Theoretical models of a liquid crystal of banana-shaped colloidal particles
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Since the discovery of liquid crystals in 1888 and the first theoretical models in the late 1940s, the interest in liquid crystals of particles of all different shapes and sizes has only increased. In addition to the nematic and smectic phases observed in liquid crystals of hard rods, liquid crystals of banana-shaped particles were observed to exhibit additional phases such as the twist-bend and splay-bend phase. In this thesis, two different theoretical models to describe a liquid crystal of banana-shaped particles are studied. Landau-de Gennes theory is shown to be able to describe the twist-bend and splay-bend phases, but has some drawbacks due to its phenomenological nature. Density functional theory in combination with bifurcation analysis is then proposed as an alternative approach that is based on the microscopic details of the particles, which are encoded in the excluded volume. With the use of symmetry arguments, a basis of the excluded volume of two banana-shaped particles in terms of symmetry-adapted functions is constructed. This microscopic approach opens up many opportunities for describing the complicated phases and phase transitions of liquid crystals of anisotropically-shaped particles.