Homogenization of a Porous Intercalation Electrode with Phase Separation

Multiscale Modeling &Simulation, Volume 22, Issue 3, Page 1068-1096, September 2024.
Abstract. In this work, we derive a homogenized mathematical model for a porous intercalation electrode with a phase separating active material. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann–boundary condition modeling the lithium intercalation reaction [math]. The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn–Hilliard equation, whereas the limit model consists of a diffusion and an Allen–Cahn equation. Thus, we observe a Cahn–Hilliard to Allen–Cahn transition during the upscaling process. In the sense of gradient flows, the transition coincides with a change in the underlying metric structure of the PDE system.