Jamming of polydisperse hard spheres: The effect of kinetic arrest

Abstract

We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the system gets arrested into a glass state as the relaxation time exceeds the compression speed. Further compression yields a jammed configuration that can be regarded as the infinite pressure configuration of that glass state. Consequently, we find that the density of jammed packings varies from 0.638 to 0.658 for polydisperse hard spheres and from 0.635 to 0.645 for pure hard spheres upon decreasing the compression rate. This demonstrates that the density at which the systems falls out of equilibrium determines the density at which the system jams at infinite pressure. In addition, we give accurate data for the jamming density as a function of compression rate and size polydispersity. [2] that the densest packing of identical hard spheres is achieved by the stacking of close-packed hexagonal planes yielding a packing fraction φ = πσ 3 N/6V ≈ 0.74. However, when a system of hard spheres is compressed quickly it does not reach this maximum density and it jams at lower densities. Jamming phenomena are generic since atomic, colloidal and granular systems can all be jammed in a state far out of equilibrium by quickly cooling, compressing or unloading [3].Many authors speculate that the packing fraction of the densest amorphous hard-sphere configuration is welldefined [4,5] although its precise value is not known as random-close-packing densities φ rcp ranging from 0.634 [5] to 0.648 [6] are reported. On the other hand, Torquato et al [7] argued that φ rcp is ill-defined as the density can always be increased by introducing crystalline order into the system. Very recently, it is speculated and/or deduced from mean-field models that jammed configurations can be regarded as the infinite pressure limit of glassy states [8,9]. The reason is that the glass phase for each density on the metastable fluid branch consists of a certain group of glassy states, which will all follow the same metastable glass branch up to the same jamming density by fast compression [8,9].In this letter, we study jammed configurations of hard spheres as a function of compression speed. We show that denser amorphous packings can be generated even without introducing any crystalline order by lowering the compression speed. However, in the case of identical spheres, the system (partially) crystallizes for sufficiently slow compressions. Crystallization can be avoided by introducing size polydispersity. A small size polydispersity affects φ rcp only slightly but hampers crystal growth severely. This allows us to study jamming for a wider range of compression rates. We find volume fractions ranging from 0.638 till 0.658 for hard spheres with 10% size polydispersity upon decreasing the compression rates. Additionally, we give accurate data for the jamming density φ J as a function of compression rate and size polydispe...

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…Now, we also relate this to the change of behavior of ν max , which is consistent with Ref. [162]. Figure 3.7 shows the maximum density ν max as a function of the inverse size ratio ω −1 for different size distributions and for different compression rates.…”

“…The reported high-density limit for random close packings [197] is 3% greater than that of Bernal packings [198] and still higher than our φ RCP values, and can be approached for extremely fast compression [66,162]. For estimates of φ RCP for random close packings of hard spheres see Ref.…”

“…The effect of using various expansion rates is more comprehensively studied in Refs. [66,67,161,162,200], so that we do not display more of our data. We did not study extremely slow rates and rate-dependence systematically.…”

“…3.8 perfect agreement with the free volume theory for all considered systems at the densities (φ J −ν) 10 −8 . Only one free parameter is required for the free volume theory, φ J , even though in other studies two fitting parameters are used [159,162]. In order to capture the deviation of the compressibility factor from the free volume theory as the density difference increases, theories which take into account the geometry and structure of the free volume should be developed.…”

“…Fluid and jammed configurations of hard sphere mixtures are examined for various size distributions at slow compression rates [66,67,161,162]. Several authors proposed theories to compute the amorphus jamming density of binary and polydisperse hard sphere mixtures, see Refs.…”