Sharp Interface Limit of the Cahn-Hilliard Reaction Model for Lithium-ion Batteries

TL;DR

This paper develops a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, crucial for understanding phase separation in lithium-ion batteries, and demonstrates convergence to a Mullins-Sekerka type evolution.

Contribution

It introduces a novel weak solution framework for the model's sharp interface limit, incorporating nonlinear boundary conditions and optimal dissipation principles.

Findings

Solutions converge to a Mullins-Sekerka type evolution

Established a variational PDE framework for lithium-ion battery modeling

Connected diffuse interface models to sharp interface limits

Abstract

We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An essential feature of this model is the use of Butler-Volmer kinetics for lithium-ion insertion, which arises as a Robin-type boundary condition relating the flux of the chemical potential to the reaction rate, itself a nonlinear function of the chemical potential and the ion concentration. To pass through the nonlinearity as interface width vanishes, we introduce solution concepts at the diffuse and sharp interface level describing dynamics principally in terms of an optimal dissipation inequality. Using this functional framework and under an energy convergence hypothesis, we show that solutions of the Cahn-Hilliard reaction model converge to a Mullins-Sekerka type geometric evolution equation.