex) Lee June 13, 2002
2
Introduction
• IS measures the resistance of a circuit to an
applied voltage
• Z(t) E(t)/I(t), Z(?)E(?)/I(?)
• When E is applied as a sinusoidal function in a
linear system, I response can be represented by a
sum of sinusoidal fuctions with phase shifts.
• If an equivalent circuit for the system being
probed can be constructed, then the resistance or
capacitance values for each circuit element can
be backed out from Z.

Especially in electrochemical impendance
spectroscopy (EIS), the the voltage probe signal
is small (1-10mV) so the current response is
pseudolinear (side benefit it doesnt perturb
the sample very much)
A Bard and L Faulkner, Electrochemical Methods
Fundamentals and Applications (2000) http//www.ga
mry.com/G2/Appnotes/Reference/eistheory/theory/EIS
_Theory.htm
3
Background Impedance and Circuit Elements
• E(t) E0cos(?t), ?2?f
• I(t) I0 cos(?t-?)
• Or, if one writes in complex notation
• E(t) E0 exp(i?t)
• I(t) I0 exp(i?t - i?)
• Z(t) Z0 exp(i?) Z0 (cos ? isin ?)

E/I response for a resistor (?0)
E/I response for a capacitor (?-90)
E/I response for an inductor (?90)
http//www.gamry.com/G2/Appnotes/Reference/eistheo
ry/theory/EIS_Theory.htm http//www.bath.ac.uk/ch
sacf/solartron/circp/html/acrci.htm
4
R

-j Xc
j Xl
For more complex circuits, use Kirchoffs rules
http//www.bath.ac.uk/chsacf/solartron/circp/html
/acrci.htm
5
Plotting Impedance
•

? 1/? 1/RC
A Cole-Cole (or Nyquist) plot of the real and
imaginary components of Zfor a circuit
containing a capacitor and resistor in parallel
(real worldexample a charged layer at an
interface).
Named after KS Cole and RH Cole, J Chem Phys 9,
341 (1941)
6
Plotting Impedance
A Bode plot of a circuit containing a capacitor
and resistor in parallel. log Z and ? vs. log ?
are plotted, showing explicitly the impact of
?impedance.
http//www.gamry.com/G2/Appnotes/Reference/eistheo
ry/theory/EIS_Theory.htm
7
Circuit Elements from Electrochemistry
• Electrolyte resistance
• Double layer capacitance (30?F/cm2 for aqueous
systems)
• Polarization resistance
• Charge transfer resistance
• Coating capacitance
• Constant phase element (a fudge factor)
• And

l
A
R l / ?A
WE, RE, CE
http//www.gamry.com/G2/Appnotes/Reference/eistheo
ry/theory/EIS_Theory.htm
8
Diffusion (aka Warburg Impedance)
• Warburg impedance diffusion of chemical species
to a large planar electrode

Infinite diffusion layer thickness
Diffusion layer thickness ?
Also, in the Warburg region, ? 45º
http//www.consultrsr.com/resources/eis/diffusion.
htm
9
Equivalent Circuit Model for Electrochemical Cells

Mixed Kinetic Diffusion model
Bode plot
Cole-Cole plot
http//www.gamry.com/G2/Appnotes/Reference/eistheo
ry/theory/EIS_Theory.htm
10
Some Applications of IS
• Determine corrosion rates of materials
• Measure capacitance and resistance of SAMs to
ascertain thickness and packing quality
• Probe linearity of electrical/electrochemical
reactions
• Characterize electrical activity across
interfaces to determine carrier concentration,
etc.
• Determine diffusion rate of counter ions in
conducting polymer/carbon nanotube composites

ASL Castela et al., Prog Org Coat 38, 1-7