In this thesis, we study equilibrium configurations in spherical droplets of nematic and ferronematic liquid crystals with strong radial anchoring. In the nematic case, we work with the commonly used fourth-order bulk potential and the more complicated sixth-order bulk potential, which predicts a bulk biaxial phase at sufficiently low temperatures, while the fourth-order bulk potential does not. In the ferronematic case, we work with a ferronematic free energy which contains a Landau–de Gennes contribution for the liquid crystal configuration; terms to account for the spontaneous magnetisation; and a nemato-magnetic coupling term. We prove a collection of analytical results regarding properties of the radial hedgehog solution in both the nematic and ferronematic cases. We use a range of numerical methods to compute critical points of the Landau–de Gennes and ferronematic free energies. We study the stability of the radial hedgehog solution as a function of temperature and droplet radius and compute bifurcation diagrams at fixed temperatures and droplet radii. We place particular emphasis on the effects of the sixth-order bulk potential on the stability of equilibrium configurations in the nematic case; and on the effects of the nemato-magnetic coupling strength in the ferronematic case. We show that the sixth-order bulk potential has a destabilising effect on the nematic radial hedgehog solution; while stronger nematomagnetic coupling has a stabilising effect on the ferronematic radial hedgehog solution. Moreover, we demonstrate that the solution landscape is richer in ferronematic systems in comparison to the pure nematic systems. In the final chapter, we introduce random noise into each system, which can account for factors such as material imperfections or uncertainties in experimental set-up, and we investigate the impact of noise on the properties of the nematic and ferronematic radial hedgehog solutions.
| Date of Award | 6 Feb 2025 |
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| Original language | English |
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| Awarding Institution | - University Of Strathclyde
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| Sponsors | EPSRC (Engineering and Physical Sciences Research Council) |
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| Supervisor | Apala Majumdar (Supervisor) & Matthias Langer (Supervisor) |
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