Simulation of Heterogeneous Colloidal Particles Immersed in Liquid Crystals

This thesis describes an investigation of interactions between colloidal particles immersed in a liquid crystal. The presence of colloidal particles in the liquid crystal distorts the director field distorted from its uniform orientation. These elastic distortions produce topological defects around the particles, which induce anisotropic interactions between them, and these anisotropic interactions can be used to manufacture non-closed packed colloidal crystals, such as diamond lattices, which are interesting in photonic applications. First, different types of liquid crystals, the mathematical tools to describe the anisotropic nature of liquid crystals, the Landau-de Gennes free-energy model to investigate the particle’s interaction, and different kinds of topological defects are described. Moreover, previous work regarding the interaction of particles with the same applied boundary conditions in both nematic and cholesteric liquid crystal are discussed. Second, the lattice Boltzmann method is introduced in order to couple the molecular dynamics particles to the computational fluid mesh, and the simulation is performed in the open source molecular dynamics package, LAMMPS. Next, we explore anisotropic interactions with minima at specific orientations of particles with heterogeneous boundary conditions inside both nematic and cholesteric liquid crystals, which have not been observed so far. The results show that when particles are put at different distances and angles with respect to each other, new types of defect structures are produced, depending on the relative distances and directions. In the cholesteric liquid crystal, the value of pitch affects the defect structures and induced forces.