Random Energy Barrier Model for AC Electrode Conductivity

We investigate the electric response of an electrolytic cell of water and KCl, limited by gold electrodes, to derive information on the role of the electrodes in the spectra of the real and imaginary parts of the electric impedance of the cell. Our experimental data can be interpreted by means of the Poisson–Nernst–Planck model with Ohmic boundary conditions for the electrodes, where the surface conductivity is consistent with that derived by a random-walk model for the charge exchange on the electrodes. By using a best-fit procedure, the direct current (DC) conductivity and the hopping time are determined. The measurements have been performed in the absence and presence of a DC bias. In the absence of DC bias, the agreement between the theoretical predictions and the experimental data is good over the full explored frequency range. On the contrary, in the presence of the DC bias, the theoretical predictions in the low-frequency range do not describe the experimental results very well and the agreement decreases, increasing the value of the bias. This result indicates that the hopping phenomenon describing the conduction across the electrodes has peculiar characteristics different from those of the bulk. The dependence of the hopping time and of the DC conductivity on the electric field is reasonably well described by the existing models proposed for the hopping conduction in the bulk.