Relaxation in a liquid proceeds by numerous pathways, each depending on temperature and pressure. It has remained a challenge to delineate different modes of relaxation and to bring them into a framework where they can be treated on a common footing. To reach such a goal, it is necessary to understand what combinations of variables control liquid dynamics in different regimes of temperature and pressure.
We have shown  that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition.
Our results suggest that free volume is controlled by two distinct mechanisms in liquids of repulsive spheres. First, thermal fluctuations perform work against the pressure to open up free volume. This mechanism is governed by the quantity T/pσ3 (where T is the temperature, p is the pressure and σ is the particle diameter). Second, at a given T/pσ3, pressure forces soft spheres to overlap so that they behave like hard spheres of smaller diameter. This mechanism is controlled by pσ3/ϵ (where ϵ is the energy scale in the inter-atomic potential). These two mechanisms combine to determine the ratio of thermal energy over an effective pressure of the system. The collapse of our soft-sphere data onto a hard-sphere relaxation time curve implies that the relaxation time of the soft-sphere liquid depends largely on this ratio.
The next challenge is to test whether systems with attractive as well as repulsive interactions can be described by generalizations of these two mechanisms for opening up free volume. Furthermore it would be interesting to see whether this method also works in systems with shear, where temperature over pressure has proven to be a useful control parameter, especially in the limit of small pressures.
 “Mapping the glassy dynamics of soft spheres onto hard-sphere behavior,” M. Schmiedeberg, T. K. Haxton, S. R. Nagel and A. J. Liu, Europhysics Lett., 96 36010 (2011)