Models for ionic contribution to the complex dielectric constant of nematic liquid crystals

Abstract

We analyze the models that account the ionic contribution to the complex dielectric constant of a nematic liquid crystal. We compare the predictions of the model of [Sawada, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 318, 225 (1998)] based on the assumption that the electric field in the liquid coincides with the applied one, with the model of Macdonald where the electric field in the sample is determined in self-consistent manner by solving the equation of Poisson. We show that the model of Sawada , widely used to determine the bulk density of ions and their diffusion coefficient in liquid crystal cells, predicts a thickness dependence of the real and imaginary parts of the dielectric constant different from that predicted by the model of Macdonald. On the contrary, the predictions of the two models coincide for what concerns the frequency dependencies of the two components of the dielectric constant. By considering a typical case, we show that the numerical values of the ionic properties derived by means of the model of Sawada may differ even more than 1 order of magnitude by those predicted by the model of Macdonald. A rescaling procedure allowing to evaluate the bulk density of ions and the ionic diffusion coefficient determined by means of the model of Sawada in agreement with the one of Macdonald is proposed.