Orientational states and phase transitions induced by microtextured substrates

Abstract

We study the orientational states induced in nematic liquid crystals by microtextured substrates with a spatially mixed pattern of different aligning potentials on the mesoscopic scale, i.e., on the order of 0.5 \ensuremath{\mu}m or less. We show that within the Landau--de Gennes framework, the existence of a finite elastic correlation length leads to the prediction of multiple (temperature-dependent) bulk orientational states, separated by phase transition(s). For an alternating stripe pattern of planar and homeotropic aligning potentials, we find three orientational states, denoted by the alignment of their bulk directors as the x, the y, and the yz states. Here z is normal to the substrate, y is parallel to the stripes, and the texturing is along the x direction. In particular, there is a first order phase transition between the two states with the bulk directors in the x direction and in the yz plane. This transition can be induced by varying either the texturing periodicity or the temperature, or through the application of an electric field in the z direction. For nematic liquid crystals sandwiched between two similarly textured substrates, an analysis of the electric-field-induced effects shows that the effective anchoring strength of the textured substrates is tunable as a function of either the texturing periodicity or the temperature. When the anchoring is weak, a field-induced orientational transition is found to be possible at applied voltages lower than that of the Fr\'eedericksz transition.