Microkinetic Models of Electrochemistry: Assumptions, Limitations, and Failures

Accurate models of electrochemical reactions at the interface between active material and electrolyte are essential for battery design and management. Current models of electron transfer processes, i.e., the Butler–Volmer equation and the Marcus–Hush–Chidsey (MHC) model, differ in their range of validity but both fail for high overpotentials and high C-rates. We show that these models, and the related Marcus theory, rely on small-parameter expansions and inadequately treat the strong interactions between inner-sphere electrochemical reactions occurring at high C-rates. By systematically detailing all assumptions made in the development of these models, we demonstrate the utility of a targeted phenomenological approach in extending these models. As a case study, we relax the wide-band approximation used in MHC to tame the inaccuracy in modeling the oxidative branch of the lithium plating/stripping reaction. Finally, for convenience, we present all models discussed in a consistent form which explicitly includes their concentration dependence, as required by macroscopic battery simulators.