Analysis of Lithium Insertion Dynamics in Graphite Particles Using a Multi-Layer Cahn-Hilliard Model

We investigate the kinetics of lithium intercalation in a single graphite particle using a multi-layer Cahn-Hilliard model. This model can resolve the lithium-rich and lithium-poor domains, and naturally exhibits the staging phenomenon. The presence of the stages leads to a complex kinetic behavior: with increasing (dis)charge rate, the system becomes inhomogeneous, and there is a transition from quasi-equilibrium to diffusion-limited dynamics. To analyze this behavior, we define weights for each of the stages thanks to a discrete Fourier analysis, as well as other indicators such as a homogeneity index. We show that (i) the apparent global intercalation kinetics differs from the law applicable for a single layer because of the presence of a structured stage at the particle surface, (ii) the effective diffusion coefficient that describes the transition from quasi-equilibrium to diffusion-limited dynamics is much lower than the tracer diffusivity, due to the non-ideal interactions between ions and their ordering in domains. Furthermore, stage 3 is suppressed with increasing charging rates, while it is hardly present in discharge, whatever the rate. This non-trivial emerging kinetics, induced by the staging phenomenon, is present even for a single graphite particle, and should be accounted for in electrode-scale models.