title: Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model.
abstract: We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.
authors.affiliation: ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland.
authors.forename: Alan M
authors.initials: AM
authors.lastname: Luo
authors.affiliation: ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland.
authors.forename: Stefan
authors.initials: S
authors.lastname: Wenk
authors.affiliation: ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland and School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, United Kingdom.
authors.forename: Patrick
authors.initials: P
authors.lastname: Ilg
mesh_terms: D016880:Anisotropy; D003102:Colloids; D003198:Computer Simulation; D004058:Diffusion; D004548:Elasticity; D050866:Liquid Crystals; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009038:Motion; D013696:Temperature
chemical_list: D003102:Colloids