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

Abstract

a b s t r a c tThe 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 j 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.

Probing three-dimensional sodiation–desodiation equilibrium in sodium-ion batteries by in situ hard X-ray nanotomography

“…It is well-known that materials degradation is directly correlated to the change in their geometric characteristics during electrochemical cycling 30 31 . The distributions of the two representative principal curvatures, which can be used to identify convex and concave surface, are evaluated on a statistical analysis of all particles ( Fig.…”

A chemo-mechanics framework for elastic solids with surface stress

“…In the past several years, many previous works [14,[17][18][19][20][21] studied the influence of surface stresses in modelling the stress distribution in LIBs when the size of the electrodes is in the nanometre range and found that nano-electrodes with suitable structure and size could be strengthened by surface stresses which can effectively inhibit crack formation. This conclusion is also valid for our study.…”

“…In the stress analysis of electrodes in LIBs, Cheng's group first studied the surface effect on the diffusion-induced stresses in spherical particle electrodes [17] and nanowire electrodes [18]. Zang & Zhao [19] introduced the effects of diffusion together with the Tolman length into the conventional theory of surface elasticity and applied it to study the diffusion-stress coupling problems in nano-structured silicon electrodes. Hao et al [20] studied the effect of surface stress on the diffusion-induced stresses of electrode nanomaterials in LIBs with different boundary conditions.…”

Dislocation effect on diffusion-induced stress for lithiation in hollow spherical electrode

“…In addition, Cheng studied the influence of surface mechanics on DIS within spherical nanoparticles [12]. Many experiments and theories indicated that the morphology of the electrode can affect the DIS because of the diffusion of lithium-ion [14][15][16]. DeLuca et al [17] developed a fully coupled diffusion-elasticity model to study the effects of particle morphology and size on stress generation during lithiumion insertion into Si particles.…”