The Non-local Effects Induced by Rapid Transient Mass Diffusion in a Spherical Silicon Electrode of Lithium-ion Batteries

For the development of the fast charging technology of lithium-ion batteries, describing the rapid transient mass diffusion process accurately is the premise to avert the mechanical degradation caused by the diffusion-induced stress. In this paper, we present a diffusion-elasticity model based on the finite deformation theory with the consideration of non-local effects of mass transfer. The proposed model is then applied to analyze the evolution and distribution of stress and lithium concentration in a silicon electrode during the rapid charging process under potentiostatic operation. The cases with and without the contribution of non-local diffusion effects are both calculated for comparative analysis. The dependence of the influence of non-local effects on diffusion relaxation time To is discussed. The results show that a diffusive wave appears when the value of To is sufficiently large, and it moves inside gradually during the rapid charging process, which is qualitatively consistent with the results from literature.