Tilted Directors at the Boundaries

In a real nematic cell, however, it is very difficult to satisfy the conditions (4.15). Moreover, to avoid degenerate solutions, when both clockwise and counterclockwise director rotations are possible (Fig. 4.1), the boundaries are specially prepared with tilted director orientation 

FIGURE 4.3. The Prederiks transition in different geometries (a) nematic between two coaxial cylinders (b) quasi-homeotropic orientation with opposite director tilt at the boundaries and (c) hybrid aligned (homeoplanar) nematic cell. 

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A new type of electrohydrodynamic instability in liquid crystals with tilted directors at the boundaries was revealed by Pikin et al. [63]. This instability is characterized by a domain pattern parallel to the projection of the initial director orientation. It is supposed that the director angle with respect to the substrate remains unchanged (x>2 -plane) while the periodic two-dimensional vortex motion appears in the yz-plane, where the 2 -axis is perpendicular to the substrates (Fig. 5.9). These domain structures seem to be observed in [64, 65] with the oblique director orientation achieved by means of oblique SiO evaporation. When the voltage exceeds its critical value the second domain pattern appears along the y-axis. 

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