Solution of the Onsager model for the structure of rigid rods confined on a spherical surface

We consider a free energy, within the framework of the Onsager approximation, for a spatially and orientationally inhomogeneous distribution of hard rods confined on a spherical surface. These rods interact with each other though the excluded-volume interaction, forming a textured nematic structure on the spherical surface at high surface coverage. Our numerical solution to the model shows that the splay state, where on average rods line up in parallel to the longitudes on the spherical surface, is the only stable state. Other types of textures that have recently been suggested were also tested and all yield higher free energy than that of a ground splay state. We also provide a study of the disorder-splay transition, which is shown to have first-order characteristics.