A modified SAFT equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain reference fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixtures of small spherical molecules such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassociating molecules were identified for 78 substances by correlating vapor pressures and liquid volumes. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor−liquid equilibria of mixtures, the equation of state shows substantial predictive capabilities and good precision for correlating mixtures. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng−Robinson model is also given for vapor−liquid equilibria of binary systems, confirming the good performance of the suggested equation of state. ...

Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules

Efficient estimation of free energy differences from Monte Carlo data

The perturbation theory previously shown to give good results for the equation of state of a square‐well fluid at liquid densities and temperatures is applied to more realistic potentials with soft repulsion, in particular the 6:12 potential. For an arbitrary potential function a modified potential is defined involving three parameters, namely a hard‐sphere diameter, an inverse‐steepness parameter for the repulsive region, and a depth parameter for the attractive region. When the latter parameters are zero, the modified potential becomes the hard‐sphere potential; when they are one, it becomes the original potential. The configuration integral is expanded in a double‐power series in the inverse‐steepness and depth parameters, the hard‐sphere diameter being chosen so that the first‐order term in the inverse‐steepness parameter is zero. The first‐order term in the depth parameter is evaluated essentially exactly and the second‐order term approximately: other second‐order terms and all higher‐order terms are neglected. The resulting equation of state is in good agreement with molecular dynamics, Monte Carlo results, and experimental data for argon at all temperatures and densities relevant for fluids.

Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids

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

A version of the statistical associating fluid theory (SAFT) is developed for chain molecules of hard-core segments with attractive potentials of variable range (SAFT-VR). The different contributions to the Helmholtz free energy are evaluated according to the Wertheim perturbation theory. The monomer properties are obtained from a high-temperature expansion up to second order, using a compact expression for the first-order perturbation term (mean-attractive energy) a1. Making use of the mean-value theorem, a1 is given as the van der Waals attractive constant and the Carnahan and Starling contact value for the hard-sphere radial distribution function in terms of an effective packing fraction. The second-order perturbation term a2 is evaluated with the local compressibility approximation. The monomer cavity function, required for the calculation of the free energy due to the formation of the chains and the contribution due to association, is given as a function of a1. We analyse the equation of state for ch...

Statistical associating fluid theory for chain molecules with attractive potentials of variable range

The equation of state for a fluid of molecules interacting according to the square‐well potential is evaluated by treating the attractive potential as a perturbation on the hard‐sphere potential. This leads to an expansion in inverse powers of the temperature. The first‐order term is evaluated exactly (except for the approximation of using the Percus—Yevick expression for the hard‐sphere radial distribution function). Two slightly different approximations for the second‐order term are given and shown to lead to similar results. With first‐and second‐order terms included, the calculated equation of state is in excellent agreement with quasiexperimental Monte Carlo and molecular‐dynamics results at all temperatures including the lowest temperatures for which such calculations have been made, far below the critical temperature and at liquid densities. The reasons for this good agreement, particularly at high densities, are discussed in terms of a novel formulation of the perturbation theory, and the implications of the results for fluids with more realistic potential functions are considered.

D. Henderson

Papers

Perturbation Theory and Equation of State for Fluids: The Square‐Well Potential