Ionic adsorption and equilibrium distribution of charges in a nematic cell

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.