Abstract
We reconstruct glass equations of state for polydisperse hard spheres with the help of computer simulations. To perform the reconstructions, we assume that hard-sphere glass equations of state have the form Zg(φ, φJ) = Zg(φJ/φ), where Zg, φ, and φJ are the reduced glass pressure (PV/NkBT), sphere volume fraction (packing density), and jamming density of the current basin of attraction, respectively. Specifically, we use the form X = ∑iciYi, where X = (φJ/φ) − 1 and Y = 1/(Zg − 1). Our reconstructions converge to the well-known Salsburg–Wood and free volume equations of state in the limit φ → φJ, but they are also applicable for values of φ ≪ φJ. We support the ansatz Zg(φ, φJ) = Zg(φJ/φ) with extensive computer simulations. We use log-normal distributions of particle radii (r) and polydispersities δ=⟨Δr2⟩/⟨r⟩=0.1−0.3 in steps of 0.05. By supplying the fluid equation of state (EOS) into the new glass EOS, we evaluate equilibrium jamming densities φEJ for a range of φ. By using the ideal glass transition densities φg as an input φ, we estimate the corresponding glass close packing limits φGCP = φEJ(φg). We use the Boublík–Mansoori–Carnahan–Starling–Leland fluid EOS, and we estimate φg from the Vogel–Fulcher–Tammann fits—but our method can work with any choice of the fluid EOS and φg estimates. We show that our glass EOS leads to much better predictions for φEJ(φ) than the standard Salsburg–Wood glass EOS.
Highlights
Collections of frictionless hard spheres are simple yet extremely popular models1–3 in condensed-matter physics, which are used to investigate properties of solids, 4 fluids,5–8 glasses,1,9–15 and colloids.16,17 Many interesting phenomena can be recovered when simulating equilibration and compression of frictionless hard spheres: the glass transition1,11,18 and glass close packing (GCP) limit;1,11,15 jamming and the J-point;19,20 and melting and freezing transitions.9,21,22 There are fundamental connections between many of these quantities
One of the areas of study of frictionless hard spheres is the determination of the “glass” equation of state (EOS),27,28 i.e., the functional form of the kinetic pressure of a system of hard spheres that is allowed to move in the configuration space only inside a current basin of attraction, belonging to a given mechanically stable configuration
Limit is the highest equilibrium jamming density because the plot φEJ(φ) is non-decreasing. It does not preclude the existence of nonequilibrium jammed configurations with φJ > φGCP, but we do not discuss them in this paper
Summary
Collections of frictionless hard spheres are simple yet extremely popular models in condensed-matter physics, which are used to investigate properties of solids, 4 fluids, glasses, and colloids. Many interesting phenomena can be recovered when simulating equilibration and compression of frictionless hard spheres: the glass transition and glass close packing (GCP) limit; jamming and the J-point; and melting and freezing transitions. There are fundamental connections between many of these quantities. The glass EOS is supposed to be in the form Zg(φ, φJ), where Zg is the glass reduced pressure and φJ is the jamming density that corresponds to the current system configuration at density φ (see Sec. II for detailed definitions). To further validate the results, we supply the estimated glass EOS into the Boublík–Mansoori–Carnahan–Starling– Leland (BMCSL) EOS, which describes the equilibrium fluid pressure Zfl(φ) of polydisperse hard spheres well.. These data are taken from our previous papers..
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