Extending Newman's Pseudo-Two-Dimensional Lithium-Ion Battery Impedance Simulation Approach to Include the Nonlinear Harmonic Response

Abstract

The pseudo-two-dimensional (P2D) model of lithium-ion batteries couples a volume-averaged treatment of transport, reaction, and thermodynamics to solid-state lithium diffusion in electrode particles. Here we harness the linear and nonlinear physics of the P2D model to evaluate the fundamental (linear) and higher harmonic (nonlinear) response of a LiCoO2|LiC6 cell subject to moderate-amplitude sinusoidal current modulations. An analytic-numeric approach allows the evaluation of the linearized frequency dispersion function that represents electrochemical impedance spectroscopy (EIS) and the higher harmonic dispersion functions we call nonlinear electrochemical impedance spectroscopy (NLEIS). Base case simulations show, for the first time, the full spectrum second and third harmonic NLEIS response. The effect of kinetic, mass-transport, and thermodynamic parameters are explored. The nonlinear interactions that drive the harmonic response break some of the degeneracy found in linearized models. We show that the second harmonic is sensitive to the symmetry of the charge transfer reactions in the electrodes, whereas EIS is not. At low frequencies, NLEIS probes aspects of the cell thermodynamics that are not accessible with EIS. In short, NLEIS has the potential to increase the number of physicochemical parameters that can be assessed in experiments similar in complexity to standard EIS measurements.