Vapour-liquid equilibria of stockmayer fluids

Abstract

By M. E. VAN LEEUWEN, B. SMIT and E. M. HENDRIKS Koninklijke/Shell-Laboratorium, Amsterdam, P.O. Box 3003, 1003 AA Amsterdam, The Netherlands (Received 16 April 1992; accepted 1 July 1992) Gibbs ensemble simulation data for Stockmayer fluids with #.2 = 3.0 and #.2 = 4.0 in the reduced temperature range of 0-77 (resp. 0.80)-098 and pre- sented and compared with predictions based on the perturbation theories of Stell, G., Rasaiah, J. C., and Narang, H., 1972, Molec. Phys., 23, 393; 1974, 27, 1393. The description of the reference fluid is improved by applying the mod- ified Benedict-Webb-Rubin equation of state instead of the Verlet-Weis imple- mentation of the Weeks-Chandler-Andersen perturbation scheme. Second virial coefficients predicted by perturbation theory to order #4 agree for Stock- mayer fluids with #,2 < 4 very well with exact values. Perturbation theory is capable of describing the low-density region of Stockmayer fluids with rather strong dipole moments. For these high values of the dipole moment, the Pad6 approximation of perturbation theory deviates significantly from the simulated coexistence curves in density and pressure. Compared with perturbation theory to order #4, however, it is a far better approximation of the Stockmayer fluid coexistence curve. The behaviour of the Pad6 approximation in the critical region is not satisfactory. 1. Introduction Electrostatic interactions affect thermodynamic behaviour. For relatively simple polar model fluids several theories have been developed [1-3]. A convenient model for a polar fluid is a 'soft-core' dipolar molecule, represented by the Stockmayer potential (Lennard-Jones potential with an embedded point dipole). The two most important molecular theories for model polar fluids are integral equation theories and (Pople-Stell) perturbation theories. If the Ornstein-Zernike equation is supplemented with an approximate closure relation, an integral equation is obtained for the direct correlation function and the radial distribution function [2]. For polar fluids this involves expansions of angular- dependent functions. Starting from the well known hypernetted-chain equation Patey and others [4-6] considered linear expressions (LHNC) and quadratic expressions (QHNC), and obtained a numerically tractable scheme. Fries and Patey [7] devel- oped a general method for fluids with anisotropic interactions, the reference hypernetted-chain (RHNC) theory. Lee et al. [8] applied this approximation to Stockmayer fluids, and found that the dielectric constant predicted with the full RHNC theory agrees better with computer simulation results than those predicted with the LHNC and QHNC theories. Another approach to describe the behaviour of simple polar model fluids is the use of perturbation theories, as pioneered by Pople and further developed by Stell et al. [9-13]. In these theories, the free Helmholtz energy is expressed as the sum of a