Surface electric-field-induced instabilities in a homeotropically orientednematic liquid crystal sample

The effect of a surface electric field produced by ionic adsorption on the molecular orientation of a nematic liquid crystal sample is analyzed. The e igenvalue problem for a semi-infinite medium is analytically solved both fo r strong and weak anchoring situations. The threshold instabilities are num erically determined and it is shown that the homeotropic pattern can be des tabilized also in the situation of strong anchoring. The dependence of the threshold field on the anchoring strength and on the surface polarization i s determined by taking into account also the coupling of the quadrupolar co mponent of the flexoelectric coefficient with the field gradient.