Modeling effects of particle size in LiMn$_2$O$_4$ cathode material on peak current level in lithium-ion batteries

Mathematical simulation of the current transfer characteristics of submicron and nanodimensional objects has been used to predict some properties of a structured electrode material in lithium-ion batteries. A diffusion model of the intercalation-deintercalation (ID) process is presented. Using this model, the current density in cathode material particles (nanocrystals) has been numerically simulated and an equation for the current density in the absence of diffusion polarization is derived. The proposed model can be used to optimize the ID process for improving the functional properties of cathode materials and increasing the working life of cathodes. Results are illustrated by examples for LiMn$_2$O$_4$ cathode material.