Modeling properties of the one-dimensional vapor-liquid interface: Application of classical density functional and density gradient theory

This study compares surface tensions as calculated from the classical density functional theory (DFT) and from density gradient theory (DGT) to experimental data. This comparison is inevitably not on equal ground, because the DFT is purely predictive for interfacial properties, both for pure substances and for mixtures, whereas DGT requires an adjustable influence parameter for each pure component (adjusted to surface tension data) and possibly a further adjustable parameter for each binary pair. In that sense, our comparison takes the perspective of a user who, because experimental data is available, finds it acceptable to correlate interfacial properties with adjustable parameters but who can alternatively decide for applying the DFT method. The perturbed-chain polar statistical associating fluid theory (PCP-SAFT) is used to determine phase equilibrium properties as well as the local Helmholtz energy density for DGT. For DFT, a Helmholtz energy functional consistent with PCP-SAFT is applied. DGT correlations and DFT predictions of surface tension for pure components as well as results for mixtures agree very well and exhibit excellent agreement to reference data for non-associating non-polar and polar molecules. Only for pure associating compounds, the adjustable parameter of DGT leads to significant improvements over DFT results. For mixtures, depending on the system, results can be better for either method. In the case of alkane-alcohol mixtures, DGT with the geometric combining rule for the cross-wise influence parameter leads to non-physically steep gradients in the density profiles. Adjusting a binary correction parameter for the influence parameter to experimental mixture surface tension data helps to alleviate this problem. However, the practical utility of this binary correction parameter to improve mixture surface tension results is very limited. We conclude that DFT is for most applications a preferable approach.