Subsurface deformations in nematic liquid crystals: The hexagonal lattice approach

In this paper the existence of subsurface deformations in the orientational ordering of a nematic liquid crystal confined to a space between two planar substrates is studied by means of a lattice model. A superposition of the anisotropic induced-dipole--induced-dipole and isotropic Maier-Saupe interaction laws is used to describe intermolecular interactions in the nematic phase. To model the nematic phase we use a simple-hexagonal lattice, which does not introduce any bulk easy axes. The interaction nematic-confining surface (external anchoring) is described with the Rapini-Papoular form. We show that there is always a subsurface deformation in a layer of a few molecules when the intermolecular interaction law contains a nonzero fraction of the anisotropic interaction. The deformation is ascribed to the competition of external and effective intrinsic anchoring arising from the incomplete intermolecular interaction close to the surface. We also estimate the extrapolation length lᵢ as a measure of the intrinsic anchoring. This length turns out to be of molecular dimensions for the pronounced induced-dipole--induced-dipole character of the interaction. However, the corresponding subsurface deformation strength, given by the normal derivative of the director component, is considerably smaller than 1/lᵢ, as the simplest estimate suggests. A realistic lᵢ can be achieved in our model only when the interaction anisotropy is considerably decreased.