Predictive density gradient theory based on nonlocal density functional theory

Abstract

Density gradient theory has become an important tool for calculating the surface tension of pure components as well as mixtures. The calculation requires knowledge about the so-called influence parameter. Since in most applications this parameter is obtained by fitting results of the density gradient theory to experimental data for surface tensions, the approach lacks predictive power. We propose a predictive density gradient theory based on nonlocal density functional theory (DFT) using the perturbed chain polar statistical associating fluid theory (PCP-SAFT) as equation of state. The formalism can also be applied to other Helmholtz energy functionals based on weighted densities. The predictive density gradient theory (pDGT) is obtained by applying a gradient expansion to the weighted densities of the PCP-SAFT Helmholtz energy functional to second order and expanding the Helmholtz energy density to first order. The resulting model approximates the DFT and can be cast into the form of a density gradient theory. The resulting influence parameter depends on local densities and on temperature. We assess the predictive power of the proposed pDGT to calculate surface tensions of vapor-liquid interfaces of pure components as well as mixtures. The results show that pDGT reduces the computational complexity compared with nonlocal DFT calculations, while largely preserving its accuracy as well as its predictive capability.