Population Balance Model of Formation and Growth of Solid Electrode Interphase in Lithium Ion Batteries

Abstract

We develop a physical-statistical model for formation and growth of the solid electrolyte interphase (SEI) in the negative electrode of Li ion batteries. During charging/discharging cycles, the SEI layer forms via a reaction between lithium ions, electrons and solvent molecules. The growth of the SEI layer leads to capacity fade and an increase of the ion transport resistance. In addition, SEI growth decreases the total porosity. Our statistical modeling framework employs the Fokker-Planck theory and it uses a statistical particle density distribution function as input. Structure-changing processes at the particle level transform this statistical distribution, causing changes in battery performance, e.g. capacity fade and power fade. The present study focuses on the impact of SEI formation, explored within this modeling framework. To this end, we have formulated a set of kinetic and transport equations. The solution of the statistical model reveals a broadening of the initial statistical distribution of SEI thicknesses and a growth of the average thickness of SEI increases from 47 nm to 80 nm at 25 oC and C/2 charge rate after 1000 cycles. This results in a 5% reduction of the battery capacity as shown in Fig.1. The statistical model of SEI formation is used to perform a multi-objective optimization to find a set of optimized battery design parameters, which lead to minimizing the capacity loss and maximizing the power density. In this optimization, the weight between capacity loss minimization and power density maximization can be adjusted as desired, as shown in Fig. 2. Figure 1