Modeling the Lithium Ion/Electrode Battery Interface Using Fick’s Second Law of Diffusion, the Laplace Transform, Charge Transfer Functions, and a [4, 4] Padé Approximant

Abstract

This work investigates a one-dimensional model for the solid-state diffusion in a LiC 6 /LiMnO 2 rechargeable cell. This cell is used in hybrid electric vehicles. In this environment the cell experiences low frequency electrical pulses that degrade the electrodes. The model’s starting point is Fick’s second law of diffusion. The Laplace transform is used to move from time as the independent variable to frequency as the independent variable. To better understand the effect of frequency changes on the cell, a transfer function is constructed. The transfer function is a transcendental function so a Padé approximant is found to better describe the model at the origin. Consider ∂c(r,t)/∂t=D∂2c(r)/∂2r+(2/r)(∂c(r)/∂r) .