Speaker: Charlotte Beckford

Title: A Poisson-Nernst Planck Model with Cross-Diffusion

Abstract: Batteries are a key element of a sustainable energy future. We are interested in predicting what is the maximum current which can be applied without causing early battery death and in determining what material properties influence this limiting current. In 2005 Bazant et al. extended the widely used Poisson-Nernst Planck (PNP) Model of ionic transport under an applied electric field by incorporating realistic nonlinear boundary conditions to represent the redox reactions occurring at electrodes.

In 2024 Kumar and Zhu presented a dynamic density functional theory to construct a thermodynamically consistent model of this system by starting with the free energy functional. By making a specific choice of the free energy functional, we derived Bazant et al.’s model from the dynamic density functional theory developed by Kumar and Zhu, establishing that the former is a specific case of the latter. By relaxing the assumptions, we obtained a generalized PNP model which includes cross-diffusion. The effect of cross-diffusion has not been previously investigated. Model derivation, validation, and preliminary results will be presented, including the sign of the cross-diffusion term’s asymmetrical effect on the limiting current.