Scaled Particle Theory for Hard Sphere Pairs. II. Numerical Analysis

TL;DR

This paper applies an extended scaled particle theory to accurately compute the pair correlation function of hard sphere fluids across a wide density range, comparing results with simulations and analyzing thermodynamic properties.

Contribution

It provides a numerical analysis of the extended scaled particle theory for hard sphere pairs, including structure, pressure, surface tension, and Tolman length predictions.

Findings

Accurately captures fluid structure across densities

Pressure predictions vary with thermodynamic route

Provides numerical estimates for surface tension and Tolman length

Abstract

We use the extension of scaled particle theory (ESPT) presented in the accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to calculate numerically pair correlation function of the hard sphere fluid over the density range $0\leq \rho\sigma^3\leq 0.96$. Comparison with computer simulation results reveals that the new theory is able to capture accurately the fluid's structure across the entire density range examined. The pressure predicted via the virial route is systematically lower than simulation results, while that obtained using the compressibility route is lower than simulation predictions for $\rho\sigma^3\leq 0.67$ and higher than simulation predictions for $\rho\sigma^3\geq 0.67$. Numerical predictions are also presented for the surface tension and Tolman length of the hard sphere fluid.