The Coupling Effect of Surface Effect and Chemical Diffusion in Lithium-Ion Battery with Spherical Nanoparticle Electrodes

Many experiments have well found that the lifespan of lithium-ion (Li-ion) batteries can be effectively improved by nanoscale structured electrodes. In order to investigate the coupling mechanical and chemical mechanism underlying the superior performance of nanoscale structured electrodes, an alternative diffusion-stress coupling model considering the surface effect of nanomaterials is proposed. The diffusion effect is included in the linearly elastic constitutive relationship, while the diffusion process is conversely mediated by the stress field. The surface effect of nanomaterials is characterized by a surface-induced traction depending on the bulk surface energy density and surface relaxation parameter. Both the displacement field and the stress field in a typically nanoparticle structured electrode are analyzed. Theoretical predictions show that when the surface effect is considered, both the diffusion-induced radial expansion and the tensile stress are obviously smaller than the classical counterparts, which are attributed to the surface-induced traction analogous to a hydrostatic pressure on the surface of nanoparticles. Furthermore, both the diffusion-induced radial expansion and the tensile stress depend on the particle size, both of which decrease with a decreasing radius of nanoparticles. The present results may not only provide a reasonable explanation for the superior performance of Li-ion batteries with nanoscale structured electrodes but also be helpful for the optimal design of high performance batteries.