A simple model of ac hopping surface conductivity in ionic liquids

The boundary conditions proposed to discuss the charge exchange taking place in an ionic liquid in contact with non-blocking electrodes are reconsidered in a dynamic situation. Assuming that the variation of the bulk ionic current density depends linearly on the surface value of the ionic current density, the frequency dependence of the phenomenological parameter is determined. The analysis has been performed in the framework where the relaxation times are smaller than a maximum relaxation time tau(M), and that the response function is independent on the value of the relaxation time. Using simple physical considerations, an expression for the surface conductivity describing the ionic charge exchange at the electrode is obtained. According to our calculations, its frequency dependence is similar to that predicted for the electric conductivity in disordered materials when the mechanism is of the hopping type. From measurements of impedance spectroscopy, by the best fit of the experimental data, the temperature dependence of the hopping time, of the dc surface conductivity, and of the diffusion coefficient are derived. They are in good agreement with the theoretical predictions obtained with the random distribution of surface energy barrier.