Analytical Modeling of Solid Phase Diffusion in Single-Layer and Composite Electrodes Under Time-Dependent Flux Boundary Condition

Abstract

Mathematical modeling of species diffusion in Li-ion cell electrodes is critical for improving performance and efficiency of electrochemical energy storage. There is a relative lack of literature in this direction for time-dependent flux boundary conditions. In this work, the method of Green’s functions is used to solve the solid-phase diffusion problem in electrodes with a time-dependent flux boundary condition. While Green’s functions have been used extensively for thermal transport problems, there is limited past work on application of Green’s functions for solving species transport problems in electrochemical systems. The concentration distribution is first determined for a thin film electrode and spherical electrode particle. The method is then extended to determine the concentration profile in two-layer composite electrodes. The mathematical models presented in this work are validated by comparison with past studies and numerical simulations. Concentration profiles for a variety of time-dependent boundary conditions are presented. It is expected that improved understanding of diffusion under time-dependent flux boundary conditions may help improve the performance and efficiency of Li-ion based electrochemical energy storage devices and systems.