Liquid-Vapor Equilibria of Polar Fluids from a van der Waals-like Theory

Abstract

A van der Waals-like theory of quadrupolar and dipolar linear fluids is presented. The reference system consists of a hard polar fluid, and attractive forces are considered through the mean field approximation. The effect of polar forces on liquid-vapor equilibria and on critical properties is analyzed for a number of molecular elongations. Trends as predicted by the theory are compared with computer simulations of linear polar fluids, and good agreement is found. Polar forces increase the critical temperature and acentric factor of a fluid. Quadrupole moment increases the critical density of a fluid. However, high dipole moments decrease critical densities. Deviations from the principle of corresponding states are analyzed. Polar forces and molecular elongation provoke a broadening of the coexistence curve and an increase of the slope of the vapor pressure curve when reduced by their critical magnitudes. The presented treatment, being quite simple, describes most of the main features of vapor-liquid equilibria of linear polar fluids. I. Introduction It is a century now since van der Waals proposed his equation of state.' A consequence of this equation is that all fluids follow the same equation of state when reduced by their critical magnitudes. That constitutes the principle of corresponding states which was later formulated on a molecular basis.* Although this principle holds quite well for spherical and almost spherical molecules, important deviations were found for molecules having a nonspherical shape or presenting a multipole (dipole or quadrupole) moment. Early attempts to account for these deviations from statistical mechanics grounds were form~lated.~.~ They were especially successful in the description of the effect of polar forces on spherical-shaped modek5 The past two decades were quite active in developing an understanding of the role of molecular shape on phase equilibria. van der Waals-like theories? perturbation theories,7-l0 or even computer simulation' ' have provided a clear understanding of the role of molecular shape on phase equilibria. The situation is less satisfactory for nonspherical polar fluids although some recent progress should be mentioned. Integral equations are now being solved for a number of linear polar models,'* and progress in the field through this line may be anticipated. Perturbation theories have recently been developed for linear polar fluids, and the consequences have not completely been explored yet.13-17 Simultaneously, a number of simulation studies concerning dipolar and quadrupolar linear fluids have been perf~rmed.'~J~ Quite recently, it has become possible to easily obtain liquid-vapor equilibria by computer simulation through the so-called Gibbs ensemble methodology.2o This new route is just being explored. In fact, Dubey et a1.*' have presented simulation results for linear dipolar fluids, and we have recently performed a very comprehensive simulation study of quadrupolar linear Kihara fluids.22 A similar study for a quadrupolar two-center Lennard-Jones model has recently been performed by using the NFT+ test particle method.23 These studies can be considered as examples of what may be learned in the near future on vapor-liquid equilibria of linear polar fluids.