Simplification of Butler-Volmer equation for proton exchange membrane fuel cell electrodes

Although the Butler-Volmer equation can be employed to determine the electrode losses in proton exchange membrane (PEM) fuel cells, the overpotentials cannot analytically be calculated in a general form. In this paper, the activation overpotential is determined as a function of asymptotic solutions of the Butler-Volmer equation. It is shown that the Tafel assumption is accurate for current densities ten times larger than the exchange current density, which is the case in the cathode of the PEM fuel cell cathode.