Recent remarkable progresses are re

Recent remarkable progresses are recapitulated below. Lai and Ciucci(12) and the Bazant group(13) reformulated the porous electrode theory in which the electrochemical potential is taken as the driving force of nonequilibrium thermodynamics in porous electrodes. Several groups have introduced the homogenization theory, which replaces the volume averaging method employed in the Newman method, to upscale the description of ion transport and reactions at the microscale to the macroscale.(14-19) Conventional theories usually assume electroneutrality in the solution phase. By accounting for electrostatic interactions, the Eikerling group(20-22) and the Bazant group(14, 23) incorporated surface charging effects into the porous electrode theory. Specifically, Eikerling et al. developed a theoretical framework for surface charging effects in electrochemical systems; the model self-consistently solves for the surface charge density as a function of electrode potential and solution properties.(22) At the microscopic scale (material scale), phase-field models have been employed by the Ceder group(24) and the Bazant group(13, 25) to describe phase transformations and microstructural evolutions in battery materials. Diffusion-induced stresses have been incorporated into the porous electrode theory, as exemplified by recent works by Ji and Guo(26) and Wu and Lu.(27)