Application of Butler–Volmer equations in the modelling of activation polarization for PEM fuel cells

Proton exchange membrane (PEM) fuel cells have been under development for many years and appear to be the potential solution for many electricity supply applications. Modelling and computer simulation of PEM fuel cells have been equally active areas of work as a means of developing better understanding of cell and stack operation, facilitating design improvements and supporting system simulation studies. In general, fuel cell models must be capable of predicting values of the activation polarization at both the anode and the cathode. Since the magnitude of an activation polarization for a particular electrode depends on the inverse of the chemical (or electrochemical) reaction rate at that electrode, reaction rate expressions are normally required for each electrode. The reaction rate is commonly expressed as an ‘exchange current density’, typical symbol i0, and mechanistic expressions to predict i0 are, therefore, components of an ideal model. Most expressions for i0 are based on the Butler–Volmer (B–V) equation or on more approximate equations derived from the B–V equation. Many publications use one of these B–V equations without a critical determination of the applicability or accuracy of the particular equation being used. The present paper examines these questions and makes some recommendations regarding the applicability of each equation in the ‘B–V family of equations’. In addition, terminology and symbols have been modified, where possible, to make modelling based on B–V equations more easily understood and applied by those without an extensive background in electrochemistry.