Ionic adsorption and equilibrium distribution of charges in a nematic cell

Abstract

We consider the steady-state distribution of ionic charges in a nematic sample of slab shape, whose limiting surfaces are supposed to adsorb positive ions. Our analysis allows the calculation of the electrical potential at the surfaces and in the bulk, and of the chemical potential versus the thickness of the sample d. The surface density of ions and the intensity of the electric field in the double layer are evaluated in terms of d. In the limit of small d we show that the surface density of adsorbed ions is proportional to the thickness, whereas in the opposite limit of large d it is nearly independent of it. We analyze also the influence of the surface charges on the effective anchoring energy of nematic liquid crystals, as well as the thickness dependence of this parameter. Our analysis generalizes similar calculations previously published. @S1063-651X~99!08902-3# The influence of adsorbed ions and the resulting surface electric field on the anchoring properties of nematic liquid crystals ~NLC! with ionic conductivity has been analyzed by different groups @1‐6#. Recently the ionic adsorption has been invoked to explain the thickness dependence @7# of the anisotropic part of the anchoring energy characterizing the NLC-substrate interface @8‐10#. To obtain the thickness dependence of the anchoring energy it is necessary ~1! to assume a selective ionic adsorption from the surfaces, due to some electrochemical forces at the walls; ~2! to evaluate the surface density of the adsorbed charges versus the thickness of the sample; ~3! to analyze the effect of the resulting electric field in the surface double layer on the NLC. In Ref. @8# a simple model was proposed to evaluate the surface density of adsorbed charges, by extending the classical Langmuir problem of adsorption @11#. The aim of this paper is to present a general theory for the adsorption phenomenon in liquids, removing all the simplifying hypotheses used in Ref. @8#. We deduce, in addition to the surface density of adsorbed charges, the chemical potential and the electrical potential at the surface and in the middle of the sample. The limiting cases of small and large thickness are considered separately. Our results show that in the limit of small thickness, the surface charge density is nearly proportional to the thickness. On the contrary, in the limit of large thickness, the surface charge density saturates to a value independent of the thickness. These results confirm the result obtained in the framework of the simple model presented in Ref. @8# in these two limiting cases. The possible applications of our study to the surface properties of the NLC are also discussed. Let us consider a sample of slab shape of a liquid. Let d be the thickness of the slab and e the dielectric constant of the liquid. The liquid is globally neutral. The chemical reaction X!B 1 1C 2 , where X is a molecule of the liquid and B 1 and C 2 the ions resulting from its dissociation, has an