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

The development of van der Waals cubic equations of state and their application to the correlation and prediction of phase equilibrium properties is presented and analyzed. The discussion starts with a brief account of the contributions to equation of state development during the years before van der Waals. Then, the original equation proposed in the celebrated thesis of van der Waals in 1873 and its tremendous importance in describing fluid behavior are analyzed. A chronological critical walk through the most important contributions during the first part of the 1900s is made, to arrive at the proposal that I consider to be the most outstanding since van der Waals:  the equation proposed by Redlich and Kwong in 1949. The contributions after Redlich and Kwong to the modern development of equations of state and the most recent equations proposed in the literature are analyzed. The application of cubic equations of state to mixtures and the development of mixing rules is put in a proper perspective, and the ...

The state of the cubic equations of state

Progress in developing equations of state for the calculation of fluid-phase equilibria is reviewed. There are many alternative equations of state capable of calculating the phase equilibria of a diverse range of fluids. A wide range of equations of state from cubic equations for simple molecules to theoretically-based equations for molecular chains is considered. An overview is also given of work on mixing rules that are used to apply equations of state to mixtures. Historically, the development of equations of state has been largely empirical. However, equations of state are being formulated increasingly with the benefit of greater theoretical insights. It is now quite common to use molecular simulation data to test the theoretical basis of equations of state. Many of these theoretically-based equations are capable of providing reliable calculations, particularly for large molecules.

http://depa.fquim.unam.mx/amyd/archivero/TEORIADEECUACIONESDEESTADO_3411.pdf

Equations of state for the calculation of fluid-phase equilibria

Peng-Robinson equation of state: 40 years through cubics

http://rozup.ir/up/paper/Documents/Modeling_ionic_liquids_and_the_solubility_of_gases_in_them_Recent_advances_and_perspectives.pdf

Modeling ionic liquids and the solubility of gases in them: Recent advances and perspectives

A new mixing rule—modified conventional mixing rule

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

Development of a five-parameter cubic equation of state

With the linear mixing rule for a covolume parameter of a cubic equation of state, the calculated excess thermodynamic properties depend on the cohesion parameter only at the specified temperature, pressure and mole fractions. Any cubic equation of state with modified conventional mixing rules gives similar predictions of the excess molar enthalpy and the excess molar volume. The excess thermodynamic property calculations are strongly dependent on the binary interaction parameters of the modified conventional mixing rules. A new method to predict a mixture thermodynamic property is proposed which combines a cubic equation of state for the excess property and a correlation method or experimental data for the pure property.

Yoshinori Adachi

Papers

A new mixing rule—modified conventional mixing rule

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

Development of a five-parameter cubic equation of state

A new method to predict thermodynamic properties of mixtures by means of a cubic equation of state.

Effects of mixing rules on phase equilibrium calculations