A diffusion and curvature dependent surface elastic model with application to stress analysis of anode in lithium ion battery

The present paper investigates the influences of surface tension and the stress distribution in the bulk induced by the surface tension, surface curvature and ions’ diffusion on the elastic properties of nanostructures. In the electro-chemical diffusion process, the surface tension, ions diffusion and stress distribution will strongly dependent with each other. Here, considering the curvature effect, a surface elastic model coupled with the ions diffusion is proposed. In the model, the coupling between the stress and ions diffusion is revealed through the chemical potential variation. To reveal the curvature effect on the surface energy, a Tolman length for solid is introduced. As a typical application of the model, we analyze the stress distributions in the silicon anode of the lithium ion battery. In recent years, silicon, due to large theoretical energy density, becomes one of the promising candidate anode materials. However, huge volume changes of silicon in charging and discharging process hinders its application. We depict the stresses provenance and evolution of hollow nanosphere and nanotube induced by lithium ions diffusion. Self-buckling induced by surface stresses of the two nanostructures is also taken into consideration. Critical buckling sizes are analyzed. All results show that hollow nanosphere will be a more suitable structure for electrode. Finally, a new dimensionless number κ related to Young’s modulus, Tolman length and surface energy is proposed to estimate the relative importance of the Tolman length with the intrinsic material length. It is believed that the diffusion and curvature dependent surface elastic model will be a powerful tool to investigate the diffusion behaviors in nanostructured electrode.