One-Dimensional Impedance of the Cathode Side of a PEM Fuel Cell: Exact Analytical Solution

A transient one-dimensional model for the coupled performance of the cathode catalyst layer (CCL) and the gas-diffusion layer (GDL) in a PEM fuel cell is linearized and an exact analytical solution for the cathode side impedance Z is derived. The solution is valid at a low current density, when the proton and oxygen transport losses in the CCL are not large. The zero-frequency resistance contains the faradaic term, the terms due to the proton and oxygen transport in the CCL and due to the oxygen transport in the GDL. The analytical equation for Z is fast enough for least-squares fitting of experimental spectra, which yields the GDL oxygen diffusivity, the Tafel slope of the oxygen reduction reaction, and the CCL proton conductivity and oxygen diffusivity. As an example, the model is fitted to three measured spectra of a high-temperature PEMFC; the fitting parameters are discussed.