Beyond Salsburg–Wood: Glass equation of state for polydisperse hard spheres

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.