Statistical Theory of Surface Tension and Molecular Orientations in Nematic Liquid Crystals. III. On Hard Flat Walls

The surface tension of nematic liquid crystals on a hard flat wall is calculated in the mean field approximation assuming that the molecules are non-polar rigid rods and interacting via attractive dispersion forces as well as hard-core repulsions. It is found that the isotropic part of the dispersion force prefers the normal molecular orientation at the wall surface, while the excluded volume effects due to the hard-core repulsions between the wall and molecules and among the molecules both promote the planar alignment on the surface. Possible orientational phase transitions on the wall are predicted to be either a discontinuous planar to normal transition or continuous planar to tilted transition as the temperature is lowered. Therefore, the former type of transition observed really in cyanobiphenyls can be well explained.