Binary mixture of hard disks as a model glass former: Caging and uncaging

I have proposed a measure for the cage effect in glass forming systems. A binary mixture of hard disks is numerically studied as a model glass former. A network is constructed on the basis of the colliding pairs of disks. A rigidity matrix is formed from the isostatic (rigid) sub--network, corresponding to a cage. The determinant of the matrix changes its sign when an uncaging event occurs. Time evolution of the number of the uncaging events is determined numerically. I have found that there is a gap in the uncaging timescales between the cages involving different numbers of disks. Caging of one disk by two neighboring disks sustains for a longer time as compared with other cages involving more than one disk. This gap causes two--step relaxation of this system

Signature of nearly icosahedral structures in liquid and supercooled liquid Copper

A growing body of experiments display indirect evidence of icosahedral structures in supercooled liquid metals. Computer simulations provide more direct evidence but generally rely on approximate interatomic potentials of unproven accuracy. We use first-principles molecular dynamics simulations to generate realistic atomic configurations, providing structural detail not directly available from experiment, based on interatomic forces that are more reliable than conventional simulations. We analyze liquid copper, for which recent experimental results are available for comparison, to quantify the degree of local icosahedral and polytetrahedral order

Crystallization in a model glass: influence of the boundary conditions

Using molecular dynamics calculations and the Voronoi tessellation, we study the evolution of the local structure of a soft-sphere glass versus temperature starting from the liquid phase at different quenching rates. This study is done for different sizes and for two different boundary conditions namely the usual cubic periodic boundary conditions and the isotropic hyperspherical boundary conditions for which the particles evolve on the surface of a hypersphere in four dimensions. Our results show that for small system sizes, crystallization can indeed be induced by the cubic boundary conditions. On the other hand we show that finite size effects are more pronounced on the hypersphere and that crystallization is artificially inhibited even for large system sizes.Comment: 11 pages, 2 figure

Defects in Crystalline Packings of Twisted Filament Bundles: II. Dislocations and Grain Boundaries

Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross section and out-of-plane interfilament twist in bundles. Using non-linear continuum elasticity theory of columnar materials, we study the favorable coupling of twist-induced stresses to the presence of edge dislocations in the lattice packing of bundles, which leads to a restructuring of the ground-state order of these materials at intermediate twist. The stability of dislocations increases as both the degree of twist and lateral bundle size grow. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist, giving rise to a rich class of "polycrystalline" packings.Comment: 10 pages, 7 figure

Geometrical Frustration: A Study of 4d Hard Spheres

The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio

Hard sphere crystallization gets rarer with increasing dimension

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].Comment: 15 pages, 5 figure

The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment

One of the most spectacular phenomena in physics in terms of dynamical range is the glass transition and the associated slowing down of flow and relaxation with decreasing temperature. That it occurs in many different liquids seems to call for a "universal" theory. In this article, we review one such theoretical approach which is based on the concept of "frustration". Frustration in this context describes an incompatibility between extension of the locally preferred order in a liquid and tiling of the whole space. We provide a critical assessment of what has been achieved within this approach and we discuss the relation with other theories of the glass transition.Comment: 48 pages, 13 figures, submitted to J. Phys : Cond. Matte

Hard Discs on the Hyperbolic Plane

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.Comment: 4 pages, 3 figures, included, final versio

Polytetrahedral Clusters

By studying the structures of clusters bound by a model potential that favours polytetrahedral order, we find a previously unknown series of `magic numbers' (i.e. sizes of special stability) whose polytetrahedral structures are characterized by disclination networks that are analogous to hydrocarbons.Comment: 4 pages, 4 figure

Locally Preferred Structure and Frustration in Glassforming Liquids: A Clue to Polyamorphism?

We propose that the concept of liquids characterized by a given locally preferred structure (LPS) could help in understanding the observed phenomenon of polyamorphism. ``True polyamorphism'' would involve the competition between two (or more) distinct LPS, one favored at low pressure because of its low energy and one favored at high pressure because of its small specific volume, as in tetrahedrally coordinated systems. ``Apparent polyamorphism'' could be associated with the existence of a poorly crystallized defect-ordered phase with a large unit cell and small crystallites, which may be illustrated by the metastable glacial phase of the fragile glassformer triphenylphosphite; the apparent polyamorphism might result from structural frustration, i. e., a competition between the tendency to extend the LPS and a global constraint that prevents tiling of the whole space by the LPS.Comment: 11, 6 figures, Proceedings of the Conference "Horizons in Complex Systems", Messina; in honor of the 60th birthday of H.E. Stanle