Theory of mixed ion-electron transfer kinetics in concentrated solutions and solids

Electron transfer (ET) reactions are often successfully described using the phenomenological Butler-Volmer (BV) equation. However, there are cases where its predictions deviate from the experimentally observed rates. To account for these shortcomings, microscopic models of electron transfer, which take into account quantum mechanical and environmental polarization effects, have been developed. The current description of ET is constrained to dilute systems only, where ionic concentrations do not contribute to the activation step of the reaction. In the present study, the classical picture of Marcus ET reactions is generalized to describe the kinetics in concentrated solutions and solids, leading to the formulation of mixed ion-electron transfer kinetics (MIET). The reaction rates that are predicted by the theory are found to be in excellent agreement with recent in-situ experimental measurements in li-ion battery systems. Finally, we investigate the decrease of the maximum capacity with increasing discharge rate under ET-limited conditions for a variety of li-ion intercalation materials.