IMPEDANCE SPECTROSCOPY

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IMPEDANCE SPECTROSCOPY
By Dr. Mehran Javanbakht
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Fundamentals of Electrochemical Impedance
Spectroscopy
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• I. Introduction physics electrotechnics
• Definition properties of impedance
• Simple RC circuits and their spectra
• Measurement principles and graphical analyses

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How to characterize a two-pole (an electrical
system)?
Case A a steady state current-voltage curve,
I(U), exists at any moment.
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How to characterize a two-pole (an electrical
system)?
Case B the current-voltage curve, I(U) depends
also on time, t
The system can be characterizedthrough the
time-dependence of the current I(t) U(t)
relations are analyzed.
Possibilities transient response (following a
jump or pulse) ac methods, frequency response
(sinusoidal perturbation)
Passive, linear electrical two-poles
I(kU)kI(U)) are considered.
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Operational definition of impedance Stimulus
U(t) Uac sin(?t) Response I(t) Iac sin(?t f)
Impedance is defined as Z ? (Uac/Iac and f)
(Since I(kU)kI(U)), the Uac/Iac is not
dependent on Uac.)
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• Impedance (at one frequency)
• is defined as Z ? (Uac/Iac and f), complex
  number
• Z ? Uac/Iac eif Zabs cos (f) i Zabs sin(f)
  Eulers formula with Zabs ?Uac/Iac and i ??-1

• admittance Y?1/Z (Yabs1/Zabs and fY -fZ)
• immittance common term for impedance and
  admittance

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• Impedance (as function of frequency, (?2pf ))
• it is called a spectrum (typically 10-3/s ltwlt
  107/s?)
• representations
• reif ? r(cos(f)isin(f)) Re
  iIm Nyquist Im(Z) vs Re(Z)
• ln(reif) ? ln(r)if
• Bode lg(Zabs) vs lg(f ) and f
  vs lg(f )

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Impedance of a network of RCL elements can be
calculated just in the same way as the resistance
of a network of resistors.

• Impedance
• of serially connected elements Zs
  Z1Z2 1/Ys 1/Y11/Y2
• of parallely connected elements Yp
  Y1Y2 1/Zp 1/Z11/Z2

• Impedance
• of a resistor ZR ? R
• of a capacitor ZC ? 1/(iwC)
• of an inductor ZL ? iwL

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• I. Introduction physics electrotechnics
• Definition properties of impedance
• Simple RC circuits and their spectra
• Measurement principles and graphical analyses

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How do the spectra look like? Examples of simple
circuits
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Resistance
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Capacitance
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Rs-Cs
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CpRp
Semicircle Characteristic frequency
?01/RpCp Time constant t01/?0
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Symmetries
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Rs-CpRp
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(Rs-Cs)Rp
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Circuits of different topologies may have the
same impedance function. There is no unique
connection of circuit and spectrum.
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RpCp sequences yield semicircle sequences they
are merged if the RC time constants are close to
each other.
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• I. Introduction physics electrotechnics
• Definition properties of impedance
• Simple RC circuits and their spectra
• Measurement principles and graphical analyses

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Simplest way using sine-wave voltages
FRA, lock-in amplifier
ac voltage source sine-wave generator
Umeas U(t) Uac sin(?t) Imeas I(t) Iac
sin(?t f)
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Typical measurement setups
for resistive systems for capacitive
systems (dielectric spectroscopy)
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Simple way of analysis plotting and determining
characteristic values
Cp1/(?0Rp)
Rs
Rs Rp
Use various representations.
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Nyquist vs Bode representations
ln(reif) ? ln(r)if

• Advantages (both are good)
• Nyquist structures are better seen
• Bode complete documentation of the data

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Simplest way using sine-wave voltages
FRA, lock-in amplifier
ac voltage source sine-wave generator
Umeas U(t) Uac sin(?t) Imeas I(t) Iac
sin(?t f)
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Turnkey EIS systems are available for 15-60 k.
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Mechanistic studies and identification of
processes

• Goal Identification of the appropriate model
• (equivalent circuit AND the underlying
  physico-chemical processes)
• Measure Z(?) as function of E, ci, T, etc
• Repeat
• Construct model with reasonable assumptions
  calculate its impedance function (perhaps
  expressed as an equivalent circuit, also as
  function of E, ci, T, etc)
• Estimate the models parameters (e.g. by NLLS
  fitting)
• Until
• a. the measured and calculated Z(?) spectra are
  similar to each other
• b. the E, ci, T, etc dependencies are correct
  (not self-contradictory).

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Determination of values of parameters (when the
model is already established)
Cp Interfacial capacitance Structure of the
interface (double layer, adsorption)
Bulk - interface
Rs Bulk conductivities General characterization
Dielectric spectroscopy
Rp Charge transfer resistance Electrochemical
kinetics Corrosion
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Measurement modes Multiple frequency mode
impedance spectrum measurement (at constant
Edc) followed by the determination of the
parameters

• Single frequency mode with scanned Edc
  examples
• ac voltammetry (for characterization of charge
  transfer)
• capacitance measurements with (high) f and with
  (slowly) scanned Edc requires the a priori
  knowledge of the equivalent circuit

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Bulk resistance

• Resistance is determined through impedance
  spectrum measurements if
• a single resistance cannot be measured (only a
  networks impedance)
• typically high resistance materials which are
  difficult to be contacted
• jointly with the determination of permittivity
• polymer membranes, ionic conductors, porous
  structures.

