Effects of concentration-dependent elastic modulus on the diffusion of lithium ions and diffusion induced stress in layered battery electrodes

A stress assisted diffusion model considering concentration-dependent elastic modulus of active material has been established for the multi-layered electrodes of lithium batteries. The physical mechanism for the effect of modulus variation on the Li-ion diffusion and corresponding biaxial stress is well elucidated. Moreover, the analytic solutions of maximum stress in both active layer and collector are respectively derived. It has been found that the modulus stiffening gives rise to the additional stress gradient and enhances Li-ion diffusion, therefore to increase the biaxial stress in the plate electrode. In contrast, modulus softening makes the stress assisted diffusion less significant and the corresponding stresses are reduced. These coupled effects are more significant during potentiostatic charging and galvanostatic charging with high charging rates. Moreover, the maximum stress in the active layer is independent of charging process, but depends upon the elastic modulus variation due to Li-ion insertion. Finally, with increasing thickness ratio between collector and active material, the impacts of concentration dependent modulus on the Li-ion diffusion in active layer decreases, whereas this effect on maximum stress in the current collector increases.