Relaxation times, jamming densities, and ideal glass transition densities for hard spheres in a wide range of polydispersities

Abstract

We computationally study the behavior of asymptotic alpha-relaxation times τα as well as jamming densities for equilibrated frictionless polydisperse hard spheres in wide ranges of particle volume fractions φ. Log-normal particle radii distribution (r) with polydispersities δ=⟨Δr2⟩/⟨r⟩=0.1−0.3 in steps of 0.05 is used. We discover that τα(φ) can be fitted well with the Vogel–Fulcher–Tammann (VFT) form. Through the VFT fits, we estimate positions of the ideal glass transition densities φg. For each equilibrated configuration, we calculate equilibrium kinetic pressure Z. Equilibrium pressures can be well described by the Boublík–Mansoori–Carnahan–Starling–Leland fluid equation of state. For each equilibrated configuration, a jammed particle configuration, which is the closest one in the configuration space, is determined. We measure jamming densities φEJ of these configurations and present plots φEJ(φ) for all polydispersities. We demonstrate that the lines τα(φ), φEJ(φ), and Z(φ), as well as values φg, depend significantly on δ. These results show that φg is, in general, distinct from the random close packing limit (φEJ at φ = 0). We plan to use these data in the future to estimate glass equations of state and the configurational entropy for these hard-sphere systems.