No abstract

The electrical impedance of an insulating solid containing ions is evaluated in the presence of the generation and recombination of ions. The case of perfectly blocking electrodes is considered. It is shown that in the case where the diffusion coefficients of the positive and negative ions are equal, the expression for the electrical impedance coincides with the one valid in the absence of the generation and recombination of ions, with the bulk density of ions fixed by the chemical reaction describing the generation and recombination of ions. In particular, in the low frequency region, the resistance tends to the value corresponding to the plateau, and the reactance diverges as the inverse of the frequency. The case where the neutral particles, that by decomposition generate the ions, and the positive ions have a vanishing small diffusion coefficient with respect to that of the negative ions is also considered. In this situation, in the series representation, the resistance of the cell presents two plateaus. One in the low frequency region is related to the generation-recombination phenomenon. The other, with a resistance smaller than the previous one, ends at the frequency of Debye. This result is of some importance because it could be the mechanism able to explain the experimental data obtained with hydrogels doped with KCl.

The non-Markovian diffusion of dispersed particles in a semi-infinite cell of an isotropic fluid limited by an adsorbing-desorbing surface is theoretically investigated. The density of dispersed particles in the bulk is a time dependent function and the time dependent density of surface particles is governed by a modified kinetic equation with a time dependent kernel. In this framework, the densities of bulk and surface particles are analytically determined, taking into account the conservation of the number of particles immersed in the sample. This system exhibits anomalous diffusion behavior as well as memory effects in the adsorption-desorption process. The results obtained here are expected to be useful to investigate the adsorption-desorption phenomena of neutral as well as charged particles in an isotropic fluid in contact with a solid substrate when the anomalous diffusion is present.