Numerical and theoretical study of a monodisperse hard-sphere glass former.

There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersaturated monodisperse four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.

Geometrical frustration: a study of four-dimensional hard spheres.

The smallest maximum-kissing-number Voronoi polyhedron of three-dimensional (3D) Euclidean spheres is the icosahedron, and the tetrahedron is the smallest volume that can show up in Delaunay tessellation. 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 Euclidean 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 four dimensions is less facile than in three dimensions, which is consistent with earlier observations [M. Skoge, Phys. Rev. E 74, 041127 (2006)]. We conclude that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.

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 to compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys. (to be published)].

Two-step vapor-crystal nucleation close below triple point.

We present the results of Monte Carlo simulations of crystal nucleation from the vapor phase. We studied the Lennard-Jones system at conditions close to, but below, the triple point. This system is expected to show surface melting. The nucleation pathway that we observe consists of two distinct steps. In the first step, a liquid droplet nucleates from the vapor. Its nucleation rate depends strongly on the vapor supersaturation. In the second step, the final crystal phase nucleates in the liquid droplet, provided that this liquid droplet exceeds a minimum size. Our simulations show that within a liquid droplet the crystal nucleation rate does not depend on the vapor supersaturation. In a recent independent study Chen et al. [J. Phys. Chem. B 112, 4069 (2008)] investigated the same phenomenon using umbrella sampling to compute free energy barriers and hence nucleation rates. We use a different numerical approach where we focus on computing the nucleation rates directly using forward-flux sampling. Our results agree with the findings of Chen et al. and both methods observe two-step nucleation. This finding indicates that this nucleation process can be described with a quasiequilibrium theory. Due to different cutoffs for the interaction potential the results cannot be compared quantitatively.