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## Electrochemical impedance spectroscopy: Applications to LixCoO2 electrodes

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### Ohm's law defines resistance in terms of the ratio between voltage E and current ... Steep sloping line at lowest frequencies accumulation of intercalant (Li) into ... – PowerPoint PPT presentation

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Title: Electrochemical impedance spectroscopy: Applications to LixCoO2 electrodes

1
Electrochemical impedance spectroscopy
Applications to LixCoO2 electrodes
• Literature
• Sundeep Kumar
• February 9, 2005

2
Impedance definition Concept of complex impedance
• Concept of electrical resistance It 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.
• R E / I
• it's use is limited to only one circuit element
-- the ideal resistor.
• An ideal resistor
• It follows Ohm's Law at all current and voltage
levels.
• It's resistance value is independent of
frequency.
• AC current and voltage signals though a resistor
are in phase with each other.
• Like resistance, impedance is a measure of the
ability of a circuit to resist the flow of
electrical current. Unlike resistance, impedance
is not limited by the simplifying properties
listed above.
• Electrochemical impedance is usually measured by
applying an AC potential to an electrochemical
cell and measuring the current through the cell.
Assume that we apply a sinusoidal potential
excitation. The response to this potential is an
AC current signal.

3
Measurement of impedance
• The excitation signal, expressed as a function of
time, has the form
• Et E0 sin(? t)
• Et is the potential at time t, E0 is the
amplitude of the signal, and ? is the radial
frequency.
• The response signal, It, is shifted in phase (f)
and has a different amplitude, I0.
• It I0 sin (? t f)
• 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, f.

4
Data Presentation
• The expression for Z(?) is composed of a real and
an imaginary part. If the real part is plotted on
the Z axis and the imaginary part on the Y axis
of a chart, we get a "Nyquist plot".
• The y-axis is negative and that each point on the
Nyquist plot is the impedance at one frequency.
• On the Nyquist plot the impedance can be
represented as an vector (arrow) of length Z.
The angle between this vector and the x-axis is
f.
• The semicircle is characteristic of a single time
constant corresponding to a physical process in
the system
• Impedance spectroscopy is used to extract the
information on these physical processes

5
Electrical Circuit Elements
• The impedance of a resistor is independent of
frequency and has no imaginary component. Current
stays in phase with the voltage across the
resistor.
• A capacitor's impedance decreases as the
frequency is raised. Capacitors also have only an
imaginary impedance component.

Z R
Z 1/j?C
6
Physical Electrochemistry and Equivalent Circuit
Elements
• Electrolyte resistance and resistance from
current collectors
• Double layer capacitance
• A electrical double layer exists on the interface
between an electrode and its surrounding
electrolyte. This double layer is formed as ions
from the solution "stick on" the electrode
surface. Charges in the electrode are separated
from ions charges.
• Charge transfer resistance
• Charge transfer resistance corresponds to
interfacial charge transfer of Li ion (related
to ionic motion) and electronic conductivity of
the electrode

7
Physical Electrochemistry and Equivalent Circuit
Elements
• Diffusion
• Diffusion also can create an impedance called the
Warburg-impedance. At high frequencies the
Warburg impedance is small since diffusing
reactants don't have to move very far. At low
frequencies the reactants have to diffuse
farther, increasing the Warburg-impedance.
• Constant Phase Element
• Capacitors in EIS experiments often do not behave
ideally. Instead they act like a constant phase
element as defined below.
• The impedance of a capacitor can be expressed
as
• where, A 1/C The inverse of the capacitance a
An exponent which equals 1 for a capacitor
• For a constant phase element, the exponent a is
less than one. The "double layer capacitor" on
real cells often behaves like a CPE, not a
capacitor.

8
Example Simulation of impedance data from known
equivalent circuit
• The parameters in this plot were calculated
assuming a 1 cm2 electrode undergoing uniform
corrosion at a rate of 1 mm/year.
• RP 250 ?, Cdl 40 µF/cm2 and Rs20 ? were
assumed to simulate the impedance plot
• One can simulate the impedance data if one knows
the equivalent circuit before hand
• OR
• One can fit the experimental impedance data to an
equivalent circuit

9
EIS on LiCoO2 electrodes
• Goodenough and co-workers _at_ Oxford University,
England
• Aurbach and co-workers _at_Bar-Ilan university,
Isreal
• Scrosati and co-workers _at_ Universita di Roma,
Italy
• M.G.S.R. Thomas, P.G. Bruce and J.B. Goodenough,
J. Electrochem. Soc., 132 (1985) 1521
• D. Aurbach et al., J. Electrochem. Soc., 145
(1998) 3024
• M.D. Levi et al., J. Electrochem. Soc., 146
(1999) 1279
• F. Nobil et al., J. Phys. Chem. B., 106 (2002)
3909

10
Goodenough and co-workers
• AC Impedance Analysis of Polycrystalline
Insertion Electrodes Application to Li1-xCoO2
M.G.S.R. Thomas, P.G. Bruce and J.B. Goodenough,
J. Electrochem. Soc. 132 (1985) 1521 - 1528
• In this paper, an equivalent circuit model is
presented for interpreting the A.C. impedance of
a pressed-powder insertion-compound electrode
(Li1-xCoO2) in contact with a liquid electrolyte

