Theoretical modeling of electrode impedance for an oxygen ion conductor and metallic electrode system based on the interfacial conductivity theory

We discuss the thermodynamic meaning of the oxygen overpotential, and derive a fundamental theoretical equation for the impedance spectrum of a system comprising an oxygen ion conductor and a metallic electrode under a mixture of oxygen and inert gas, as might be found at the cathode of a solid oxide fuel cell. Our derivation combines aspects of classical irreversible thermodynamics, Wagnerʹs theory and the concepts of the interfacial conductivity theory. The oxygen overpotential at the oxygen ion conductor/metallic electrode interface under steady state conditions is found to be related to the rate of entropy production by neutral oxygen diffusion and desorption from the interface to the gas phase. The generalized impedance equation derived in this study can be applied not only under open cell conditions but also in the steady state polarized condition, which corresponds to experimental impedance measurements under a d.c. bias voltage. When the oxygen flux, resulting from a small perturbation force, follows Fickʹs first law, and the relaxation process proceeds via the change in adsorbed concentration of oxygen on the electrode surface, the impedance spectrum becomes semicircular in the Nyquist diagram. The electrode resistance and the electrode capacitance estimated from equivalent electric circuit analysis reflect the chemical reaction response, or in other words, the chemical resistance and chemical capacitance.