How Free Volume Does Influence the Dynamics of Glass Forming Liquids.

In this article we show that inverse free volume is a natural variable for analyzing relaxation data on glass-forming liquids, and that systems obey the general form, log(τ/τ ref ) = (1/ V free ) × f ( T ), where f ( T ) is a function of temperature. We demonstrate for eight glass-forming liquids that when experimental relaxation times (log τ), captured over a broad pressure-volume-temperature ( PVT ) space, are plotted as a function of inverse free volume (1/ V free ), a fan-like set of straight line isotherms with T -dependent slopes ensues. The free volume is predicted independently of the dynamic results for each state point using PVT data and the Locally Correlated Lattice (LCL) equation of state. Taking f ( T ) ∝ 1/ T b , we show that, for each of the systems studied, only the single, system-dependent parameter, b , is required to collapse the fan of linear isotherms into a straight line. We conclude that log τ is a function of the combined variable, 1/( V free T b ), and because it is linear, it allows us to write an explicit analytic expression for log τ that covers a broad PVT space.