Isotope effect and proton hopping in high-temperature protonic conductors

Studies of the 'isotope effect' in proton migration most often involve substitution of D for i-I. In the case of high-temperature protonic conductors (HTPCs) having the perovskite structure, Arrhenius behavior of the conductivity is consistently found, with activation energy for deuterium E-D > E-H by 0.03 to 0.06 eV, and a ratio of preexponentials A(H)/A(D) < 1. In addition, the magnitude of the preexponentials is generally lower than expected by about one order of magnitude. These results are examined in terms of four theories. Satisfactory description of the principal facts is given by a formal semi-classical theory, which is widely used in chemistry, and alternatively by the escape theory, originated by Kramers, which treats collisions of a light atom with a matrix of more massive atoms.