Configurations and stability of thin films of nematic liquid crystal

Al Ghabshi, Bushra (2021) Configurations and stability of thin films of nematic liquid crystal. PhD thesis, University of Glasgow.

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Abstract

Liquid crystals are unique materials exist between the solid phase and liquid phase, and in certain ranges of temperature they show different arrangements of the molecules. Depending on the amount of order in the material, there are many different types of liquid crystal states. The nematic liquid crystals are an example of a material that has no positional order but has local orientational order, this gives rise to textures (patterns in the material) that are attractive to study. Nematic liquid crystal is an example of a material that has orientational order and no long-range positional order, this gives rise to textures (patterns in the material) that are attractive to study. This thesis concerns liquid crystals in thin films and their configurations and stability. The aim of this thesis to to explore minimum energy configurations for thin liquid shells, coupled with surface energy and curvature effects. In particular we study a thin film of liquid crystal spanning two coaxial rings, where we use the energy derived in [66] for a thin nematic liquid crystal and study the nematic film within the Landau-de Gennes model which is described through the Q-tensor theory. This thesis consists of a study of two main problems. The first is the study of the equilibrium of open surfaces (with a boundary) and involves a careful derivation of natural boundary conditions associated with minimising a general surface energy. We prove a number of results about the equations and also derive a framework to study the stability of the solutions to the equilibrium by considering the incremental equations. We demonstrate this approach in some simple examples. The second main problem is a study of the equilibrium of a thin film of liquid crystal suspended between two coaxial rings. We use the results developed in the first part of the thesis to derive the equilibrium equations and boundary conditions and solve these equations numerically for a range of dimensionless parameters related to the thin film. We perform our numerical study using two different, but related, parameterisations of the order tensor. We specialise to consider axisymmetric solutions. Finally we study the stability of the isotropic distribution (state) on a fixed catenoidal geometry, we demonstrate the emergence of defects of charge -1/2 at the onset of nematic order. We study the nonlinear equations numerically using a nonlinear Jacobi iteration.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Supported by funding from Sultan Qaboos University.
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
Supervisor's Name: Roper, Dr. Steven
Date of Award: 2021
Depositing User: Theses Team
Unique ID: glathesis:2021-82720
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 03 Mar 2022 09:33
Last Modified: 08 Apr 2022 16:47
Thesis DOI: 10.5525/gla.thesis.82720
URI: https://theses.gla.ac.uk/id/eprint/82720

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