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Abstract

Of our main interest in this work is the stabilization of assemblies of topological defects (TDs) in liquid crystals (LCs). Due to the topological origin of TDs, the physics of defects is of interest for all branches of physics, including condensed matter systems, particle physics, and cosmology. LCs represent an ideal testbed for the physics of TDs. In the thesis, we mainly focus on the impact of chirality and different nanoparticles (NPs) on the stability and positioning of assemblies of TDs. The thesis research activities include experimental measurements, theoretical modeling, and numerical simulations. In the experimental part, we focus on the preparation of mixtures of magnetic NPs and CE8 LC. Further, using polarized optical microscopy (POM) and high-resolution calorimetry, the stabilization of Blue Phase (BP) and Twist Grain Boundary A (TGBA) phases have been studied. In theoretical modeling, we use Landau-de Gennes-Ginzburg's mesoscopic approach in terms of nematic tensor and smectic complex order parameters.
We first consider the impact of chirality and saddle-splay elasticity on the stabilization of multiple-twisted structures in nematic LCs. For this purpose, we used the Frank-Oseen approach, where the nematic order is described solely by the nematic director field. Cylindrical geometry was used in which we were able to determine critical conditions for the onset of multiple-twisted structures for different boundary constraints. Such structure leads inevitably contain lattices of TDs in three dimensions due to topological reasons. Next, we were interested in the mechanical forces on NPs immersed in nematic LC structures.
Finally, we considered LC structures exhibiting qualitatively different lattices of line defects. These are realized in blue phases and smectic A (SmA) twist grain boundary phases. BPs and TGBA exhibit disclinations (line TDs in nematic orientational order) and dislocations (line TDs in translational order), respectively. The core structure of disclinations is essentially biaxial and of screw dislocations essentially nematic uniaxial. The fundamental mechanism stabilizing these structures is in fact curvature. However, the efficiency of stabilizing specific TDs depends on NPs’ geometrical details.
The above theoretical results were experimentally verified in mixtures of quasi-spherical magnetic NPs and CE8 liquid crystal. POM and high-resolution calorimetric results demonstrated stabilization of TGBA long-range order as well as modest stabilization of BPI phase, while suppression of the disordered BPIII phase. These results are similar to those found in mixtures of the same LC with gold nanorods, demonstrating that magnetic nanoparticles filling the topological defect cores form probably elongated clusters, which mimic highly anisotropic nanorods.