Effects of symmetry and novel geometries on observable properties of liquid crystal systems

From atoms to galaxies, symmetry plays a key role in providing structure and coherence to the laws of nature. The aim of this thesis is to investigate the effects of symmetry on a variety of liquid crystal systems. Liquid crystals are anisotropic fluids, in which the rigid and anisotropic constituent molecules have a strong tendency to form mesophases with long-range orientational order. Within this classification, there exists a rich variety of distinct mesophases with varying degrees of orientational and positional order. Tilted smectic liquid crystal phases, such as the smectic-C phase seen in calamitic liquid crystals, are usually treated using the assumption of biaxial orthorhombic symmetry. However, the smectic-C phase has monoclinic symmetry, thereby allowing a disassociation of the principal optic and dielectric axes based on symmetry and invariance principles. In this thesis, we demonstrate this by comparing optical and dielectric measurements for two materials with highly first order direct transitions from the nematic to the smectic-C phases. The results show a high difference between the orientations of the principal axes sets, which is interpreted as the existence of two distinct cone angles for optical and dielectric frequencies. Dispersion of microparticles in nematic liquid crystals offers novel means for controlling both their orientation and position through the combination of topology and external stimuli. In this thesis, we use double emulsions of water droplets inside radial nematic liquid crystal droplets to form various structures, ranging from linear chains to three-dimensional fractals. These systems are modelled as a formation of satellite droplets, distributed around a larger, central core droplet. Furthermore, we extend this reasoning to explain the formation of fractal structures. We show that a distribution of droplet sizes plays a key role in determining the symmetry properties of the resulting geometric structures. Finally, we disperse cuboid and triangular prism shaped particles in a nematic liquid crystal. Experimental observations are compared with numerical simulations to understand the influence of geometry and symmetry on the orientation and position of the particles, both with and without the application of electric fields. We find that a particle’s orientation depends on its aspect ratio and the applied voltage for both particle types. We show that geometric symmetry breaking plays a key role in the dynamics, which prompts the field induced rotation of the particles and allows the triangular prisms to travel perpendicular to the applied electric field.