Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

Abstract

Numerous recent investigations have been devoted to the determination of the equilibrium phase behavior and packing characteristics of hard nonspherical particles, including ellipsoids, superballs, and polyhedra, to name but just a few shapes. Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calcu- * To whom correspondence should be addressed lations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two firstorder phase transitions as the density increases: first a liquid-solid transition and then a solidsolid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities, verifying the result of a previous qualitative study [J. Chem. Phys., 2011, 135, 151101]. The freezing-and melting-point packing fractions for this transition are respectively φ F = 0.496 ± 0.006 and φ M = 0.591 ± 0.005. At higher densities, we find that the CT phase undergoes another firstorder phase transition to one associated with the densest-known crystal, with coexistence densities in the range φ ∈ [0.780±0.002, 0.802± 0.003]. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. Specifically, we systematically study the structural characteristics of the MRJ packings, including the centroidal pair 1 correlation function, structure factor and orientational pair correlation function. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (≈ 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers.

Perspective: Basic understanding of condensed phases of matter via packing models

“…Hard nonspherical particles exhibit a richer phase diagram than that of hard spheres because the former can possess different degrees of translational and orientational order; see Refs. 74,281,283,285,289,291,299,300,302,306,307,[310][311][312]314, and 317. Nonsphericalparticle systems can form isotropic liquids, a variety of liquid-crystal phases, rotator crystals, and solid crystals.…”

“…300 A study of the entire phase diagram of truncated tetrahedra showed that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. 314…”

Ensemble Theory for Stealthy Hyperuniform Disordered Ground States

“…2 for a vivid illustration. During the last decade, a variety of disordered hyperuniform states have been identified that exist as both equilibrium and nonequilibrium phases, including maximally random jammed particle packings [33][34][35][36], jammed athermal granular media [37], jammed thermal colloidal packings [38,39], cold atoms [40], transitions in nonequilibrium systems [41,42], surfaceenhanced Raman spectroscopy [43], terahertz quantum cascade laser [44], wave dynamics in disordered potentials based on supersymmetry [45], avian photoreceptor patterns [46], and certain Coulombic systems [47]. Moreover, disordered hyperuniform materials possess novel physical properties potentially important for applications in photonics [25][26][27]48,49] and electronics [50][51][52].…”

Confined disordered strictly jammed binary sphere packings

“…For example, while bulk MRJ packings of nonspherical particles that span a wide range of shapes, including ellipsoids [78][79][80], superballs [81,82], and polyhedra [24,25,72,83] have been studied in detail, nothing is known about confined MRJ packings of nonspherical particles. Understanding how confined MRJ packings of nonspherical particles differ from their bulk counterparts and confined MRJ sphere packings are outstanding questions.…”