A Critical Review of the Butler-Volmer Equation for the Activation Polarization of Solid Oxide Fuel Cells

The Butler-Volmer equation is widely used to describe the activation polarization for the electrode reaction of solid oxide fuel cells. However, it is found that there are no less than 12 types of the Butler-Volmer equation in the last decade, attributed to the choice of symmetry factor or transfer coefficient, as well as ambiguous corrections of species concentration, operating temperature, and electrode microstructure. The standard Butler-Volmer equation is rigorously derived based on the transition-state theory and is recommended for future applications. The difference between the symmetry factor and the transfer coefficient is discussed. The value of these coefficients is mostly 0.5, resulting in identical effects on the Butler-Volmer equation. Concentration corrections are correctly carried out at the common factor position. The individual concentration correction on the forward and reverse reactions and the double concentration corrections are unreasonable. The exponential factor for oxygen in the oxygen reduction reaction is recognized as 0.25. However, the value for hydrogen and steam in the hydrogen oxidation reaction is 1 instead of the theoretical value of 0.5. Finally, a simulation flow for industrial-scale solid oxide fuel cells with concentration distribution is provided, which benefits the accurate application of the Butler-Volmer equation.