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Title: Defects in liquid crystals : mathematical and experimental studies
Author: Lewis, Alexander
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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Nematic liquid crystals are mesogenic materials that are popular working materials for optical displays. There has been an increased interest in bistable liquid crystal devices which support two optically distinct stable equilibria. These devices typically exploit a complex geometry or anchoring conditions, which often induces defects in the equilibria. There remains a great deal to be understood about the structure of the defects and how they stabilize multiple equilibria in modern devices. This thesis focuses on four problems: the first three explore the effect of confinement and defects on nematic equilibria in simple geometries, with the aim of exploring multistability in these geometries; the fourth problem concerns the fine structure of point defects, essential for future modelling of nematic equilibria in more complex geometries. Firstly, we study nematic liquid crystals confined to two-dimensional rectangular wells using the Oseen-Frank theory. Secondly, we study equilibria within a semi-infinite rectangular domain with weak tangential anchoring on the surfaces. Thirdly, we study nematic equilibria within two-dimensional annuli. We derive explicit expressions for the director fields and free energies of equilibria within these geometries and discuss the stability of the predicted states. These three problems are motivated by the experimental work on colloidal nematic liquid crystals, which we interpret in the context of our results. Finally, we study the fine structure and stability of the radial hedgehog defect in the Landau-de Gennes theory with a sixth order bulk potential, relevant to the observability of global biaxial phases in a model with higher order potential terms.
Supervisor: Aarts, Dirk ; Majumdar, Apala ; Howell, Peter Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Liquid Crystals ; Defects in liquid crystals ; Radial hedgehog ; fd-virus