Exact Calculation of the Effect of Three-body Axilrod-teller Interactions on Vapour-liquid Phase Coexistence

The Gibbs ensemble algorithm is implemented to determine the vapour-liquid phase coexistence of a pure fluid interacting via a two-body Lennard-Jones + three-body Axilrod-Teller potential. The contribution of both two-body and three-body interactions are calculated exactly. The results are compared with both experiment and two-body only simulation data. The position of the vapour branch of the coexistence curve is almost unaffected by the inclusion of three-body interactions. In contrast, the liquid branch occurs at substantially lower densities compared with Lennard-Jones simulation data. However, the approach to the critical point is improved by including three-body interactions, and the estimated critical point is in good agreement with experiment. INTRODUCTION The phase equilibria exhibited by fluids is the direct consequence of intermolecular interactions. Historically, theories of liquids have almost invariably assumed that intermolecular interaction is limited to pairs of molecules. Consequently, calculations of phase coexistence (Sadus, 1992) typically ignore the contributions of threeor more-body interactions. The available evidence (Barker et al., 1971; Monson et al., 1983; Rittger, 1990a-c; Elrod and Saykally, 1994) suggests that the effect of three-body interactions may be important in some circumstances. However, the role of three-body interactions on phase equilibria is unclear. The few studies (Smit et al., 1992; Miyano, 1994) which have attempted to include three-body interactions have relied on various approximation procedures rather than rigorous calculation. Recently, simulations have been reported (Sadus and Prausnitz, 1996; Sadus, 1996) which estimate the contribution of three-body effects via periodic calculation of three-body interactions. Although these approximations can provide a valuable insight into the relative magnitude of three-body interactions, an exact calculation is required to determine their effect on phase coexistence. In this work, the Gibbs ensemble (Panagiotopoulos et al., 1988) is used to calculate the vapour-liquid phase coexistence of a fluid interacting via a Lennard-Jones + Axilrod-Teller intermolecular potential. Unlike earlier work, the calculation of three-body interactions is exact. Both twoand three-body interactions contribute to the acceptance criterion of each and every attempted Monte Carlo move. Therefore, the coexistence properties of the fluid are the outcome of both the twoand three-body interactions. The results are compared with both experimental data and two-body only simulation data. THEORY Intermolecular Potential The intermolecular potential (u) is the sum of contributions from two-body interactions(u(ij)) and three-body dispersion interactions (u(ijk)), i.e., ( ) ( ) u u ij u ijk disp = + (1) The Lennard-Jones potential was used to calculate interactions between pairs of molecules separated by a distance rij u ij r r ij ij ( ) = 