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

Abstract

A Helmholtz energy functional for inhomogeneous fluid phases based on the perturbed-chain polar statistical associating fluid theory ͑PCP-SAFT͒ equation of state is proposed. The model is supplemented with a capillary wave contribution to the surface tension to account for long-wavelength fluctuations of a vapor-liquid interface. The functional for the dispersive attraction is based on a nonlocal perturbation theory for chain fluids and the difference of the perturbation theory to the dispersion term of the PCP-SAFT equation of state is treated with a local density approximation. This approach suggested by Gloor et al. ͓Fluid Phase Equilib. 194, 521 ͑2002͔͒ leads to full compatibility with the PCP-SAFT equation of state. Several levels of approximation are compared for the nonlocal functional of the dispersive attractions. A first-order non-mean-field description is found to be superior to a mean-field treatment, whereas the inclusion of a second-order perturbation term does not contribute significantly to the results. The proposed functional gives excellent results for the surface tension of nonpolar or only moderately polar fluids, such as alkanes, aromatic substances, ethers, and ethanoates. A local density approximation for the polar interactions is sufficient for carbon dioxide as a strongly quadrupolar compound. The surface tension of acetone, as an archetype dipolar fluid, is overestimated, suggesting that a nonisotropic orientational distribution function across an interface should for strong dipolar substances be accounted for.

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

“…The deviation of model prediction for mixed-gas adsorption is listed in Table III. It should be pointed out that the model results depend on the weight function as shown in Eq. (12). For the developed model, the weight function can be two options: one is based on square-well potential and the other is based on LJ potential.…”

“…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.…”

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

“…In planar geometry, the detailed expressions of functional derivative integrals of hard sphere and chain terms can be referred to Gross's work. 26 The derivatives of X j with respect to density were calculated using the generalized procedure proposed by Tan et al 37 Derivatives were formulated as linear simultaneous equations and then written in a matrix form. The method solving the linear equations and the corresponding code were given in the literature of Tan et al 37 …”

“…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. The free energy functional for dispersion attraction is expressed as a first order perturbation term.…”

Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

“…These virtues make PC-SAFT EOS a widely used EOS for polymers in engineering. 7,8 Gross 9 proposed a PC-SAFT EOS-based DFT, where the free energy functional for the dispersion interaction is approximated as a first-order perturbation. The functional is not consistent with the dispersion part of the free energy in the bulk EOS and the difference is locally absorbed by an ad hoc shift in the chemical potential.…”