where 𝐷 is the concentration-dependent diffusivity and 𝜇 is the phase-field chemical potential. The particle's reaction rate 𝑅 between the particle of concentration 𝑐, and the electrolyte of concentration 𝑐 "# ! is modeled through the Coupled Ion Electron Transfer Theory , specifically the electron-coupled ion transfer approximation: following the experimental particle size distribution. The electrode-level ionic and electronic losses were modeled implying porous electrode theory . Moreover, wiring losses within the sub-volume are considered, similar to the work of Li et al. . A more detailed description of the model can be found in Supplemental information sections 2.a.