Classical density functional theory for the prediction of the surface tension and interfacial properties of fluids mixtures of chain molecules within the SAFT-VR approach

The SAFT-VR DFT Helmholtz free energy functional developed by Gloor et al., [J. Chem. Phys. 121, 12740 (2004)] is revisited and generalised to treat mixtures. The functional, which is based on the statistical associating fluid theory for attractive potentials of variable range (SAFT-VR) for homogeneous fluids, 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). In this work, two different functionals are compared. In the first, one uses a mean-field version of the theory to treat the long-range dispersive interaction, incorporating an approximate treatment of the effect of the correlations on the attractive energy between the segments by introducing a short range attractive contribution in the reference term. In the second, one approximates the correlation function of the molecular segments in the inhomogeneous system with that of a homogeneous system with an average density of the two positions, following the ideas proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The SAFT-VR DFT formalism is then used to study interfacial properties and adsorption phenomena at the interface. A detailed analysis of the influence of the molecular parameters on the surface tension and density/composition profiles of the mixtures is undertaken for binary mixtures with molecules of different chain length, segment diameter, dispersive energy and attractive range. The effect of the asymmetry of the molecular species on the adsorption phenomena is examined in some depth. The adequacy of the approach is demonstrated by comparison of the theoretical predictions with the interfacial properties of some real mixtures. The relative merits of the two approximate free energy functionals are assessed by examining the vapour-liquid interfacial tension of selected mixtures of n-alkanes. The theory generally provides an excellent description of the interfacial properties of the mixtures without the need for a further adjustment intermolecular parameters obtained solely from an examination of the bulk fluid phase behaviour.