Classical Density Functional Theory for Liquid–Fluid Interfaces and Confined Systems: A Functional for the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State

Abstract

A Helmholtz energy functional based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State is proposed. A weighted density approximation is used to develop two variants of dispersion functionals. We conduct molecular simulations (Monte Carlo) in order to assess both models. The structure of thin liquid adsorbed layers of a few molecular diameters thickness are shown to be particularly meaningful to detect deficiencies of Helmholtz energy functionals and thus discriminate between models. We further compare the model to experimental data of interfacial tensions for pure components and for binary mixtures exhibiting vapor–liquid equilibria and liquid–liquid equilibria. The proposed Helmholtz energy functional is in good agreement with experimental data of pure (organic) substances and mixtures and compares well with molecular simulation data of fluids adsorbing at solid interfaces.

Tolman lengths and rigidity constants from free-energy functionals—General expressions and comparison of theories

“…Parameters for this system, including the binary interaction parameter k ij were obtained by Klink and Gross 59 and the DFT results using them were shown to concur well with experimental data. 56 In Fig. 6, the Tol- This effect is most pronounced at higher concentrations of THF and for smaller alkanes, with the Tolman length of the n-hexane/THF mixture being up to 50 % higher than both pure component values.…”

“…For the association contribution F assoc [ρ(r)], we use the model by Yu and Wu 55 and dispersive and polar interactions are combined in an attractive functional F att [ρ(r)], which uses a weighted density approach to account for the range of the interactions. 56 For the vector weight functions appearing in the FMT and association functionals, the expressions in Sec. II B have to be amended according to Appendix D. In previous works, the functional has already been applied to calculate the properties of adsorbed 57 and free droplets 12 as well as adsorption isotherms of pure components and mixtures.…”

Gas Adsorption and Interfacial Tension with Classical Density Functional Theory

“…Therefore, it is recommended to treat the factor λ as an adjustable parameter. 36 From here on, the approaches to the dispersive contribution will be labeled DFT-D1, DFT-D2 and DFT-D3 according to equations 16, 17 and 18, respectively.…”

“…45,50 There have been DFT implementations that use WDA together with the reduced Helmholtz free energy expression of the PC-SAFT equation of state, in particular the work of Shen et al 3032 They calculate the weighted density as a density average over the volume of a sphere with a radius equal to λd, where d is the temperature-dependent diameter dened in PC-SAFT and λ is a factor related to the width of the potential. 51 Later, Sauer and Gross 36 adopted the previously mentioned approach and treated λ as an adjustable parameter and showed that it can be treated as a unique parameter for all compounds they studied. They proposed two dierent dispersion functionals based on WDA, one of which slightly dierent than the one proposed by Shen et al 31 More recently, Wang et al 37 proposed a functional also using the PC-SAFT dispersion term in the functional form, and treat it locally together with the weighted densities dened in mFMT in order to account for short range interactions.…”

“…57 In this work, DFT is implemented using the PC-SAFT equation of state as reference for the calculation of interfacial tension and adsorption of non-associating systems. We adopted the WDA approach presented by Sauer and Gross 36 together with their dispersion functionals, and also include in our calculations the one developed by Shen et al 31…”