The Butler-Volmer Equation for Polymer Electrolyte Membrane Fuel Cell (PEMFC) Electrode Kinetics: A Critical Discussion

Most recent publications on PEMFC modelling describe the electrode kinetics of the catalytic reactions with a mechanistically simple equation usually called the "Butler-Volmer equation". Here we argue that the Butler-Volmer equation is unsuited to PEMFC kinetics and offers no advantages over simpler empirical approaches. We also demonstrate that the most widely used formulation of this equation in the literature is inconsistent with the textbook equation. In order to critically assess the literature, we derive fundamental concepts underpinning the Butler-Volmer equation, without specific mechanistic assumptions. Through illustrative PEMFC simulations using various possible kinetic treatments, we demonstrate how models using an inappropriately formulated kinetic equation can give inaccurate predictions, or can contain superfluous detail. Since deviations in current distribution are often appreciable even when the polarization curve changes negligibly, experimental validation of models by comparison to the polarization curve alone can be inadequate. For simple, empirical models, we advocate linear reversible kinetics for the hydrogen oxidation reaction (HOR) and irreversible kinetics for the oxygen reduction reaction (ORR), avoiding superfluous parameterization in the Butler-Volmer equation. Reduction of empiricism requires more mechanistically detailed models than the Butler-Volmer equation. We emphasize that incorrectly formulated kinetic equations risk generating incorrect data or misleading conclusions.