Modeling the Effects of Morphology in Lithium-Ion Battery Electrodes

Abstract

In order to be competitive with gasoline engines, electric vehicles need much higher lithium capacities than what is possible using the graphite anodes available today [1]. To overcome this problem, materials such as silicon, tin and tin oxide which have much higher lithium capacity have been suggested as alternate anode materials[2][3][4]. However these materials undergo large volume changes on cycling which leads to pulverization of the anode [5]. Nanostructuring the electrode has shown promise in improving the cycle life of cells made from these materials[3]. However, the effect of surface morphology on stress generation is not very well understood. In this work we present a model for predicting the stress generated for given surface morphology for silicon and tin oxide as the anode materials. The model assumes a columnar nanostructure which is a thin film deposited on a current collector. Conventional Li-ion battery models assume a porous electrode with spherical constituent particles and are pseudo 2-d. Nanostructures are represented as rectangular 2-d structures in the model, which are projections of an array of cuboidal nano-columns. Transport phenomena equations used by Doyle et. al[6] are adapted for modeling charge and mass transfer. Lithium intercalates directly into silicon, and hence mass transfer equations similar to those used for graphite can be used. However, tin oxide undergoes phase change upon intercalation[7] and hence phase field theory[8] is used to model mass transfer into tin oxide anodes. Christensen et. al's model[9] predicts concentration and stress profiles in a spherical particle upon lithium intercalation and deintercalation. The equations, generalized to 2-dimensions, are used for predicting stress and strain in the nanostructure. Results will be compared with in-situ stress measurements made on single crystal nano-columns of tin oxide (deposited using aerosol chemical vapor deposition [10]) using Multibeam optical stress sensor (MOSS)[11].