A novel test-area ͑TA͒ technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface ͑the relation of Kirkwood and Buff ͓J. Chem. Phys. 17, 338 ͑1949͔͒͒. For particles interacting through discontinuous intermolecular potentials ͑e.g., hard-core fluids͒ this involves the determination of ␦ functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two ͑or more͒ systems with different interfacial areas ͑the method of Bennett ͓J. Comput. Phys. 22, 245 ͑1976͔͒͒, which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo ͑TAMC͒ simulations are compared with the data obtained with other techniques ͑e.g., mechanical and free-energy differences͒ for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo ͑TAMC͒ or molecular-dynamics ͑TAMD͒ algorithms for different types of interfaces ͑vapor-liquid, liquid-liquid, fluid-solid, etc.͒ of pure systems and mixtures consisting of complex polyatomic molecules.

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range ͑SAFT-VR͒ for the homogenous fluid ͓A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 ͑1997͔͒. A standard perturbative density functional theory ͑DFT͒ is constructed by partitioning the free energy density into a reference term ͑which incorporates all of the short-range interactions, and is treated locally͒ and an attractive perturbation ͑which incorporates the long-range dispersion interactions͒. In our previous work ͓F. J. Blas, E. Martín del Río, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 ͑2001͒; G. J. Gloor, F. J. Blas, E. Martín del Río, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 ͑2002͔͒ we used a mean-field version of the theory ͑SAFT-HS͒ in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd ͓S. Toxvaerd, J. Chem. Phys. 64, 2863 ͑1976͔͒. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes ͑dimerization, straight and branched chain formation, and network structures͒ are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits ͑both of which correspond to equivalent nonassociating systems͒. The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic ''s shaped'' behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.

The SAFT-VR DFT Helmholtz free energy density functional [Gloor, G. J.; Jackson, G.; Blas, F. J.; Martín del Río, E.; de Miguel, E. J. Chem. Phys. 2004, 121, 12740] is used to describe the vapor−liquid interface of nonassociating and associating molecules ranging in size from small molecules to long chains. The functional, which is based on the statistical associating fluid theory for attractive potentials of variable range (SAFT-VR) description of the homogeneous fluid [Gil-Villegas, A.; Galindo, A.; Whitehead, P. J.; Mills, S. J.; Jackson, G.; Burgess, A. N. J. Chem. Phys. 1997, 106, 4168], is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). This functional accounts explicitly for the correlations between the segments using a density-averaged correlation function incorporated into the perturbative term in a similar way to that proposed by Toxvaerd. The SAFT-VR DFT formalism is used to examine the vapor−liquid interfacial tension of a number of pure components, including: n-alkanes; small associating molecules, such as water; linear alkan-1-ols; and some selected replacement refrigerants. In the case of the hydrocarbons and other weakly polar substances, the surface tension can be predicted from intermolecular parameters derived in the usual way from the bulk fluid phase equilibria (vapor-pressure and saturated liquid density). By contrast, when one describes the interfacial properties of associating compounds, it is important to include the surface tension data as well as the bulk vapor−liquid phase equilibria in developing the intermolecular potential model. This provides a means of determining the balance between the dispersive and associative (hydrogen bonding) contributions to the intermolecular potential. The use of interfacial data in the refinement of the potential model allows one to obtain a reliable set of parameters, which can be used to predict the bulk and interfacial properties of mixtures for a broad range of thermodynamic conditions.

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