Surface and chemical diffusion effects of nanowire electrodes in lithium-ion batteries

Nanostructured electrodes with surface effect show a distinct advantage in prolonging the lifetime of lithium-ion (Li-ion) battery. In order to characterize the surface and chemical diffusion effects in a cylindrical nanowire electrode, a new theoretical model is proposed based on a combination of the diffusion theory and a surface energy density-based elastic theory. With the reformulation of the stress boundary condition in terms of a surface-induced traction, the bulk surface energy density and surface relaxation parameter are introduced as two simple parameters characterizing the surface effect in nanowire electrodes, instead of the surface elastic constants always used in existing models. Closed-form solutions of the diffusion-induced elastic fields under potentiostatic operation are derived. It is found that the radial expansion and tensile stress in nanowire electrodes become smaller than the classical predictions without surface effect and decrease monotonically with a decreasing nanowire radius when the surface effect is considered. Such phenomena can be basically attributed to the action of surface-induced traction on the nanowire surface. These results demonstrate the convenience and effectiveness of the present model in predicting the chemo-mechanical behavior of nanowire electrodes, which should be of guidance value for the optimal design of durable electrodes.