Step impedance spectroscopy: High speed GITT
Electrochemical impedance spectroscopy (EIS) is typified by sequential application of sinusoidal perturbations over a range of fixed frequencies from mHz to MHz. The time bottleneck is the low frequency measurements. A more advanced EIS excitation signal consists of multiple of sine-waves. The fast Fourier transformations (FFT) response analysis requires non-overlapping second harmonics, requiring expensive, complex signal generators. The need for complex generators is obviated by use of square wave excitation. The analysis of a current square wave is the basis for the galvanostatic intermittent titration technique (GITT). The FFT analysis is supplanted by analysis of time domain data in terms of analyst selected circuit models. GITT takes advantage of measurable boundary values associated with the start and end of the GITT excitation signal. EIS lacks this capability. GITT directly provides physically relevant model parameters from the fit of the time-domain data, such as the change of voltage with respect to state-of-charge, solid state diffusion relaxation (after the end of pulse), and more.
Consider analysis of 2 year old Panasonic (LC-R064R5P) 6V, 4.5Ah/20HR, lead acid battery by a Powerstat-05 potentiostat/galvanostat. Figure 1 shows the voltage response (black line) to a current square wave (red line) applied to the battery. The amplitude (ip) was 0.5 A (red line) with a pulse width (tpw) 0.5 seconds. The precipitous drop in voltage (ΔV1) corresponds to the Randles cell series resistance. This information is equivalent to that obtained with the high frequency intercept of a Nyquist plot . The ΔEeq is due to the change in the state-of-charge occurring during the pulse duration (tpw). Such information is not accessible through EIS. If tpw is short, E(t) is approximately linear with respect to the state-of-charge. This simplifies fitting of the decay during tpw for double layer capacitance and charge transfer resistance. In the case of a simple Randles cell, the tpw decay has an RC time constant related to double layer capacitance and charge transfer resistance. When the pulse signal reverts to zero current during the post pulse relaxation period (trp), there is no further change in the state-of-charge. A battery equivalent circuit (Reference 3) is shown (Fig. 1). The remainder of this treatment shows how the differential equation for the circuit is solved and used in the NuVant EZware software to deliver parameters specific to the circuit model. Screen shots of EZware demonstrate how circuit elements are easily obtained using any NuVant potentiostat/galvanostat for battery testing.
It is noteworthy, that end users must select a reasonable value for the trp. If trp is too short, ΔEeq will be overestimated. For the lead acid battery of this study, the relaxation time is on the order of a second. For a deep current pulse with a lithium ion battery, the relaxation time could be greater than days. Diffusion coefficients in liquid phase are on the order of 10-6 cm2s-1. Solid state diffusion coefficients are 4 – 5 orders of magnitude smaller: The relaxation time for Li to redistribute in solid state cathodes is substantial longer than the relaxation time required for macroscopic lead acid battery electrodes to relax. Thus much can be learned from a simple but powerful SIS analysis. The ΔV3 current transient provides information concerning diffusional processes in electrochemical devices in addition to double layer capacitance. NuVant provides additional equivalent circuit solutions addressing corrosion, fuel cells, batteries and more in the EZware software. SIS is an affordable and powerful alternative to EIS for equivalent circuit analysis.The data for the entire analysis below was acquired in less than a second. Our instruments can be multiplexed such that thousands of batteries can be tested by a single instrument in one day.
|Glossary Abbreviations for GITT|
|t0||Beginning of the pretreatment period|
|tp,i||Pulse initiation time|
|tp,f||Pulse final time|
|tr,f||End of relaxation time|
|tpw = tpf – tpi||Pulse width|
|trp = trf – tpf||Relaxation period|
|E(t) = Eeq1||For ( tp,i – tinterv ≤ t ≤ tp,i )|
|Eeop = E(tp,f)||Potential at end of pulse|
|τ||RC time constant specific to differential equation|
|tinterv||Sampling interval time|
|Battery Equivalent Circuit|
|Figure 2. Equivalent circuit for lead acid battery analysis|
|The differential equation applicable to the circuit is below:|
|Current pulse solution to the differential equation:|
|When I=ip (tpi ≤ t ≤ tpf)|
|When I= O (tpf ≤ t ≤ trf)|
|Where and tpw=tpf – tpi
Zcp(t) and E(t) vary linearly with t when tpw is short (i.e., E(t) contributes a linear component to ΔV2). EZware uses Eeq1 and Eeq2 to calculate ΔEeq. ΔV1 = f(Rs, ip) ΔV2 = f(Rct, E(t), Cdl) ΔV3 = f(Rct , Cdl)
GITT or Step Impedance Spectroscopy References
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