Effective modulus of Si electrodes considering Li concentration, volume expansion, pore, and Poisson’s ratio of Li-ion batteries

We propose a novel mathematical model for predicting the effective modulus of Si electrodes in Li-ion batteries by considering the large volume expansion of Si during lithiation and porosity variation, as well as the influence of change in Li-ion concentration and Poisson’s ratio, assuming the Si electrode as a particulate composite material. Though previous studies considered the Li-ion concentration and Poisson’s ratio in their models, they rarely considered the porosity and a large change in the volume of silicon, which degrade the performance of Li-ion batteries with Si electrodes. The proposed model is formulated on the basis of a three-phase particulate composite material composed of silicon particles, pores, and binders. Through parametric studies, it is found that the Li-ion concentration in silicon increases nonlinearly and the Poisson’s ratio decreases during charging, regardless of the structure (crystalline or amorphous) of the silicon particles. The effective modulus of the three-phase particulate composite electrode decreases during charging as a result of the changes in the Li-ion concentration, Si and binder volumes, pores, and Poisson’s ratio. The accuracy of the developed model is validated by comparing the predicted moduli of this model with other 3 experimental data and 2 model predictions.