11
Goodenough and co-workers
• LiLiBF4 (in PC)LiCoO2
• Galavanostatically charged up to Li0.65CoO2
• Impedance measurements at 10mV-rms AC
perturbation sweeping the frequency range 10kHz
to 0.1 mHz.
• Assumption The electronic conductivity of the
insertion compound is high and that each particle
is in contact with the aggregate across a
solid-solid interface making an ohmic contact of
low resistance to electron flow

12
Goodenough and co-workers
Solution resistance
At least six circuit components 3 resistors,
two capacitors and a Warburg component are
required to produce the basic form of the response
13
Goodenough and co-workers
• Two processes
• Adsorption of Li ions or PC onto the surface of
the electrode without charge transfer
• And formation of an ionically conducting but
electronically insulating surface layer at the
electrode surface

14
Goodenough and co-workers
15
Goodenough and co-workers
• Three separate types of experiments
• The time dependence of the AC impedance response
• The influence of premixing of the electrolyte
with the cathode material
• The variation of circuit parameters with applied
voltage

16
Goodenough and co-workers
• Initially a CdlgtCads is found, this is physically
unreasonable situation
• And it is most improbable that adsorption should
cause Cdl to decrease with time, rather
increasing electrolyte penetration with time
should increase Cdl
similar basis

17
Goodenough and co-workers
• According to SL model
• Rsl ?(L/A)
• CSL ?(A/L)
• Hence RSL should increase and CSL should decrease
with time
• Therefore, a SL model contains equivalent circuit
parameters that vary in self-consistent manner
with the electrochemical processes they represent
as the cell conditions are varied.

18
Goodenough and co-workers conclusions
• Evidences of surface layer formation on
electrode surface

19
Aurbach and co-workers
• Solid-State Electrochemical Kinetics of Li-Ion
Intercalation into Li1-xCoO2 Simultaneous
application of Electroanalytical Techniques SSCV,
PITT and EIS M.D. Levi et al., J. Electrochem.
Soc., 146 (1999) 1279.
• Li1M LiAsF6 in ECDMC(13) LiCoO2 (with carbon
and binder)
• The analysis of impedance spectra in terms of
equivalent circuit
• Impedance measurements were taken during charging

20
Aurbach and co-workers
• Low solution resistance (25 ohms compared to
60 ohms observed by Goodenough et al.
• Semicircles are more resolved than reported by
Goodenough and coworkers
• Medium frequency semicircle becomes smaller on
increasing the voltage

21
Aurbach and co-workers
• High-frequency semicircle surface layer related
• Medium-frequency semicircle Charge transfer
resistance related to slow Li ion interfacial
transfer, coupled with a capacitance at the
surface film/Li1-xCoO2 particle interface
• At low frequency, a narrow Warburg region
solid-state diffusion of Li ions into the bulk
cathode material
• Steep sloping line at lowest frequencies
accumulation of intercalant (Li) into the bulk

22
Aurbach and co-workers
• Simulated and experimental impedance data

At E 4.07V Li0.50CoO2
23
Aurbach and co-workers
• There is some correlation between decrease in Rct
and increase in the LixCoO2 electrical
conductivity with potential in this range.
• However, Rct for such an electrode does not
reflect only the electronic conductivity of the
particles, but also interfacial charge transfer
that relates to ionic transport.

24
Aurbach and co-workers conclusions
25
Scrosati and co-workers
• An AC Impedance Spectroscopic Study of LixCoO2
at Different Temperatures F. Nobili et al., J.
Phys. Chem. B., 106 (2002) 3909.
• The paper presents an EIS of LiCoO2 electrodes at
various temperatures (0-30 C) (Temperature
dependence)
• Li1M LiClO4 (ECDMC- 11)LiCoO2 (Composite
cathode with bonder and carbon)
• 10mV perturbation and frequency sweep of 100kHz
to 1mHz

26
Scrosati and co-workers
• At any potential, a not well defined semicircle
is present at high frequency limit
• As potential increases, another semicircle
develops at medium frequency
• And at lowest frequency limit, Warburg branch
appears

27
Scrosati and co-workers
• The ill-defined semicircle present at 24C in
both graphs splits progressively into two
distinct semicircles that become fully developed
at the lowest temperature

28
Scrosati and co-workers
• A high frequency dispersion (gt1kHz) because of
presence of passivating layer
• An intermediate frequency dispersion (between
10Hz and 1kHz) because of charge transfer
• A low-frequency semicircle associated with the
electronic properties of the material
• Very low frequency spike of the ionic diffusion
• The drop of the resistance associated with the
low frequency semicircle occurs over the narrow
x-range that corresponds to the insulator to
metal transition
• The growth of the additional semicircle in the
middle frequency range becomes noticeable in
correspondence of potential values at which the
intercalation process takes place at an
appreciable rate.

29
Scrosati and co-workers
CPE
• Both the circuits give same impedance plots and
they both are equivalent
• However, the (b) is more close to the physics of
the processes.

30
Scrosati and co-workers
• Insulator to metal transition can be seen from
activation
• barriers

31
Scrosati and co-workers Conclusions
32
Equivalent circuits Conclusions