On the Free-Volume Model of the Liquid-Glass Transition

TLDR

The free‑volume model assumes a step‑function correlation factor that separates gas‑like and solid‑like displacements, and molecular‑dynamics studies show that at high densities the self‑diffusion coefficient drops sharply below Enskog predictions. The authors refine the free‑volume model by linking a step‑function correlation factor to each displacement magnitude and expressing the free volume relative to the Bernal glass, thereby clarifying its connection to Enskog theory. The improved model accurately captures the density‑dependent deviation from Enskog predictions, indicating that the liquid–glass transition can be explained within a van der Waals framework with temperature‑dependent hard‑core corrections.

Abstract

We have improved the free-volume model for molecular transport in dense fluids, as developed in earlier papers, by taking account of the variable magnitude of the diffusive displacement. The development is carried through in a way which may display more clearly the relation between the free-volume model and the Enskog theory. Implicit in the free-volume development is the association, on the average, of a correlation factor f(a) with each magnitude, a, of the displacement. It is assumed that f(a) is a step function which is zero, because of the predominance of back scattering, for a < a* and unity for a > a.* This corresponds to dividing the displacements sharply into two categories, one “gaslike” and the other “solidlike.” Molecular dynamics computations have shown that the self-diffusion coefficient in the hard-sphere fluid at the highest densities is falling precipitously, with increasing density, away from the Enskog values. It appears that this density trend, which was attributed to back scattering, if continued, would lead to a continuous solidification. It is shown that the magnitude and density trend of this deviation are described satisfactorily by the free-volume expression, where the free volume is referred to the specific volume of the Bernal glass. We conclude that at least the molecular transport manifestation of a liquid–glass transition can be deduced entirely within the framework of the van der Waals physical model for liquids with due corrections for the variation of the effective hard-core radius with temperature. The free-volume model results from a crude, but physically plausible, approach to this problem.