Influence of ionic transport on deformations of homeotropic nematic layers with positive flexoelectric coefficients

Electric field-induced deformations of homeotropic nematic liquid crystal layers were studied numerically. A positive sum of the flexoelectric coefficients and a small negative dielectric anisotropy of the nematic material were adopted. Finite surface anchoring strength was assumed. The flow of ionic current was taken into account, the weak electrolyte model being used for description of the electric properties. The director orientation, the electric potential and the ion concentrations were calculated as functions of the coordinate normal to the layer. Calculations show that the threshold for deformation depends on the distributions of the ions (which are influenced by their mobilities), by the ion generation constant and by the properties of the electrodes. When the electrodes have pronounced blocking character and the ion concentration is large, a high and non-uniform electric field is created by the subelectrode ion space charges. This causes drastic decrease of the threshold voltage, much below the value U_f valid for an insulating nematic. At moderate concentrations, the electric field gradient arises in the bulk due to the difference between the mobilities of positive and negative ions. It favours deformation, therefore the threshold is reduced below U_f. When the electrodes are well conducting, there are no significant space charges and the threshold voltage remains close to U_f. The same value occurs when the space charges are negligible at very low ion contents.