Non-Debye relaxation in the dielectric response of nematic liquid crystals: Surface and memory effects in the adsorption-desorption process of ionic impurities

We demonstrate theoretically that the presence of ions in insulating materials such as nematic liquid crystalsmay be responsible for the dielectric spectroscopy behavior observed experimentally. It is shown that, at lowfrequencies, an essentially non-Debye relaxation process takes place due to surface effects. This is accomplishedby investigating the effects of the adsorption-desorption process on the electrical response of an electrolytic cellwhen the generation and recombination of ions is present. The adsorption-desorption is governed by a non-usualkinetic equation in order to incorporate memory effects related to a non-Debye relaxation and the roughness ofthe surface. The analysis is carried out by searching for solutions to the drift-diffusion equation that satisfy thePoisson equation relating the effective electric field to the net charge density. We also discuss the effect of themobility 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 experimentalresults measured for the impedance of a nematic liquid crystal sample and a very good agreement is obtained.