Numerical simulation of phase separation in cathode materials of lithium ion batteries

A nonlinear initial boundary value problem for the lithium ion concentration, the electric potential and the electrode-electrolyte interface currents is introduced on the microscale. The model enables the resolution of porous electrode microstructures. Different exchange current densities for Butler-Volmer interface conditions are evaluated. The Cahn-Hilliard equation is used to describe the phase transition from solid-solution diffusion to two-phase dynamics. The resulting phase-field model is then discretized on a regular mesh. A first-order finite-volume scheme with an adaptive time integration method is applied. The parameters and their effects in the non-convex Helmholtz energy are investigated and explained. Furthermore, the numerical convergence of the scheme is examined. In order to illustrate the method, the charging process of several single-particles and a complex structure is numerically simulated.