Orientational behavior of particles in self-assembled crystalline states of hard polyhedra

Hard particles are good models of self-assembly, can produce rich phase behavior in self-assembled states in terms of translational and orientational configuration of particles. These can form liquid crystals, plastic crystals (which exhibit long range translational order but complete orientational disorder), different types of complex crystal structures and even disordered structures in entropy driven self-assembly. In spite of having translational symmetry breaking present in the self-assembled states, different types of orientational configurations can occur in the system i.e. complete orientational disordered states i.e. plastic crystals, complete orientational ordered states and orientational glass phase where few particles are ordered and others are disordered, independent of the system length scales. We report these three kinds of orientational configurations in crystal phases in NPT Monte Carlo simulations for both sharp and sphero polyhedra (polyhedra with rounded vertices). In spite of having more rotational entropy in sphero shapes, rather than their underlying sharp shapes, we found the robustness of self-assembled structures and the existence of different kind of orientational states present in the systems. We predict a direct correlation between the shape attributes of the building blocks and the occurrence of the different kinds orientational states in self-assembled crystalline structures which can be used for material designing.