Phase behavior and design rules for plastic colloidal crystals of hard polyhedra consideration of directional entropic forces

Plastic crystals - like liquid crystals - are mesophases that can exist between liquids and crystals and possess some of the characteristic traits of each of these states of matter. Plastic crystals exhibit translational order but orientational disorder. Here, we characterize the phase behavior in systems of hard polyhedra that self-assemble plastic face-centered cubic (pFCC) colloidal crystals. We report a first-order transition from a pFCC to a body-centered tetragonal (BCT) crystal, a smooth crossover from pFCC to an orientationally-ordered FCC crystal, and an apparent orientational glass transition wherein long-range order fails to develop from a plastic crystal upon an increase in density. Using global order parameters and local environment descriptors, we describe how particle shape influences the development of orientational order with increasing density, and we provide design rules based on the arrangement of facets for engineering plastic crystal behavior in colloidal systems. We show how directional entropic forces (which are set by particle shape) give rise to distinct behaviors in entropic systems with translational order and orientational disorder.