Phase-field model of ion transport and intercalation in lithium-ion battery

The unified 3D phase-field model for the description of the lithium-ion cell as a whole is developed. The model takes into account the realistic distribution of particles in porous electrodes, percolative transport of ions, and the difference in size of solute and solvent molecules. We use spatially dependent interaction and dynamic parameters that are considered as a function of the order parameter determining the space and size distribution of particles in nanostructured porous electrodes. The model describes the dynamics of ions in a battery at the constant value of overpotential across the electrode/electrolyte interface. The electrochemical reaction is naturally determined by the chemical potential difference at the interface. The proposed model is applied to simulate charging and discharging process in 3D lithium-ion cell with porous cathode and anode characterized by the realistic size distribution of electrode particles. We demonstrate that the condition of constant overpotential provides nearly constant current density in the battery. The obtained results indicate non-diffusive motion of the concentration front during charging or discharging, nonuniform intercalation flux over the surface of electrode particles, and violation of the equipartition of electric current density over the electrode surface. All these facts are not taken into account by the most commonly used models.