The Wagner theory of mixed conduction was applied to foreign and native species simultaneously in order to determine the open-circuit potential of a concentration cell. General derivations of the open-circuit potential were presented for mixed conductors which contained protonic species, native ions and electrons. The equations which were derived for oxides with mixed electronic, native ionic and protonic conductivity showed that transport number determinations in gradients of O pressure included possible contributions from protonic species. Moreover, the presence and nature of the protonic conductivity contributions could be determined by measuring the open-circuit potential in a gradient of water vapor or H pressure, without any O pressure gradient. In this case, the sign and the magnitude of the open-circuit potential depended upon, and provided information concerning, the type of protonic charge carrier. Investigations indicated that protonic conductivity made a significant contribution in the case of many oxides, and that free proton transport predominated over hydroxyl and hydronium mechanisms.

D.P.Sutija, T.Norby, P.Björnbom: Solid State Ionics, 1995, 77, 167-74