Correct use of excess configurational entropies to study the ideal glass transition in hard-sphere systems with continuous polydispersity

Abstract

We systematically apply the resolution to the configurational entropy paradox from our previous paper [V. Baranau and U. Tallarek, J. Chem. Phys. 147, 224503 (2017)] to study configurational entropies and the glass transition in polydisperse hard-sphere systems with log-normal particle radius distributions (r) over a wide range of polydispersities δ=⟨Δr2⟩/⟨r⟩=0.1−0.3. The resolution implies the careful use of excess quantities for vibrational and configurational entropies. We obtain the fluid entropy from the fluid equation of state and the vibrational entropy from the glass equation of state; thereby, the configurational entropy becomes their difference. We discovered that the Adam–Gibbs relation is able to fit the asymptotic alpha-relaxation times τα of the hard-sphere systems under study at high volume fractions φ when our excess configurational entropies are supplied. For polydispersity δ = 0.1, the Adam–Gibbs relation is able to fit the data over the entire range of φ studied. Ideal glass transition densities φg obtained in this way are below predictions from the Vogel–Fulcher–Tammann fits. Our results indicate by extrapolation that the glass close packing limit φGCP for monodisperse systems is ∼0.65, consistent with granular matter studies. Our configurational entropies extrapolated to the monodisperse case are found to match Edwards entropies from granular matter studies very well.