Phase behavior and defect structure of soft rods on a sphere

Using particle-resolved molecular-dynamics simulations, we compute the phase diagram for soft repulsive spherocylinders confined on the surface of a sphere. While crystal (K), smectic (Sm), and isotropic (I) phases exhibit a stability region for any aspect ratio of the spherocylinders, a nematic phase emerges only beyond a critical aspect ratio lying between 8.0 and 9.0. As required by the topology of the confining sphere, the ordered phases exhibit a total orientational defect charge of +2. In detail, the crystal and high-density smectic phases exhibit two +1 defects at the poles, whereas the high-density nematic phase features four +1/2 defects, which are connected along a great circle. For aspect ratios above the critical value, lowering the packing fraction drives a sequence of transitions: the crystal melts into a smectic phase, which then transforms into a nematic through the splitting of the +1 defects into pairs of +1/2 defects. Our simulations data can be experimentally verified in Pickering emulsions and are relevant for understanding the morphogenesis in epithelial tissues.