Frequency Dependence of the Proton Conductivity of Ice and Water

The frequency dependence of the proton conductivity of ice and water is theoretically investigated in a wide frequency range. The electric field of the inhomogeneous distribution of proton current carriers and their finite mass are taken into account. The first factor is responsible for the difference in the behavior of the transverse and longitudinal conductivities, the appearance of two different characteristic times, and an additional increase in the conductivity at frequencies above the Debye frequency. Physically, the difference in the behavior of the transverse and longitudinal conductivities is due to the collective oscillations of current carriers in the second case. At the same time, the finite masses or inertial properties of current carriers lead to a faster asymptotic decrease in the conductivity as the frequency tends to infinity and to the elimination of the violation of the sum rule characteristic of the conventional Debye frequency dependence. The obtained results are compared to the experiment.