QUASI-STEADY STATE SOLUTION OF LITHIUM ION CONCENTRATION OF HALFCELL CATHODE IN DILUTE ELECTROLYTE

Abstract

This paper focuses on a mathematical model of a Lithium ion battery in dilute electrolyte. The macroscopic model takes into account the conservation of ions in the electrolyte, diffusion within particles, and transfer of Lithium at the electrolyte/electrode particles interface. The asymptotic analysis for the dimensionless model has led to Tafel reaction rate of Lithium intercalation at the electrolyte/electrode particles interface and a quasi–steady state model. Analytic solutions for the Lithium ion concentration and the cell voltage are derived, specifically for electrode materials that have a flat discharge curve characteristic. The analytic solutions give rational results of the concentration profile in the electrolyte across the cell at various currents. The results show that the rate of lithium intercalation into particles is high in the region near the separator. At high discharge rate, the concentration in the electrolyte is depleted, hence limit the discharge.