Mathematical Model to Predict the Effective Modulus of a Silicon Electrode Considering Lithium Concentration, Volume Expansion, Pore, and Poisson's Ratio of Li-Ion Batteries

摘要

An accurate mathematical model to predict the effective modulus of silicon electrodes is proposed considering newly the effects of large volume expansion of silicon material by Li-on intercalation and porosity variation as well as the influence due to changes in lithium ion concentration and Poisson's ratio. While silicon plays the role of an anode active material in lithium ion batteries, the Si electrode is considered in this study as particulate composite materials. Even if some literatures have recently included in their material models lithium-ion concentration and Poisson's ratio, they did not consider porosity and large silicon volume change which degrades the performance of lithium ion batteries with Si electrodes. The proposed mathematical equation is formulated on the basis of the three-phase particulate composite material consists of silicon particles, pores, and binder. Throughout parametric studies using the developed model, followings are found. The li thium concentration of silicon nonlinearly increases and Poisson's ratio nonlinearly decreases as charging goes on, regardless of the structural forms of silicon particles, crystalline or amorphous. As the volume fraction of the pore increases in silicon particles during discharging, the electrode modulus decreases. The effective modulus of the three-phase particulate composite model decreases as charging goes on, in other words as results of considering simultaneously changes in lithium concentration, Si volume, pore, and Poisson's ratio. The accuracy of the present model is validated with an error of 5.6% by comparing the results calculated by our model to other existing experimental data in case of charging.