Effect of quenched size polydispersity on the ordering transitions of hard polyhedral particles

Monodisperse polyhedral nanocrystals with O(h) (octahedral) symmetry self-assemble into various mesophases and crystal structures at intermediate and high concentrations. In this work, the effect of quenched size polydispersity on phase and jamming behavior has been studied via molecular simulations for three representative O(h) polyhedral shapes; namely, cubes, cuboctahedrons, and truncated octahedrons. Polydispersity is set by the standard deviation "δ" of an underlying Gaussian distribution of particle sizes, and is "quenched" in that it is fixed in a given uniphase sample. Quenched polydisperse states are relevant to: (i) equilibrium behavior for small enough δ when phase segregation does not occur, and (ii) actual experimental behavior for arbitrary δ when dense states are reached at a rate faster than the relaxation of slow diffusion-driven fractionation modes. Space-filling polyhedrons (cubes and truncated octahedrons) are found to be more robust with respect to the nucleation of orientational and translational order at high polydispersities compared to the non-space-filling cuboctahedron, with the former shapes exhibiting an onset of jamming behavior at a critical polydispersity δ(t) that is about twice larger than that for the latter (δ(t) ≈ 0.08). Further, the orientational ordering in cubes is found to be highly resilient to polydispersity, leading to the formation of a dense, orientationally aligned, and translationally jammed state. Overall, increasing size polydispersity enhances the range of pressures where the mesophases occur.