An independent link model of simple fluids; random close packing limit

TL;DR

This paper introduces a novel statistical approach to model simple fluids, deriving analytical expressions for key properties and accurately predicting the random close packing limit of 0.637.

Contribution

It presents a new independent link model that simplifies the fluid's behavior, applicable to hard sphere fluids, and accurately predicts the random close packing density.

Findings

Predicts the radial pair correlation function g(R) qualitatively correctly.

Provides an analytical equation of state matching low and medium densities.

Accurately predicts the random close packing density as 0.637.

Abstract

A new approach to modelling the behaviour of simple fluids is presented. Starting from the usual expression of the partition function of N molecules, a Fourier transformation is performed. It is argued that the N(N-1)/2 dynamical variables kpq in the reciprocal space featuring the link between 2 molecules p and q can reasonably be considered independent in the thermodynamical limit. Treated as a set of effective independent particles, their statistical behaviour is analogous to a Bose-Einstein gas. Expressions of the partition function, of the radial pair correlation function and of the pressure are derived, and a special attention is given to the mathematical inter-consistency of those quantities. The results, which are independent of the exact shape of the intermolecular potential, are applied to the simple case of hard sphere fluids. An analytical expression of the radial pair correlation function is derived as well as of the equation of state. The model predicts a qualitatively satisfactory behaviour for g(R), and it provides numerically correct values for the equation of state at low and medium densities, although at higher densities the contact value of g(R)is underestimated. Quite interestingly it predicts for the maximum random close packing density the correct value 0.637 .