Revisiting the Butler–Volmer equation

Abstract

The Butler–Volmer (BV)-equation is central to a phenomenological description of electrochemical processes in chemistry and materials science. It provides a qualitative and semi-quantitative description allowing an understanding of electrode processes which are central for materials e.g. in energy science and catalysis. Herein, it describes the simultaneous transfer of electrons at electrode interfaces and as such it employs an exponential law. Interestingly, the BV-equation within its conceptual background is not yet connected to a characteristic reference point. In this work, we derive the so called “golden overpotential” η_φ ≈ 24.22 mV as a measure for estimating the exchange current density starting from a given equilibrium potential which is valid for all electrochemical processes. Central to our approach is the golden ratio in the symmetrical form of the BV-equation. We verify the validity of our approach by a comparison of the predicted values against experimental data for different electrochemical processes.