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

Abstract

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.

Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

“…After all, this also implies that the effect of experimentally inevitable size and shape polydispersity calls for further developments to analyze the stability of structures, e.g., along the lines of Refs. [44,45]. Our present results provide a solid basis for future studies of anisotropic particle systems and pave the way for a full understanding of the recent experimental studies performed on systems of nanoscopic truncated cubes.…”

Variable-cell method for stress-controlled jamming of athermal, frictionless grains

“…Both the Platonic and Archimedean solids have recently received attention with regard to optimal [39] and jammed [6,7,40] packing. Also, the selfassembly of thermalized grains belonging to this class have been explored recently [41,42]. Knowledge of how these grains jam at zero temperature will yield insight into the kinetic barriers that inhibit ordering in thermalized systems.…”

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

“…[6][7][8][9][10][11] Concurrently, new simulation techniques were developed to explain the experimentally observed phenomenology and to tackle the complex numerical problems that such investigations bring about. 8,[12][13][14][15][16][17][18][19][20][21][22][23] Most of these simulation studies focussed on convex particles in two-and three-dimensional (2D and 3D) systems, see Refs. 7, 9, 10, 12-14, 18, and 20-22 among others.…”