SUBSURFACE DEFORMATIONS IN NEMATIC LIQUID-CRYSTALS - THE HEXAGONAL LATTICE APPROACH

In this paper the existence of subsurface deformations in the orientat ional ordering of a nematic liquid crystal confined to a space between two planar substrates is studied by means of a lattice model. A super position of the anisotropic induced-dipole-induced-dipole and isotropi c Maier-Saupe interaction laws is used to describe intermolecular inte ractions in the nematic phase. To model the nematic phase we use a sim ple-hexagonal lattice, which does not introduce any bulk easy axes. Th e interaction nematic-confining surface (external anchoring) is descri bed with the Rapini-Papoular form. We show that there is always a subs urface deformation in a layer of a few molecules when the intermolecul ar interaction law contains a nonzero fraction of the anisotropic inte raction. The deformation is ascribed to the competition of external an d effective intrinsic anchoring arising from the incomplete intermolec ular interaction close to the surface. We also estimate the extrapolat ion length l(i) as a measure of the intrinsic anchoring. This length t urns out to be of molecular dimensions for the pronounced induced-dipo le-induced-dipole character of the interaction. However, the correspon ding subsurface deformation strength, given by the normal derivative o f the director component, is considerably smaller than 1/l(i), as the simplest estimate suggests. A realistic l(i) can be achieved in our mo del only when the interaction anisotropy is considerably decreased.