Prediction of the Vapor−Liquid Interfacial Tension of Nonassociating and Associating Fluids with the SAFT-VR Density Functional Theory

Abstract

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.

A density functional theory for vapor-liquid interfaces using the PCP-SAFT equation of state

“…Gloor et al, [40][41][42] however, proposed a prescription to consistently apply the DFT with these bulk-phase equations of state. It was shown that a DFT treatment of the dispersive attraction can be established based on perturbation theory, while any ͑small͒ difference between this dispersion term and the dispersion term of the engineering equation of state can with sufficient accuracy be described with a local density approximation ͑LDA͒.…”

Classical density functional theory for the prediction of the surface tension and interfacial properties of fluids mixtures of chain molecules based on the statistical associating fluid theory for potentials of variable range

“…For a recent overview of the numerous applications of DFT to pure fluids, the reader is referred to some of our previous publications [57][58][59][60] and to the recent work of Gross…”

“…The attractive non-local term was calculated using a mean-field approximation. Moreover, they considered the capillary-wave "correction"by means of a mode-coupling theory for the mean-square roughness of the interface for the SAFT-VR approach which can be formulated as a DFT 59,60 ; the accuracy of this approximation has been confirm by comparison with the simulation data for vapour-liquid surface tension of square-well fluids of variable range 96 …”

“…Note that this partitioning will provide a methodology for the generalisation of the original SAFT-VR DFT treatment 59,60 to mixtures; we emphasize that this does not mean that our current description involves a mean-field approximation of the type employed in the less rigourous augmented van der Waals approaches (e.g., see references [129][130][131][132][133][134] , which include studies with equations of state of the SAFT form).…”

A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores

“…[20][21][22] Based on SAFT EoS, several groups have developed DFT models and further used them to describe the phase behaviors of mixture as well as interfacial tensions. Gloor et al [23][24][25] developed a DFT model on the basis of SAFT-VR with a local density approximation, and the model accurately predicts the interfacial tension. Based on perturbed-chain polar statistical associating fluid theory (PCP-SAFT), Gross 26 proposed a DFT reproducing the surface tension of non-polar and polar substances.…”