Practical Second Harmonic Nonlinear Electrochemical Impedance Spectroscopy for Lithium-Ion Batteries

Abstract

Lithium-ion batteries (LIBs) are intrinsically nonlinear electrochemical devices with two highly reactive electrodes separated by microns. Understanding the complex chemical and physical interaction between, and within, electrodes of practical LIBs requires in-situ and non-destructive characterizations to advance the field. Electrochemical impedance spectroscopy (EIS) is widely used for this purpose, but the method relies on linear approximations of nonlinear processes, leading to loss of information and model degeneracy. Second harmonic nonlinear electrochemical impedance spectroscopy (2nd-NLEIS), when measured simultaneously with EIS, is shown to address the challenges of model degeneracy and loss of information found in EIS. In this work, we provide a practical pathway for characterizing LIBs using 2nd-NLEIS, from simplified physics-based models and experimental data validation methods to quantitative 2nd-NLEIS analysis strategies and open-source software tools. Simplified physics-based models for 2nd-NLEIS consider the nonlinear contribution from Butler-Volmer kinetics and Warburg-like solid-state transport and thermodynamics. Analytical theories for 2nd-NLEIS in planar (Randles circuit) and macro-homogeneous porous electrodes are examined to fill the gap between complex full-physics modeling and the needs for practical physical parameter extraction from experimental data. For experiments involving aged LiBs, transmission line models (TLMs) extended to include the second harmonic response provide the flexibility needed to describe complex core-shell particles in the aged cells. Extended TLMs capture the evolution of EIS and 2nd-NLEIS spectra as commercial NMC|C cells age. We show that 2nd-NLEIS spectra comply with Kramers–Kronig (KK) relations, enabling data quality tests that evaluate the stationarity and causality of EIS, and through this work, 2nd-NLEIS experiments. A nonlinear measurement model (MM) test coupled with measured total harmonic distortion (THD) of less than 1% is shown to be a foundation for ensuring data quality and a suitable perturbation amplitude required for simultaneous EIS and 2nd-NLEIS analysis. The practical implementation of these strategies is included in nleis.py, an open-source Python package, to ensure the reproducibility of the simultaneous EIS and 2nd-NLEIS analysis. EIS and 2nd-NLEIS have complementary parity signals. In a full-cell measurement, the full-cell EIS signal is from the sum of the two half-cell signals whereas full-cell 2nd-NLEIS signals arise from the difference between the two half-cell signals. The summative EIS signals are denoted positive parity whereas the subtractive nature of 2nd-NLEIS is denoted negative parity, and when fit simultaneously to a common physics-based model, enable the first definitive impedance-based quantification of the evolving charge transfer symmetry for the NMC cathode during aging. Combining differential voltage analysis with simultaneous EIS and 2nd-NLEIS analysis, we have successfully quantified the growth of asymmetric charge transfer, especially at low states of charge (SOC). By varying SOC, it was observed that the cathode approaches symmetric charge transfer at intermediate SOC (50% SOC). This phenomenon perfectly aligns with the direction of lattice strain reduction given the formation of Ni-rich rocksalt surface layers on NMC particles, providing a non-invasive probe to the surface reconstruction of NMC cathode. The last piece of this thesis focuses on the real-world impact of the advancements in 2nd-NLEIS. The importance of considering asymmetric charge transfer in time domain application (i.e., SOC estimation) was demonstrated using the full physics pseudo-two-dimensional (P2D) model. We also generated 10228 pairs of unique EIS and 2nd-NLEIS spectra using the full-physics P2D model to support data science assisted parameter estimation and the determination of the domain of applicability for simplified models in the future.