Linear and Nonlinear Electrochemical Impedance Spectroscopy for Lithium-ion Batteries

Abstract

Whole cell, <em>in situ</em> diagnostics capable of sensitive and selective characterization of the physicochemical processes governing lithium-ion battery performance are critical for improving battery safety, cost, and lifetime. Electrochemical impedance spectroscopy (EIS) is a powerful and widely used technique for noninvasively characterizing many electrochemical systems including lithium-ion batteries; however, the restriction of probing only the linearized physics artificially limits the information that can be extracted from an inherently nonlinear system. Here we describe a natural extension to EIS, called nonlinear EIS (NLEIS), which can break the degeneracy of linearization and provide complementary information to EIS. In this work, the initial theoretical and experimental groundwork for NLEIS as a powerful characterization method for lithium-ion batteries is developed. A physics-based mathematical model describing the fundamental (linear) and higher harmonic (nonlinear) response of a lithium-ion battery is used to analyze the first experimentally measured full-frequency second harmonic NLEIS spectra. Modeling results indicate that the information contained in NLEIS spectra compliments EIS characterization of charge-transfer kinetics (through the sensitivity of the second harmonic to reaction symmetry) and thermodynamic and transport processes (through a more distinct and sensitive low frequency response). Experimentally, we show that NLEIS and EIS are able to characterize early degradation (< 1% capacity loss) in commercially available (1.5 Ah LiNMC|C) batteries. While NLEIS shows that fresh cells have high symmetry charge transfer (α_a = α_c = 0.5), a shift toward kinetics that favor oxidation on the positive electrode (α_a,pos > 0.5, α_c,pos < 0.5) occurs as the cell is aged. Furthermore, modeling insights and experimental measurements of linear EIS and second harmonic NLEIS spectra at different states-of-charge (SoC) and states-of-health (SoH) suggest that combining EIS and NLEIS shows promise for improved battery characterization, parameter estimation, and model validation. To accelerate the adoption and reproducibility of experimental EIS and NLEIS analysis, several open software tools are also presented in this work. In particular, the Randles equivalent circuit model is extended to account for nonlinearities in charge transfer kinetics and thermodynamics to create a second harmonic NLEIS equivalent circuit. We show that EIS and NLEIS Randles circuits can be used to easily capture reaction asymmetry via the ratio of arc widths in the linear EIS and second harmonic NLEIS spectra. Analysis of experimental EIS and NLEIS measurements at different SoC for an aged, commercially available battery indicate that positive electrode charge transfer is more asymmetric at low SoCs (α_a,pos^{50% SoC} = 0.49, α_a,pos^{10% SoC} = 0.68). We also describe a web-based platform, the ImpedanceAnalyzer, for the easy-to-use estimation of physics-based parameters from experimental linear EIS spectra. We show that an a priori computed dataset can be used to quickly and robustly provide a best-matching spectrum that can be further explored with interactive visualizations or local parameter optimization. A global sensitivity analysis shows the increased sensitivity and complementary information content of second harmonic NLEIS spectra. The implications of NLEIS as a sensitive, whole-cell, <em>in situ</em> diagnostic for studying typically hard to detect degradation modes, such as lithium plating, are also discussed.