Monte Carlo simulations of confined nematic systems

In this thesis, a systematic Monte Carlo simulation study of confined nematic and cholesteric systems is carried out. A simple off-lattice model is developed to explore a range of confined systems. Double emulsion nematic shells are investigated with planar anchoring which is then extended to solid particles of different geometries with nematic coatings before progressing to single and n-fold toroidal droplets. For shells and coatings with planar anchoring the total topological charge on both surfaces must be +2. A bipolar structure is found in thick shells and four s=+1/2 defects are found for thin nematic shells. A metastable defect configuration comprising of two s=+1/2 and one s=+1 defects is occasionally observed for intermediate thicknesses. With the addition of chirality, a transition to a twisted bipolar director configuration is observed at all thicknesses. A single toroidal droplet with planar anchoring has a defect free ground state. Previous work has predicted the presence of a twisted director configuration ground state. The relative stabilities of the twisted and untwisted configurations are investigated here. It was found that, for all the systems investigated, the twisted director configuration is only stable for a cholesteric torus. For multiple tori system, with each additional handle the total topological charge on the surface decreases by 2. In a non-chiral nematic system the constraint on the topological charge on the surface is fulfilled by the required number of s=-1 defects located at either the innermost surface of a handle or the join between two tori. With increasing chirality, the s=-1 defects detach from the surface and migrate to form s=-1/2 disclination lines through the cholesteric. In handled droplets with homeotropic anchoring, two s=+1/2 disclination lines are found that, with the addition of chirality form a helical structure around the tube.