The influence of an external field on the effective anchoring energy of a nematic liquid crystal in contact with a substrate is theoretically analyzed. Our analysis is performed on the hypothesis that the electrodes are perfectly blocking and that there is no selective ion adsorption. The proposed 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. Our theory is in qualitative agreement with published data investigating the influence of the bias on the saturation voltage.

The influence of the bias-voltage on the anisotropic part of the nematic surface energy is analyzed. The experimental data show a strong dependence of the anchoring strength on the bias-voltage when the electrodes of the nematic cell are covered with WO3. The observed dependence can be interpreted taking into account the ions dissolved in the liquid crystal. We propose a model in which the effect of the bias-voltage is to collect the ions near the electrodes, in a surface layer whose thickness is of the order of the Debye's screening length. The surplus of electric field due to this ions confinement gives rise to an electrostatic contribution to the total energy that can be considered as a surface energy. The proposed model is in good agreement with the experimental data. The model is used to interpret the observed independence of the anchoring strength on the bias-voltage when the (indium-tin-oxide) electrode is covered with a film of polyimide, or it is without any covering. The influence of a charge emission from the electrodes under the bias voltage on the anchoring energy is also analyzed. Possible applications of the observed phenomenon are discussed.

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We present a general model to describe the influence of the ionic 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 quadratic and linear on the density of adsorbed ions, respectively. 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 both found to depend linearly on the surface density of adsorbed charges. Approximated formulas reported in literature are derived from our general equations as particular cases, and their limits discussed. An expression for the surface polarization in nematic liquid crystal due to the ionic adsorption is also deduced. Our analysis is performed in the framework of the Poisson-Boltzmann theory, where dimensionless ions are treated within a mean field approach. Possible extensions of our model are indicated.

A model to determine the steady-state distribution of ionic charges in a liquid sample, in the shape of a slab, whose limiting surfaces are supposed to adsorb positive ions with different adsorption energies, is proposed. It is used to explain the asymmetric electro-optical response in a liquid-crystal cell recently observed. The ionic adsorption gives rise to a difference of potential between the surfaces which can be responsible for the existence of an internal field. It changes the effective voltage thresholds for the reorientation of the liquid crystal when external fields are applied.