Schimming, Cody2022-09-262022-09-262022-07https://hdl.handle.net/11299/241713University of Minnesota Ph.D. dissertation. July 2022. Major: Physics. Advisor: Jorge Vinals. 1 computer file (PDF); xvi, 166 pages.Nematic liquid crystals are materials in which the underlying constituents are anisotropic which, in turn, leads to anisotropic properties and response at the meso and macro scales. As has been shown in recent experiments on nematic systems composed of complex aggregates, anisotropic polymers, and biologically inspired active materials, as the constituents become more complicated, the material properties become more anisotropic. Thus, nematic liquid crystals represent an interesting opportunity to probe the interplay between elasticity, anisotropy, geometry, and topology. This dissertation focuses on these interplays in an effort to expand the understanding of the structure and dynamics of mesoscopic textures in nematics, particularly two phase domains and topological defects. To accomplish this, we review the shortcomings of the classical Landau-de Gennes theory when posed with the problem of anisotropic elasticity. We then develop a computational, self-consistent field theory to advance the state of computational mesoscale modelling of anisotropic nematics. We show that, despite the increased computational complexity, this theory can resolve three dimensional nematic configurations well. We apply it directly to the case of two phase domains and disclinations in systems of lyotropic chromonic liquid crystals, of which many recent experiments have demonstrated anisotropic properties and structures. We find good qualitative and quantitative agreement with the experiments, while positing new directions for further experimental research. We also review existing theoretical gaps in the study of three dimensional nematic disclination lines and loops. These are much more complicated objects, both geometrically and topologically, than their two dimensional counterparts. We develop a mathematical construction of the disclination loop charge, which leads to the definition of a novel tensor which we call the “disclination density tensor.” This tensor is locally defined in terms of the nematic tensor order parameter and can be used to identify both the location and geometric structure of line disclinations. We further show that the disclination density tensor is related to the conservation of topological charge, and this connection is used to derive a kinematic law of motion for nematic disclinations. We show with analytical calculation and numerical computation that the disclination density tensor and the derived line velocity are important tools that give insight into the structure and dynamics that reflect the complex interplay between elasticity, anisotropy, geometry, and topology of disclination lines in three dimensional nematics. The results of this dissertation represent not only a new set of tools for future research and engineering endeavors, but also fundamental insights into the nature of complex structures in nematic liquid crystals.enDefect IdentificationDisclinationsElasticityField TheoryNematic Liquid CrystalsTactoidsThesis or Dissertation