One-dimensional analysis of the coupling between diffusion and deformation in a bilayer electrode

Diffusion-induced deformation during electrochemical cycling plays an important role in determining structural durability of the electrodes in lithium-ion batteries. In this work, we investigate the coupling between diffusion and stress in the boundary conditions of a bilayer electrode, and analyze the evolution of the lithium concentration and stress. Numerical simulations are performed under four different combinations of the boundary conditions between diffusion and mechanical deformation. The stress distributes uniformly in the bilayer electrode for all four cases. The concentration of lithium at the interface is discontinuous for the cases with fixed boundary conditions and is continuous for the cases with a surface at stress-free state. For the bilayer electrode fixed at both surfaces, the magnitude of the stress in the bilayer electrode increases with the increase of the diffusion time. This study reveals the importance of incorporating the coupling between diffusion and stress in the boundary condition in the analysis of the structural durability of lithium-ion batteries and in the design of multilayered and/or gradient electrodes.