Structure of hard-sphere metastable fluids

Abstract

A rational-function approximation method to analytically derive the radial distribution function $g(r)$ and the structure factor $S(q)$ of a hard-sphere fluid is revisited. The method provides a fluid structure thermodynamically consistent with a given equation of state. The Carnahan-Starling and a recently derived Pad\'e (4,3) equations of state are considered. While the Carnahan-Starling equation leads to functions $g(r)$ and $S(q)$ even for densities larger than the crystalline close-packing density, their physical value is questionable already in the metastable fluid region. In the case of the much more reliable Pad\'e equation of state, the method shows the existence of a threshold density, beyond which no meaningful fluid structure can be derived. This threshold value, whose signature is a diverging slope of $g(r)$ at the contact distance, coincides with the one associated in the literature with the glass transition.