ABSTRACT
In the first part of this chapter, we present a general model to describe the influence of the ion adsorption on the anisotropic part of the surface energy of a nematic liquid crystal in contact with a substrate. We show that in the limit of small adsorption energy, the exponential approximation for the electric field of ionic origin works well. In this limit, the dielectric and flexoelectric contributions to the surface energy are, respectively, quadratic and linear on the density of adsorbed ions. In the opposite limit of large adsorption energy, the exponential approximation for the electric field does not work, and the two contributions to the surface energy are found to depend both linearly on the surface density of adsorbed charges. Approximated formulae reported in literature are derived from the general equations as particular cases, and their limits discussed. An expression for the surface polarization in nematic liquid crystal due to the ion adsorption is also deduced. In the second part of the chapter the influence of an external field on the effective anchoring energy of a nematic liquid crystal in contact with a substrate is theoretically analyzed in the hypothesis that the electrodes are perfectly blocking and that there is no selective ion adsorption. We discuss the ionic contribution to the surface energy in general terms, obtaining explicit formulae valid for the weak and strong adsorption energies. The analysis is performed in the framework of the Poisson-Boltzmann theory, where the ions are assumed dimensionless, and the problem is faced by a mean field approach. The theory predicts an effective anchoring energy dependent on the applied dc voltage. According to the sign of the dielectric anisotropy and of the flexoelectric coefficient the dependence of the anchoring energy strength with the bias can be monotonic or not. For large bias voltage the effective anchoring energy strength tends to a constant value.
