Transport through mixed proton, oxygen ion and electron (hole) conductors: Goldman–Hodgkin–Katz-type equation

Many high temperature oxides and low temperature polymeric materials transport protons, oxygen ions, and electrons or holes. These materials are candidates as membranes for fuel cells and electrolyzers. This manuscript examines non-equilibrium steady state transport through such membranes under the assumption of local equilibrium. A simple equivalent circuit analysis is given for transport through mixed proton, oxygen ion, and electron (hole) conducting membranes. The cell potential can be described in terms of transport parameters of charged species (H+, O2− and e or h) and internal EMFs given in terms of chemical potentials of neutral species (μH2μH2, μO2μO2). The resulting equation for cell potential is similar to the Goldman–Hodgkin–Katz (GHK) equation used in cell physiology. Transport through a fuel cell based on such materials is examined. Effects of electrolyte/electrode interfaces are explicitly included in the analysis. Fluxes of H2 and O2 through the membrane are evaluated at open circuit and under load. They obey Onsager reciprocity relations, inclusive of interface effects. The analysis also shows that the chemical potentials of H2 and O2 and electric potential, φ, exhibit abrupt changes across interfaces.