In electrochemical impedance spectroscopy (EIS), the cell is held at equilibrium at a fixed dc potential and a small amplitude ac signal (5-10 mV) is superimposed on it [12,16,17]. The response of the system to this perturbation from equilibrium is measured in terms of the amplitude and phase of the resultant current, which in turn is a measure of the overall impedance of the cell. The frequency of the ac signal is varied to study the impedance variation of the cell as a function of frequency. The impedance can be represented as a vector diagram displaying the in- phase (real, Z´) and out of phase (imaginary, Z") impedances, total impedance and the phase angle. Such plots that display the imaginary vs the real impedance at each frequency are called Nyquist plots. EIS is a non-destructive and powerful technique for the evaluation of wide range of materials, including corrosion inhibitors, batteries and fuel cells. EIS can provide detailed kinetic and mechanistic information and can be used to monitor changes in battery properties under different usage and storage conditions such as:
1 Analysis of state of charge 1 Study of reaction mechanisms
1 Change of active surface during operation 1 Separator evaluation
1 Passivating film behaviour
1 Separation and composition of electrode kinetics on each electrode 1 Identification of possible electrode corrosion process
1 Investigation of the kinetics at each electrode
The total impedance is determined by the impedances of the various components of the cell, e.g., electron transfer kinetics, diffusion, passivating layers, charge transfer impedance, bulk impedance etc. The relative contributions of the various components vary with frequency. The electron transfer kinetics dominates at high and intermediate frequency range(1 MHz-1 kHz) whereas diffusion dominates in the low frequency range (1kHz-3 mHz). Hence, measurements over wide frequency range facilitate to distinguish between such time-dependent contributions to the over all impedance.
Quantitative data may be obtained from EIS by modeling the aforementioned time-dependent components of the impedance with the physical and mathematical components, viz., using a combination of resistors and capacitors in series or parallel fashion such that each equivalent circuit element corresponds to a component of the electrochemical cell and thus the model simulates the experimental impedance spectrum. For example, a resistor may be used for solution resistance and a parallel combination of resistor and a capacitor for the charge transfer at the electrode- electrolyte interface. A number of circuit elements and their corresponding values of impedance are presented in Table 2.1.
Table 2.1 Common circuit elements used in EIS models.
Circuit element Impedance
R (resistance) R
C (capacitance) 1/j$C (j=%-1, $=angular frequency)
L (inductance) j$L
W (infinite Warburg) (Diffusion impedance) Y/2(j$), Y=Diffusion resistance
CPE (constant phase element) 1/(j$C),, C=ideal capacitance and ,=empirical constant, 0<,<1; when ,=1, CPE acts as ideal capacitor
A simple model (Fig. 2.5a) built from these circuit elements is the Randles circuit comprising R and C combination includes solution resistance Ro, a charge transfer resistance Rct (associated double layer capacitance Cdl) and Diffusion or Warburg impedance, Zw. The corresponding Nyquist plot (Fig. 2.5 b) comprises a single frequency-dependent semicircle (representing charge-transfer impedance) followed by two straight lines in the low frequency region, representing solid-state diffusion of ions, with slopes, 45" and 90" with the Z &-axis.
Cdl
(a) (b)
Fig. 2.5 (a) Equivalent circuit using R and C combination with (b) Nyquist plot for the same.
Rct Zw
Cdl
Ro
The Nyquist plots for real electrochemical cells are more complex and need more circuit elements for proper modeling [16,17]. The EIS experiments in the present work were performed on coin-cells using the Solartron Impedance/Gain-Phase Analyzer (SI 1260) coupled with a Battery Test Unit (1470). An ac signal with amplitude of 5 mV was used to measure the impedance response over the frequency range varying from 0.35 MHz to 2 mHz. Data acquisition and analysis were carried out using the electrochemical impedance software, ZPlot and Zview (Version 2.2, Scribner Associates Inc., USA).
2.11.3.1 Determination of diffusion coefficient of ions from EIS
In a Nyquist plot, the low frequency straight line (Warburg-type region) represents the solid-state diffusion of ions in the electrode and can be used for determination of diffusion coefficient of ions (Di(EIS)) [18]. Following expression is used for the determination of Di(EIS).
2 dx dE FAA
V 2 (EIS) 1 D
W m
i 33
4 5 66
7
8 99:
<< ;
=
0 > (2.5)
where, Vm is the molar volume, F is the Faraday constant, A is the electrode area, AW
is the Warburg coefficient obtainable from the Warburg region of the Nyquist plots.
The dE/dx, change in the voltage due to a change in the Li-content x, in the active material, is determined from the galvanostatic intermittent titration technique (GITT).