Nematic ordering and defects on the surface of a sphere: a Monte Carlo simulation study

We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s = + 1/2 defects. However, the predicted tetrahedral symmetry for the defects and the "baseball" director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.