Analytical Warburg Impedance Model for EIS Analysis of the Gas Diffusion Layer with Oxygen Depletion in the Air Channel of a PEMFC

In this study, an analytical mathematical expression to simulate the low frequency impedance spectrum that represents the gas diffusion layer (GDL) and air channel of a proton-exchange membrane fuel cell (PEMFC) has been developed. The analytical expression considers the impedance response of the GDL with oxygen depletion in the air channel/GDL interface. Parameters of the finite-length Warburg impedance (Z(W)) reported in the literature and estimated from EIS measurements carried out in a PEMFC at different oxygen stoichiometry are considered as a base-line to simulate the GDL-channel impedance spectrum. The results demonstrate that non-stationary depletion of oxygen at the air channel/GDL interface during AC conditions yields the formation of a second loop on the GDL-channel impedance spectrum at low frequencies. In addition, it is demonstrated that the contribution of the AC current amplitude increases the second loop of the GDL-channel impedance spectrum and drifts the GDL-channel impedance spectrum away from its steady-state value which is related to the real component of the impedance response as the frequency is approaching zero. The resulting analytical expression of the GDL-channel impedance is analogous to the general mathematical expression of the finite-length Warburg component. The developed GDL-channel impedance model can simulate and separate the contribution of the impedance response of the GDL from the impedance response associated to oxygen depletion in the channel/GDL interface. This developed model could support other studies focusing on the estimation of diffusion parameters of the GDL from EIS measurements carried out in PEMFCs at different operating conditions.