Nonlinear electrochemical impedance spectroscopy of lithium-ion batteries: Experimental approach, analysis, and initial findings

Abstract

Nonlinear electrochemical impedance spectroscopy (NLEIS) is a moderate-amplitude extension to linear EIS that provides a sensitive and complementary whole-battery diagnostic for charge transfer kinetics, mass transport, and thermodynamics. We present the first full-frequency, second harmonic NLEIS spectra for lithium-ion batteries using commercially available, 1.5 Ah LiNMC|C cells. The mathematical framework for NLEIS shows, and experiments confirm, that moderate-amplitude input modulations can generate a second harmonic output that does not intrinsically corrupt the linear EIS response. Experimental measurements at varied states-of-charge (SoC) and states-of-health (SoH) are used to illustrate and compare NLEIS and EIS data. At low frequencies, the second harmonic NLEIS spectrum is shown to produce a much more distinct response to SoC dependent thermodynamic and diffusion processes than linear EIS. By combining NLEIS and EIS, we are able to characterize degradation in early cell cycling (where cells lost less than 1% of initial capacity). We also show that NLEIS complements the characterization of charge transfer kinetics of linear EIS through the second harmonic sensitivity to symmetry. For example, NLEIS shows that fresh cells have high symmetry charge transfer (α_a = α_c = 0.5) on both electrodes, whereas early in the cycling there is a shift toward kinetics that favor oxidation on the positive electrode (α_(a,pos) greater than 0.5, α_(c,pos) less than 0.5). Combined analysis of EIS and NLEIS spectra shows promise for improved parameter estimation and model validation. All experimental data and analysis code for this manuscript can be found on ECSarXiv.

Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy: Part II. Model-Based Analysis of Lithium-Ion Battery Experiments

“…Experimental procedures and data availability for the lithiumion batteries under test.-Here we reuse and quantitatively analyze, for the first time, the triplicate EIS and 2nd-NLEIS experimental datasets we have previously published 33 and archived. 47 The cells are 1.5 Ah Li NMC|C Samsung cells (INR 18650-15 M) with mixed NMC 532/LMO cathodes and graphite anodes. 48 Briefly, the datasets were acquired for fresh cells and modestly aged cells that were cycled between 4.2 V and 2.5 V 100 times at a 2 C discharge, 2 C CCCV charge, and controlled temperature of 25 °C.…”

Operando electrochemical impedance spectroscopy and its application to commercial Li-ion batteries

“…For a sinusoidal excitation, the nonlinear distortions are located at integer multiples of the frequency of the excitation. It is worth noting that the nonlinear distortions also contain information about the dynamics of the battery [14]. These nonlinear dynamics can, for instance, be studied through nonlinear electrochemical impedance spectroscopy (NLEIS) [36], which computes the ratio between the response at the integer multiples of the excited frequency, for instance the second harmonic, and the excitation.…”

“…Accordingly, the battery is assumed to be a linear time-invariant (LTI) system [13]. However, on the one hand, the behaviour of Li-ion batteries is inherently nonlinear [14]. Still, the behaviour can be linearised by considering an appropriate excitation amplitude.…”

Understanding non-linearity in electrochemical systems using multisine-based non-linear characterization

“…In recent years, nonlinear characterization methods have been developed for investigations of battery nonlinearities (Murbach et al 2018;Harting et al 2017;Firouz et al 2016;Fan et al 2021). Unlike conventional techniques such as the pulse power characterisation (PPC) test and the electrochemical impedance spectroscopy (EIS) test applied in the time domain, the nonlinear characterization methods are performed in the frequency domain to capture and quantify battery nonlinearities.…”

“…According to the characteristic frequency range of each electrochemical process, the processes can be distinguished and analysed separately (Wolff et al 2019). Murbach et al (2018) proposed a moderate-amplitude extension technique to linear EIS to provide a complementary diagnostic for the wholebattery behaviours, termed as nonlinear electrochemical impedance spectroscopy (NLEIS). Nevertheless, nonlinear frequency response analysis (NFRA), a single sine sweep based method which involves the second and the third harmonics, was first performed on lithium-ion batteries at weakly nonlinear regime to discriminate different electrochemical processes (Harting et al 2017).…”