We review the existing simulation data and equations of state for the Lennard-Jones (LJ) fluid, and present new simulation results for both the cut and shifted and the full LJ potential. New parameters for the modified Benedict-Webb-Rubin (MBWR) equation of state used by Nicolas, Gubbins, Streett and Tildesley are presented. In contrast to previous equations, the new equation is accurate for calculations of vapour-liquid equilibria. The equation also accurately correlates pressures and internal energies from the triple point to about 4·5 times the critical temperature over the entire fluid range. An equation of state for the cut and shifted LJ fluid is presented and compared with the simulation data of this work, and previously published Gibbs ensemble data. The MBWR equation of state can be extended to mixtures via the van der Waals one-fluid theory mixing rules. Calculations for binary fluid mixtures are found to be accurate when compared with Gibbs ensemble simulations.

The Lennard-Jones equation of state revisited

An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior are better than for existing equations of state.

Equation of State for the Lennard-Jones Fluid

Equilibrium molecular dynamics simulations were performed for a Lennard-Jones fluid at 171 conditions spanning the range 0≤p
 +≤1.0 and 0.8≤T
 +≤4.0. The Einstein or, mean-squared-displacement (MSD) formula was used to compute the self-diffusion coefficient and a recently suggested, modified MSD equation was used to compute the shear viscosity at each condition. Analytical equations for the self-diffusion and viscosity coefficients were then fitted to the simulated data as polynomial functions ofp
 + andT
 +. The resultant smoothing equations correlate the simulated data quite well and agree with argon experimental data within the uncertainty of the data.

Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations

For the Lennard‐Jones fluid, a new approximation for the bridge function is introduced and tested. The approximation is semi‐phenomenological in nature. The structure predicted by the new approximation, in the form of the pair correlation function g(r), agrees extremely well with recent computer simulations for large systems, over the full range of density and temperature. The thermodynamic properties of the Lennard‐Jones fluid are predicted and are in better agreement with computer simulations than earlier theories. The gas‐liquid phase diagram predicted by this work is displayed and discussed.

Integral equation theory for uncharged liquids: The Lennard‐Jones fluid and the bridge function

A recently proposed method, Monte Carlo simulation in the Gibbs ensemble, allows the prediction of phase equilibria from knowledge of the intermolecular forces. A single computer experiment is required per coexistence point for a system with an arbitrary number of components. The new technique has significant advantages relative to free-energy methods that have been used for phase equilibrium calculations is the past. In this work, a variation of the Gibbs method appropriate for calculations in mixtures with large differences in molecular size is developed. The method is applied for the calculation of high-pressure phase equilibria in two mixtures of simple monatomic fluids, the systems argon-krypton and neon-xenon. Pairwise additive potential functions of the Lennard-Jones type are used to describe the intermolecular interactions. Agreement with experimental results is generally good over a wide range of temperatures and pressures, including the fluid-fluid immiscibility region for the neon-xenon system. Results from the Van der Waals one-fluid theory are compared with experimental data and computer simulation predictions. Agreement is excellent for the mixture with small differences in size (argon-krypton), but the theory fails to describe the coexistence curve for the highly asymmetric system neon-xenon.

Ichiro Fijihara

Papers

Generalized equation of state for Lennard-Jones fluids—I. Pure fluids and simple mixtures