WIAS Preprint No. 2905, (2021)

Homogenization of a porous intercalation electrode with phase separation


  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Landstorfer, Manuel
    ORCID: 0000-0002-0565-2601
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915

2020 Mathematics Subject Classification

  • 78A57 35Q92 35B27 78M40 80A22


  • Battery, homogenization, two-scale convergence, porous electrode, non-equilibrium thermodynamics, phase separation




In this work, we derive a new model framework for a porous intercalation electrode with a phase separating active material upon lithium intercalation. 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. 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 goes in hand with a change in the underlying metric structure of the PDE system.

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