Nematic liquid crystal in contact with periodically patterned surfaces

Abstract

Nematic liquid crystals confined between two different substrates, possessing alternating stripe patterns of planar and homeotropic anchoring, are studied within the Frank–Oseen theory, in which the anchoring energy function is given by the Rapini–Papoular expression. By numerical minimization of the free energy we determine phase transitions between uniform and distorted nematic textures. The calculations reveal that these phase transitions can be triggered by changing the shift of the stripe patterns with respect to each other. A hybrid nematic cell model together with an effective anchoring strength can be used to describe the phase behaviour for sample thicknesses larger than the periodicity of the stripe pattern. Rich phase behaviour is predicted for the case of a generalized expression for the surface free energy.