Polarized states of hybrid aligned nematic layers

Electric polarization arising in hybrid aligned nematic liquid crystal layers with rigid boundary conditions is studied numerically by solving the torques equation and Poisson equation. Three phenomena that give rise to the polarization are taken into account: flexoelectricity, surface polarization and adsorption of ions. The director orientation within the layer, as well as the distribution of electric potential and space charge density are calculated for layers deformed by an external magnetic field. The role of the ionic space charge is investigated. For a particular set of parameters of a model substance, the voltage arising between the layer surfaces varies from 10(-1) V (in an extremely pure nematic) to 10(-3) V ( in material with a typical ion concentration). The surface polarization yields an additional voltage (of the order 10(-2) V) nearly independent of the ion concentration. The effect of simultaneous flexoelectric polarization and ion adsorption is evidently different from a linear superposition of their separate contributions. The flexoelectric polarization leads to partial separation of ions of opposite signs. In the case of positive flexoelectric coefficients, a thin sublayer of positive charge arises at the planar-orienting boundary plate. The negative charge is displaced towards the homeotropically aligning plate. The magnitude of this effect increases with the magnetic field. The surface phenomena introduce additional subsurface charges.