Topological Defects in Spherical Nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S^2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S^2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle rather than at the vertices of a regular tetrahedron. This arises from the high elastic anisotropy of the system in which splay (K_1) is far softer than bending (K_3). We also introduce and study a lattice nematic model on S^2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We establish the existence of a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_1/K_3 -> 0. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.