Recent Trends in the Mathematical Modelling of Electrochemical Impedance Spectroscopy of Lithium-Ion Batteries

Electrochemical Impedance Spectroscopy (EIS) has emerged as a great alternative tool to characterize electrochemical energy storage systems such as batteries1, 2. A commercial Li-ion battery is essentially an electrochemical system having a multitude of physical and chemical processes occurring simultaneously while in operation. Each of these processes is governed by thermodynamic and kinetic principles and possesses a characteristic time scale. Thus, based on the frequency response, we can distinguish between individual mechanisms operating within the battery in a non-destructive manner via EIS 1. Numerical modeling is a powerful tool to understand the battery system from a theoretical perspective3. Development of high-fidelity, multiscale, and multicomponent models can be a complex and computationally expensive endeavor. Therefore, simple models, with generalization about the physics of the problem, are sought initially upon which more complex models are built. Traditional EIS simulation approaches include Equivalent Circuit Models (ECMs), which aim to represent the battery as an electrical circuit. This approach suffers from its empirical nature and lack of physical interpretability2. Another approach is to work with physics-based models. Electrochemical Impedance Spectroscopy, being a frequency domain technique, needs a special treatment to be done on the time domain Partial Differential Equations (PDEs) to be solved in a steady state. This process involves linearizing the model equations and applying the Laplace transform. Physics-based models have a better fidelity but suffer from high computational costs.4 Therefore, fast, reduced-order physics-based models have been developed by researchers that aim to maintain the physical consistency of the model at the same time reducing the computational cost.5 Recent years have also seen a surge in new machine learning-based techniques to replicate the impedance response of the batteries.6 The present work aims to summarize the various techniques of EIS modeling and discuss their relative advantages and shortcomings in a comprehensive manner. References: Gaberšček M (2021) Understanding Li-based battery materials via electrochemical impedance spectroscopy. Nat Commun 12:19–22. https://doi.org/10.1038/s41467-021-26894-5 Meddings N, Heinrich M, Overney F, et al (2020) Application of electrochemical impedance spectroscopy to commercial Li-ion cells: A review. J Power Sources 480:. https://doi.org/10.1016/j.jpowsour.2020.228742 Ramadesigan V, Northrop PWC, De S, et al (2012) Modeling and simulation of lithium-ion batteries from a systems engineering perspective. J Electrochem Soc 159:R31–R45. https://doi.org/10.1149/2.018203jes Meyers JP, Doyle M, Darling RM, Newman J (2000) The Impedance Response of a Porous Electrode Composed of Intercalation Particles. J Electrochem Soc 147:2930. https://doi.org/10.1149/1.1393627 Pathak M, Murbach MD, Pathak C, et al (2018) Fast impedance simulation of lithium-ion batteries with pseudo-two dimensional electrochemical models. J Electrochem Soc 165:A1324–A1337. https://doi.org/10.1149/2.0831805jes Telmasre T, Goswami N, Concepción A, et al (2022) Impedance response simulation strategies for lithium-ion battery models. Curr Opin Electrochem 36:101140. https://doi.org/10.1016/j.coelec.2022.101140