Résumé
An appropriate description of the lithiation dynamics in biphasic primary cathode particles of Li-ion batteries requires an accurate treatment of the conditions holding at the interface between the particle and the surrounding liquid electrolyte. We propose a phase field model based on the Allen-Cahn approach within which the particle-electrolyte interface is smooth [smoothed boundary method (SBM)], to simulate arbitrarily shaped particles. Surface terms are added to the evolution equations, and SBM calculations are compared with benchmark simulations for which the boundary conditions are explicitly imposed at the borders of the calculation domain. Our findings highlight the necessity of introducing strengthening factors for the surface terms to achieve the desired conditions for the phase and elastic fields, and to enable an accurate reproduction of stress distributions within the particle. This refinement of the SBM is critical for reliable predictions of Li insertion/extraction rates and lithium diffusion behavior in the context of Li-ion batteries. We perform also a simulation under potentiostatic conditions with a full coupling of the different physical processes at play. It illustrates the applicability of our approach and demonstrates the capabilities of the SBM for a simulation of lithiation dynamics with coupled electrochemistry and mechanics.