Electrochemical impedance spectroscopy: Applications to LixCoO2 electrodes

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Electrochemical impedance spectroscopy
Applications to LixCoO2 electrodes

• Literature
• Sundeep Kumar
• February 9, 2005

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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.

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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.

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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

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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
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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

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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.

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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

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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

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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

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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

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Goodenough and co-workers
Faradic process at electrode
Solution resistance
Non-Faradic process
At least six circuit components 3 resistors,
two capacitors and a Warburg component are
required to produce the basic form of the response
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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

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Goodenough and co-workers
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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

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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
• Both the adsorption based model were discarded on
  similar basis

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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.

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Goodenough and co-workers conclusions

• Evidences of surface layer formation on
  electrode surface

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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

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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

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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

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Aurbach and co-workers

• Simulated and experimental impedance data

At E 4.07V Li0.50CoO2
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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.

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Aurbach and co-workers conclusions
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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

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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

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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

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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.

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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.

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Scrosati and co-workers

• Insulator to metal transition can be seen from
  activation
• barriers

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Scrosati and co-workers Conclusions
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Equivalent circuits Conclusions