Role of symmetry in the correlated orientational disorder phase of entropic crystals

Correlated orientational disordered phase is a thermodynamic phase with the constituent particles following some conserved laws or correlation despite the orientational disorder present in the system. Polyhedral particles in the presence of hard interaction serve the purpose of studying the orientational disorder in entropy driven self-assembly. We report the computational evidence of the role of symmetry of both particle and self-assembled crystal in the single-component system of anisotropic polyhedra in the correlated orientational disordered phase. The point groups of the particle and crystal structure appear to make a direct correspondence with the existence of multiple unique orientations of the system satisfying all the orientational conserved quantities towards the correlation. As a signature of correlation, the system exhibits orientationally frozen state at sufficiently higher packing fractions and discrete orientational hopping of the particles are observed at comparatively lower density solids. This symmetry relationship appears to control all the aspects of orientational correlation in the crystalline solids which might be useful to draw fundamental insights about the disordered crystalline solids with orientational correlation as well as designing the disorder in the crystals.