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

Abstract

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 2

Interfacial tensions of industrial fluids from a molecular‐based square gradient theory

“…Of course, both equations, Equation (19) and Equation (20), must provide the same numerical results as we compare the exact results from MD to those predicted from the theory.…”

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

“…Therefore, in the part of model verification, in order to compare the DFT model predictions with molecular simulation results, the DFT model developed in this work was extended to the first version of PC-SAFT by replacing the temperaturedependent segment diameter with a fixed segment diameter and the set of constants for calculating dispersive interaction as well as the weighted density calculated by Eq. (16).…”

“…(16). As the squarewell length is needed for integral, it was assumed to be 1.5 in our work after the preliminary study.…”

“…Meanwhile, statistical associating fluid theory (SAFT)-based DFT models have been developed to account for the contribution to the free energy functional due to chain connectivity and site associating of inhomogeneous fluid. [10][11][12][13][14][15][16][17] Among them, the models proposed by Xu et al, 14 Hu et al, 15 Llovell et al, 16 and Oliveria et al 17 can be used to represent the interfacial properties where the external field is weak. For other models, little effort has been put into incorporating the long-range attraction perturbation that reduces to the SAFT EoS in the bulk limit.…”

Using Molecular Modelling Tools to Understand the Thermodynamic Behaviour of Ionic Liquids

“…An additional advantage of SAFT is that the underlying theory of the equation allows systematic extensions in a well-sounded manner. In this sense, different versions of the equation have been recently extended into several directions: 1. the calculation of second order thermodynamic derivative properties (Colina et al, 2002;Llovell & Vega 2006b;Llovell et al, 2006;Laffite et al, 2006) and tricritical points (Vega & Blas, 2000) 2. the precise characterization of the critical region of pure fluids and mixtures (Llovell et al, 2004;Llovell & Vega 2006a;) through a crossover treatment based on White's work (White, 2002;Salvino & White, 1992) from the renormalization group theory or through other approaches (Kiselev & Ely, 2000); and 3. the calculation of interfacial vapor-liquid and liquid-liquid properties by coupling the van der Waals density gradient theory to the soft-SAFT equation (Duque et al, 2004;Mejia et al, 2005;Mejia & Vega, 2006; or a density functional theory to the SAFT-VR version (Blas et al, 2001;Gloor et al, 2004;Llovell et al, 2010a). As other SAFT-type equations, soft-SAFT is written in terms of the total Helmholtz energy of the system.…”