Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential

Abstract

In the same sense as in the extended law of corresponding states [M. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], we propose the use of the second virial coefficient to map the hard-sphere potential onto a continuous potential. We show that this criterion provides accurate results when the continuous potential is used, for example, in computer simulations to reproduce the physical properties of systems with hard-core interactions. We also demonstrate that this route is straightforwardly applicable to any spatial dimension, does not depend on the particle density and, from a numerical point of view, is easy to implement.

Comment on ‘Pseudo hard-sphere viscosities from equilibrium molecular dynamics’

“…After equilibration, the thermostat was switched off, velocities were reinitialized, and the simulation was continued in the microcanonical ensemble, running for 10 4 τ with an integration step size of 2 × 10 −4 τ . As a check, we have confirmed that the simulations accurately reproduce the deviations from the Carnahan-Starling equation of state reported in [9]. For both methods, each simulation contained N = 15 3 = 3375 particles, and results were averaged over ten independent simulations.…”

“…In particular, we simulate true hard spheres using event-driven molecular dynamics simulations using the approach of Alder et al [3]. The code used is an adaptation of the one in [4], modified to periodically output the stress tensor integrated over a short time interval (using equation (9) in [3]). Simulations were run for 7.5 × 10 4 τ after equilibration, with τ = √ βmσ 2 the time unit.…”

“…For the PHS system, we used the LAMMPS simulation package [8]. Note that the PHS pair interaction is given by [9] U PHS (r) = { 50 ( 50 49…”

Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

“…A continuous potential has been proposed using a physical criterion based on the extended law of corresponding states [79] and the Mie potential [73] Baéz et al mapped the HS potential to a continuous function [80]. This equivalent function is referred as pseudo hard-sphere (PHS) and has been used to successfully reproduce thermodynamic properties of the HS fluid in a wide range of volume fractions [80]. Here, we use the PHS pair potential to straightforwardly determine the force between HS particles in a standard MD algorithm.…”

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft-repulsive colloidal rods

“…In the case of spherical particles, Medina-Noyola and coworkers demonstrated that structural properties and diffusion coefficients of spheres interacting with a repulsive Sutherland potential can be mapped onto the corresponding properties of hard-sphere (HS) systems, using effective diameters dependent on density and temperature [13,14]. More recently, Jackson and coworkers obtained an effective soft-repulsive potential based on the Mie model in order to reproduce structural properties of the HS system [15], a procedure that has been extended to square-well potentials [16] and applied successfully in molecular simulations of colloidal systems [17]. The approach of using potential models with soft repulsive and attractive interactions of variable range, such as the Mie model for chain molecules [18,19], have had important implications in the prediction of a wide variety of phase diagrams for molecular fluids [20].…”