Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

Abstract

Silicon oxide (SiO) is a promising anode material for high-energy lithium-ion batteries, as it is made from low-cost precursors, has a potential close to that of Li, and has high theoretical specific capacity. However, the applications of SiO are limited by the intrinsic low electrical conductivity, large volume change, and low coulombic efficiency, which often lead to poor cycling performance. A common strategy to address these shortcomings is to blend SiO with graphite active materials to form a composite anode for better capacity retention. In this work, we derive a reduced order model (ROM1) using perturbation theory. We employ the multi-site, multi-reaction (MSMR) framework of a composite porous electrode blend consisting of two lithium-host materials, SiO and graphite. The ROM1 model employs a single-particle model (SPM) approach as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation for each host material that describes diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for the diffusion. The first-order correction treats losses other than that of the SPM.