Analytical and Fast Numerical Models for PEM Fuel Cell Impedance with Damjanović Kinetics of the Oxygen Reduction Reaction

The impedance spectra of many PEM fuel cells exhibit a low-frequency inductive loop. Among possible mechanisms of the loop formation is the slow dynamics of the oxygen reduction reaction (ORR) intermediates on the platinum surface. Because of the time required to change the coverage of species adsorbed on the platinum surface, variations in cell potential do not lead to an immediate response in cell current. This results in inductive-type impedance behavior. In this work, we rederive the previously obtained solutions to the equations describing the Damjanović kinetics of the ORR. We report corrected analytical solutions for the steady-state surface coverages of intermediate species and for the small AC perturbation amplitudes of the coverages. Based on these solutions, a fast analytical model for the ORR impedance is developed. Fitting the ORR impedance model to experimental spectra of a rotating disk electrode is demonstrated. Further, incorporation of the ORR kinetics into analytical and numerical models for PEM fuel cell impedance is performed. The numerical model is fitted to the experimental impedance spectra of a button-size PEM fuel cell. In the limit of zero frequency, the model converges to the DC cell resistivity determined from the polarization curve.