Heterogeneity in structurally arrested hard spheres

When cooled or compressed sufficiently rapidly, a liquid vitrifies into a glassy amorphous state. Vitrification in a dense liquid is associated with jamming of the particles. For hard spheres, the density and degree of order in the final structure depend on the compression rate: simple intuition suggests, and previous computer simulation demonstrates, that slower compression results in states that are both denser and more ordered. In this work, we use the Lubachevsky-Stillinger algorithm to generate a sequence of structurally arrested hard-sphere states by varying the compression rate. We find that while the degree of order, as measured by both bondorientation and translation order parameters, increases monotonically with decreasing compression rate, the density of the arrested state first increases, then decreases, then increases again, as the compression rate decreases, showing a minimum at an intermediate compression rate. Examination of the distribution of the local order parameters and the distribution of the root-mean-square fluctuation of the particle positions, as well as direct visual inspection of the arrested structures, reveal that they are structurally heterogeneous, consisting of disordered, amorphous regions and locally ordered crystal-like domains. In particular, the low-density arrested states correspond with many interconnected small crystal clusters that form a polycrystalline network interspersed in an amorphous background, suggesting that jamming by the domains may be an important mechanism for these states. Copyright c © EPLA, 2008 Solidification of a liquid —either into amorphous glass [1] or periodic crystal [2]— is a ubiquitous phenomenon in nature and in numerous applications, whose mechanism remains one of the most challenging questions in the physical sciences. Intuitively, slow cooling or compression leads to a perfect crystal, while an amorphous or glassy state is obtained upon rapid cooling or compression, the structural mechanism for the latter being jamming of the particles which prevents their relaxation to the equilibrium crystalline state [3]. As the simplest system that exhibits both jamming and crystallization, the hard-sphere model provides an excellent platform for studying structures of liquids, glasses, granular materials, and random media. An important recent insight in the study of hard-sphere packing is the clarification of the so-called random close packing (RCP). Torquato et al. [4,5] showed that the (a)ZQL and ZYS contributed equally to this work. (b)E-mail: [email protected] (c)E-mail: [email protected] notion of RCP as the maximum attainable density with a unique value in a random collection of spheres was ill-defined. These authors proposed instead the concept of maximally random jammed state (MRJ), corresponding to a state that minimizes an appropriately defined order parameter among all statistically homogeneous and isotropic jammed structures. Using an algorithm due to Lubachevsky and Stillinger [6] for increasing the sphere diameters linearly in time (mimicking the compression of the spheres), these authors found that the density of the final jammed state increases monotonically with decreasing rate, with an attendant increase in the structural order, as measured by a bond-orientation order parameter and a translation order parameter. In this letter, we show that the density of a structurally arrested state obtained by compression of hard spheres can in fact be a non-monotonic function of the compression rate, that increased order does not necessarily result in higher packing density for an arrested state, and that the structure of the arrested states is highly heterogeneous.