Soft-Sphere Equation of State

Abstract

The pressure and entropy for soft-sphere particles interacting with an inverse twelfth-power potential are determined using the Monte Carlo method. The solid-phase entropy is calculated in two ways: by integrating the single-occupancy equation of state from the low density limit to solid densities, and by using solid-phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice-dynamics high-density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two-thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.

Density of states estimation for soft core system

“…That concavity produces a double peak in the probability distribution when the temperature is T ∼ 0.23. The scaled density estimated by assuming T = 0.23 is ρ † ∼ 1.155, which is quite similar to the value obtained by Hoover et al [2,3] Therefore, the origin of solid-fluid first-order phase transition of this system must be ascribed to the concavity of the DOS. The system size, N = 108, is smaller than that commonly used in the conventional molecular dynamics simulation.…”

“…[2,3] Hereafter, length, temperature and energy are scaled by σ, ε/k B and ε, respectively. The Helmholtz free energy of this system are expressed as follows:…”

Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

“…Figure 8 presents the phase diagram of the IPL model, spanned by the softness parameter 1/n and by the scaled quantity γ. We also plotted fluid-solid coexistence data obtained by other authors using different approaches [25,26,27,33]. The data reported in [25] refer to a single-occupancy solid in which each particle is confined within a spherical cell whose diameter is set equal to the FCC nearest-neighbor lattice spacing.…”

“…The IPL potential has been the subject of many studies [25,26,27]. This potential provides a continuous path from hard spheres (n → ∞) to the one-component plasma (n = 1).…”

Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization

“…A variety of purely repulsive forces have been considered, including power law potentials as the high-temperature limit of the van der Waals interaction, 44 8,7,46 as well as their variants. 47 With its flat plateau and as sharp a cutoff as possible, the square-shoulder potential is very sensitive to the structure of the pair distribution function and thus the quintessential shortranged interaction.…”