Electrochemical Impedance Spectroscopy Beyond Linearity and Stationarity
Authors: Hallemans Noël , Howey David , Battistel Alberto , La Mantia Fabio , Widanalage Dhammika , Hubin Annick , Lataire John 
Published: August 2024

Electrochemical impedance spectroscopy (EIS) is a widely used experimental technique for characterising materials and electrochemical devices. By measuring the impedance at selected frequencies, one can distinguish between electrochemical processes happening at different time-scales (such as diffusion and charge transfer).
Classical EIS measurements [1,2] require the electrochemical processes under investigation to behave as a linear time-invariant (LTI) system. However, electrochemical processes do not naturally satisfy this requirement: their dynamics are inherently nonlinear, and evolve depending on several parameters. For lithium-ion batteries, the dynamics change with temperature, state-of-charge, and state-of-health [3]. Due to the time-invariance constraint of EIS, the technique can only reveal information about electrochemical processes at operating points, that is, at fixed temperature and state-of-charge, while in steady-state. Moreover, due to the linearity constraint, EIS can only reveal information on linear dynamics about these operating points. Hence, classical EIS cannot be used to characterise electrochemical processes in operating conditions such as charge and discharge, or relaxation. These are severe limitations!
In this contribution, we demonstrate how to measure impedance data beyond the limiting constraints of linearity and stationarity [4]. As a case-study, we measure the impedance of commercial lithium-ion batteries during charge and discharge using a recently-developed operando EIS technique [5,6] (leveraging the use of the frequency domain and multisine excitations). The measurements show that impedance data during operation is different from ‘classical’ impedance data (at rest). More specifically, the charge transfer resistance is shown to decrease during operation, which can be explained via physics-based battery models. This showcases that operando EIS is a promising experimental tool enabling the characterisation of electrochemical processes during operation (which is not possible with classical EIS). Examples of applications where operando EIS is promising include monitoring fast-charging [7] and parametrising physics-based models.
[1] Orazem, M.E. and Tribollet, B., 2008. Electrochemical impedance spectroscopy. Wiley.
[2] Wang, S., Zhang, J., Gharbi, O., Vivier, V., Gao, M. and Orazem, M.E., 2021. Electrochemical impedance spectroscopy. Nature Reviews Methods Primers, 1(1), p.41.
[3] Doyle, M., Fuller, T.F. and Newman, J., 1993. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6), p.1526.
[4] Hallemans, N., Howey, D., Battistel, A., Saniee, N.F., Scarpioni, F., Wouters, B., La Mantia, F., Hubin, A., Widanage, W.D. and Lataire, J., 2023. Electrochemical impedance spectroscopy beyond linearity and stationarity—A critical review. Electrochimica Acta, p.142939.
[5] Hallemans, N., Pintelon, R., Van Gheem, E., Collet, T., Claessens, R., Wouters, B., Ramharter, K., Hubin, A. and Lataire, J., 2021. Best linear time-varying approximation of a general class of nonlinear time-varying systems. IEEE Transactions on Instrumentation and Measurement, 70, pp.1-14.
[6] Hallemans, N., Widanage, W.D., Zhu, X., Moharana, S., Rashid, M., Hubin, A. and Lataire, J., 2022. Operando electrochemical impedance spectroscopy and its application to commercial Li-ion batteries. Journal of Power Sources, 547, p.232005.
[7] Zhu, X., Hallemans, N., Wouters, B., Claessens, R., Lataire, J. and Hubin, A., 2022. Operando odd random phase electrochemical impedance spectroscopy as a promising tool for monitoring lithium-ion batteries during fast charging. Journal of Power Sources, 544, p.231852.

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