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Time evolution of the impedance spectra of a
physically drying styrene-acrylate self-standing
resin film in 0.1M KNO3 solution (100 kHz - 1
Hz), Lendvay-Gyorik et al, 2007.
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Interfacial capacitance
1. Calculation of adsorbate coverages
thus

• 2. Determination of zero points (of space
  charge layers)
• Metal / solution of a binary electrolyte of low
  concentrationHg (Au, Ag) in 1-100 mM NaF
  solution (two mobile charge carriers)
• II Metal / extrinsic semiconductor junction n
  or p doped semiconductor metallized or a
  semiconductor electrode in aqueous solution (one
  fixed and one mobile charge carrier)

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Interfacial capacitance Determination of zero
points (of space charge layers)
Model The distribution of the mobile charges
(ions or electrons or holes) is determined by the
electrostatic potential and the thermal
motion Poisson - Boltzmann equation
Expressed quantity space charge layer
capacitance vs potential.
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Determination of zero points, A Metal /
solution of a binary electrolyte of low
concentration (two mobile charge carriers)
Capacitance has a minimum at the pzc (potential
of zero charge - at which the ion accumulation
nearby the metal, in the solution vanishes).
Gouy-Chapman minimum, Hg in NaF solution,
Grahame (1947)
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Determination of zero points, B Metal (or
electrolyte) / extrinsic semiconductor junction
(one fixed and one mobile charge carrier)
Mott-Schottky plot (ZnO, Freund Morrison, 1989)
1/C2 vs E determination of n0 and Efb (flatband
potential at which the space charge layer in
the semiconductor vanishes)
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Parallel resistance

• Parallel resistance interpreted as a charge
  transfer resistance
• exchange current density is calculated (
  kinetics information)
• typical use average corrosion rate is
  calculated
• for details, see many application notes

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Determination of Rp - corrosion tests
Fe in H2SO4 (5..100mM) at corrosion potential
(Lendvay-Gyorik et al, 2000)
TiCxNy film (on steel) in Na2SO4 (0.5M) at
function of time (Senna et al, 2000)
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Determination of Rp - corrosion tests, inhibitor
studies
Fe in 1M HCl with and without 1 mM oct-1-yn-3-ol
(octynol, inhibitor), at corrosion potential
(Lendvay-Gyorik et al, 2003)
c
b
a
a without 1-octynol b with 1 mM 1-octynol c
with 1 mM 1-octynol, after an anodic treatment
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• Coating tests
• An ideal polymer, insulating coating is
  capacitive.
• Corrosion transport through the pores causes
  a shunt term - CR.

EIS response of a pipeline coating in 5 NaCl at
65C, L. Gray et al (2003) in D. Loveday et al,
JCT CoatingsTech, 2005
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Technical issues
 
1. EIS can be used for characterizing stable
systems only. A good practice for testing
stability is to repeat the measurements (e.g.
with decreasing then increasing frequencies).
Kramers-Kronig test may help.
2. Decrease noise. Use Faraday-cage. Use the
preamplifier supplied with the potentiostat.
Connect an oscilloscope to the E output of the
potentiostat to monitor noise level.
3. TroubleshootingCheck the system by
measuring the impedance spectra of resistors and
dummy cells of similar characteristics to the
systems studied.
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4. Cells for high frequency (gt1..10 kHz)
impedance measurements
 
a. Low impedance reference electrode should be
usedb. Avoid cells of low feedback
ratio c. Ensure uniform current density
distribution
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Traditional, clean cells may have bad hf
behaviour
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a. Low impedance reference electrode
 
Avoid high resistance solution paths between
cell and reference electrode.
To shunt the high resistance paths, use a
capacitively coupled auxiliary reference
electrode (C1-10µF)
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b. Low feedback ratio
 
Do not place the counter electrode far away
from the W and R
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c. Uniform current density distribution
From www.mpmtechnologies.com, MPM Technologies,
Inc., State College, PA, USA
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5. Calibrationwith dummy cells having Z(?)
similar to the system studied with two
resistors (approx. Rsol,1 and Rsol,2) for the hf
accuracy.
 
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Fitting of impedance spectrum a demo
measurement Ir(100) in 0.1M HCl, 0.1V vs SCE,
model
?,? measured, x, calculated absolute values and
phase angles
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Always plot the measured and fitted curves
together in various representations (Bode is the
best for this)
Calculate plot the difference of the
measured and fitted points try to get rid of
the systematic deviations
Inspect errors of parameters
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How to present data?
1. Raw data measured impedance spectra Nyquist
(reif ? r(cos(f)isin(f)) Re iIm)
Im(Z) vs Re(Z), structures are better
seen Scale of Im(Z) and Re(Z) must be identical
Bode (ln(reif) ? ln(r)if) lg(Z) vs
lg(f ) and f vs lg(f ), for documentation of the
data Other representations like log(Im(Z)) vs
log(Re(Z)) avoid
2. Processed impedance data (with or without
fitting) a. Normalize to unit area (Ohmcm2)b.
Subtract series (solution) resistance ?
interfacial Zic. Zi ? interfacial admittance,
Yi(?) ? interfacial capacitance, Ci(?) Ci (?) ?
Yi(?) /i ?1/ i ?(Z(?)-Z(???)) is also a
complex function ? Bode, Nyquistd. Plot together
fitted and measured spectra

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VIII. Summary and closing
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What should impedance spectroscopy be used for?

• Impedance perturbation method to study
• kinetics (of transport in bulk and of charge
  transfer across the interface dk/dE)
• interfacial structures (through differential
  capacitance of the double layer dqM/dE)

Use EIS if the mechanism of the processes are
known then numbers (rate coefficients,
interfacial charges, diffusion coefficients)
can be obtained (determination of corrosion
rates) else for testing reaction kinetics
hypotheses endif
END.