Melting of rods on a sphere via an intermediate hexatic phase

We have studied, using molecular dynamics simulations, the pressure-induced melting in a monolayer of soft repulsive spherocylinders whose centers of mass are constrained to move on the surface of a sphere. We show that the orientational degrees of freedom of the spherocylinders exhibit nematic order, whereas the positions of their centers of mass exhibit melting transitions that depend on the radius of the confining spherical surface. Our system presents a unique scenario where the decoupling of the orientational degrees of freedom from the positional degrees of freedom leads to an effectively two-dimensional (2D) crystal-to-liquid transition on a spherical surface. Further study of the nature of this 2D melting on a sphere shows that the transition is a two-step process, and there exists a very small window of an intermediate hexatic phase between crystal and liquid phases. Similar results are found for flat monolayers (with the radius of the sphere R → ∞). We show that, interestingly, the structure of the defects, originating from the curvature of the substrate, also changes during melting.