A new semi-empirical approach to performance curves of polymer electrolyte fuel cells

We derive a semi-empirical equation to describe the performance curves of polymer electrolyte membrane fuel cells (PEMFCs). The derivation is based on the observation that the main non-linear contributions to the cell voltage deterioration of H2/air feed cells are deriving from the cathode reactive region. To evaluate such contributions we assumed that the diffusion region of the cathode is made by a network of pores able to transport gas and liquid mixtures, while the reactive region is made by a different network of pores for gas transport in a liquid permeable matrix. The mathematical model is largely mechanistic, with most terms deriving from phenomenological mass transport and conservation equations. The only full empirical term in the performance equation is the Ohmic overpotential, which is assumed to be linear with the cell current density. The resulting equation is similar to other published performance equations but with the advantage of having coefficients with a precise physical origin, and a precise physical meaning. Our semi-empirical equation is used to fit several set of published experimental data, and the fits showed always a good agreement between the model results and the experimental data. The values of the fitting coefficients, together with their associated physical meaning, allow us to asses and quantify the phenomenology which is set on in the cathode as the cell current density is increased. More precisely, we observe the development of the flooding and of the local decrease of the oxygen concentration. Further developments of such a model for the cathode compartment of the fuel cell are discussed.