Elasticity of defects and structures in uniaxial liquid crystals

This dissertation consists of six chapters. Following the introductory review of defects and elastic distortions in liquid crystals (Ch. 1), crossing of disclination lines in nematic slabs is discussed in Ch.2. Depending on the Frank index of the original pair of disclinations, the crossing transforms the lines either into surface disclinations or into bulk disclinations. In the first scenario, the stability of surface lines depends on the relative homotopy group, π₁(R, R˜). In the second scenario, the ensuing lines remain topologically stable.; The third chapter is devoted to the theoretical discussion of the enercretical stability of ring defects of strengths 1/2 against point defects. The divergence (also called surface-like) elastic terms dramatically change the stability of point and ring defects.; In the fourth chapter, we discuss the role of the non-linear elastic term in the properties of defects and structures in systems with one-dimensional periodicity. Using finger print texture of cholesteric liquid crystals, we demonstrate that the profile of dislocation can be described properly only if the nonlinear term is included into the free energy density.; Static as well as dynamic aspects of layer undulation instability of the cholesteric stripe phase are discussed in the fifth chapter. Macroscopic periodicity enables one to study experimentally (by polarized microscope) various phenomena in detail. Observed displacement of layers around the onset of instability is far larger than the value predicted by the existing theory. We explain this discrepancy by assuming “soft anchoring” of the layer at boundaries. The sinusoidal to saw-tooth transformation of the undulation pattern is explained by a simple model. Dynamics of undulation are described. A summary follows at the end.