A statistical theory of the isotope effect in proton conducting oxides

The anomalous kinetic isotope effect for high temperature proton conductors such as doped SrCeO3 is theoretically investigated in the framework of a Kramers' turnover approach. Application of this approach leads to the good accord between theory and observation data. It is suggested that proton transfer processes in such materials may correspond to a regime when the friction coefficient is small but the average energy loss of the charge carrier to the local environment is not too small. In this sense, the proton conducting oxides are rather corresponding to intermediate-to-underdamped regime of viscous damping than to the extremely low damped case. We picture the transfer of protons as though there is a strong coupling between degrees of freedom of the system that affects the attempt frequency for the protons. This explains the known contradiction between experimental results (in particular, observed isotope effects for these materials) and predictions of the absolute rate theory and gives some evidence for a collective mechanism of proton transport processes. Comparison with other theoretical approaches which describe relevant dynamic aspects of the proton/lattice system is made. It is shown that the present theory is consistent with a dynamic extension of the transition state theory. The most likely speculation is that such an extension may be motivated by a dynamical chemical bonding in oxides.