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

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

Quantification of Order in the Lennard-Jones System

We conduct a numerical investigation of structural order in the shifted-force Lennard-Jones system by calculating metrics of translational and bond-orientational order along various paths in the phase diagram covering equilibrium solid, liquid, and vapor states. A series of non-equilibrium configurations generated through isochoric quenches, isothermal compressions, and energy minimizations are also considered. Simulation results are analyzed using an ordering map representation [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000); Truskett et al., Phys. Rev. E 62, 993 (2000)] that assigns to both equilibrium and non-equilibrium states coordinates in an order metric plane. Our results show that bond-orientational order and translational order are not independent for simple spherically symmetric systems at equilibrium. We also demonstrate quantitatively that the Lennard-Jones and hard sphere systems sample the same configuration space at supercritical densities. Finally, we relate the structural order found in fast-quenched and minimum-energy configurations (inherent structures).Comment: 35 pages, 8 figure