An Extended Formulation of Butler-Volmer Electrochemical Reaction Kinetics Including the Influence of Mechanics

The Butler-Volmer equation is widely used to describe ion-transport across an interface in electrochemical systems. In recent years, a strong focus has been placed on solid state batteries with Li-metal electrodes which promise an increase of energy density and safety, but also introduce new complexity, for example, due to the process of material deposition and stripping which is conceptually different to intercalation and de-intercalation. Especially the understanding of the heterogeneous growth of lithium, in the form of dendrites, requires a consistent model taking all mechanical effects into account. In this work, we use transition state theory based on a purely energetic concept to derive the Butler-Volmer equation for a monovalent reaction that is also consistent with the Nernst equation and discuss the energetic contribution due to deposition and stripping. With the help of the Bronsted-Evans-Polanyi principle, we generalize several approaches to include mechanical stress in the Butler-Volmer equation, discuss the underlying assumptions and suggest, through theoretical considerations, a fairly simple extended version of the Butler-Volmer equation. Beside addressing the novel aspects of the effects of mechanics, which impacts both open circuit potential and exchange current density, this work also sharpens the need for consistent use of the Butler-Volmer equation.