RESUMO
The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and negative ions have the same mobility and that the electric potential profile across the sample satisfies the Poisson's equation. The results cover a rich variety of scenarios, including the ones connected to anomalous diffusion.
RESUMO
We demonstrate theoretically that the presence of ions in insulating materials such as nematic liquid crystals may be responsible for the dielectric spectroscopy behavior observed experimentally. It is shown that, at low frequencies, an essentially non-Debye relaxation process takes place due to surface effects. This is accomplished by investigating the effects of the adsorption-desorption process on the electrical response of an electrolytic cell when the generation and recombination of ions is present. The adsorption-desorption is governed by a non-usual kinetic equation in order to incorporate memory effects related to a non-Debye relaxation and the roughness of the surface. The analysis is carried out by searching for solutions to the drift-diffusion equation that satisfy the Poisson equation relating the effective electric field to the net charge density. We also discuss the effect of the mobility of the ions, i.e., situations with equal and different diffusion coefficients for positive and negative ions, on the impedance and obtain an exact expression for the admittance. The model is compared with experimental results measured for the impedance of a nematic liquid crystal sample and a very good agreement is obtained.