Thermodynamics and dynamics of the hard-sphere system: From stable to metastable states

- Three different scaling laws, devoted to transport properties of hard-sphere system, are investigated over a wide range of packing fractions.
- A new semiempirical relation linking the transport properties to the excess pressure is derived.
- The present relation allows to better understand the link between the thermodynamic and the dynamic properties of the hard-sphere system.

A set of three different scaling laws is investigated, which are devoted to link the transport properties, i.e. diffusion coefficient, shear viscosity, bulk viscosity and thermal conductivity, to the thermodynamic properties for the athermal hard-sphere system, over the wider range of packing fraction covering the stable and metastable regimes. Except for the thermal conductivity, the Rosenfeld (1999) [15] relation is found to be applicable to the stable states while the Adam and Gibbs (1965) [24] relation holds well for the metastable states. In contrast, the modified Cohen and Turnbull (1959) [25] relation proposed here gives sound support for a universal scaling law connecting the dynamic and thermodynamic properties, over the domain of packing fraction including the stable and metastable states. In particular, it is found that the most relevant control parameter is not the excess entropy, but the logarithm derivative of the excess entropy with respect to the packing fraction. In the same context, the Stokes-Einstein relation between the diffusion coefficient and the shear viscosity is also examined. The possible violation of the Stokes-Einstein relation is investigated over a large domain of packing fractions.