Pergamenshchyk V. Continuum theory of a spatially restricted nematic liquid crystal.

Thesis is devoted to the problem of consistent incorporation of a surface and the divergence elastic and free energy terms in the continuum theory of a spatially restricted nematic liquid crystal, and to studying related orientational and elastic effects. It is shown that the fundamental inconsistency of the standard elastic theory is that it presupposes the symmetry of an infinite nematic medium whereas in the proximity of a surface this symmetry is violated. A consistent theory is developed, which sets a microscopic relation between the behaviour of the density and scalar order parameter in a thin surface layer and macroscopic behaviour of the observable bulk director, and provides a general procedure of finding the director for a finite . An effective boundary condition, through which the divergence terms contribute to the director distribution, is derived. This boundary condition shows that the divergence elasticity of a nematic liquid crystal can be an intrinsic source of pattern formation in the director field. It is shown that it is the joint action of the K24 and K13 terms that is responsible for stripe domains, observed in submicrometer thin hybrid nematic films on isotropic substrates. Other effects related to the surface like elasticity are predicted. Hierarchy of stripe and circular domains that occurs in a surface polarized homeotropic layer under the electric field action is explained. A non-Debye power low mechanism of screening of the field induced by surface-adsorbed charges is found, and а self-consistent theory of anchoring phenomena related to such charges is developed.