Multi-scale analysis of an electrochemical model including coupled diffusion, stress, and nonideal solution in a silicon thin film anode

The electrochemical performance of Li-ion batteries strongly depends on the interaction between atomic scale and micro scale phenomena in high capacity electrode materials such as silicon and sulfur. Local thermodynamic interactions between host and guest species on atomic-scale significantly influence transfer kinetics and deformation kinematics on the micro-scale. We propose a multi-scale model to characterize the electrochemical and mechanical response of an amorphous silicon thin film during discharge/charge cycling. In the atomic-scale simulation, the stress-dependent energy barrier for the migration of lithium and the molar excess Gibbs free energy were calculated using density functional theory. These atomic-scale effects account for the nonlinear lithium diffusion behavior in the continuum simulation. In the continuum simulation, we considered the coupled diffusion and large deformation model on the cell-scale to determine the non-equilibrium cell potential as a function of the surface lithium concentration using Butler-Volmer kinetics. We clearly show that Li macroscopic kinetics is significantly affected by the stress induced by the volumetric strain associated with diffusion and the mixing formation energy of LixSi. Our simulation results demonstrate that the multi-scale model is consistent with experimental observations at different C-rates. (C) 2016 Published by Elsevier B.V.