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The leading order terms in a curvature expansion of the surface tension, theTolman length (first order), and rigidities (second order) have been shown toplay an important role in the description of nucleation processes. This workpresents general and rigorous expressions to compute these quantities for anynon-local density functional theory (DFT). The expressions hold for pure fluidsand mixtures, and reduce to the known expressions from density gradient theory(DGT). The framework is applied to a Helmholtz energy functional based on theperturbed chain polar statistical associating fluid theory (PCP-SAFT) and isused for an extensive investigation of curvature corrections for pure fluidsand mixtures. Predictions from the full DFT are compared to two simplertheories: predictive density gradient theory (pDGT), that has a density andtemperature dependent influence matrix derived from DFT, and DGT, where theinfluence parameter reproduces the surface tension as predicted from DFT. Allmodels are based on the same equation of state and predict similar Tolmanlengths and spherical rigidities for small molecules, but the deviationsbetween DFT and DGT increase with chain length for the alkanes. For allcomponents except water, we find that DGT underpredicts the value of the Tolmanlength, but overpredicts the value of the spherical rigidity. An importantbasis for the calculation is an accurate prediction of the planar surfacetension. Therefore, further work is required to accurately extract Tolmanlengths and rigidities of alkanols, because DFT with PCP-SAFT does notaccurately predict surface tensions of these fluids.

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