Abstract
The leading order terms in a curvature expansion of the surface tension, the Tolman length (first order),
and rigidities (second order) have been shown to play an important role in the description of nucleation
processes. This work presents general and rigorous expressions to compute these quantities for any nonlocal
density functional theory (DFT). The expressions hold for pure fluids and mixtures, and reduce to the
known expressions from density gradient theory (DGT). The framework is applied to a Helmholtz energy
functional based on the perturbed chain polar statistical associating fluid theory (PCP-SAFT) and is used
for an extensive investigation of curvature corrections for pure fluids and mixtures. Predictions from the full
DFT are compared to two simpler theories: predictive density gradient theory (pDGT), that has a density
and temperature dependent influence matrix derived from DFT, and DGT, where the influence parameter
reproduces the surface tension as predicted from DFT. All models are based on the same equation of state
and predict similar Tolman lengths and spherical rigidities for small molecules, but the deviations between
DFT and DGT increase with chain length for the alkanes. For all components except water, we find that
DGT underpredicts the value of the Tolman length, but overpredicts the value of the spherical rigidity. An
important basis for the calculation is an accurate prediction of the planar surface tension. Therefore, further
work is required to accurately extract Tolman lengths and rigidities of alkanols, because DFT with PCP-SAFT
does not accurately predict surface tensions of these fluids.
and rigidities (second order) have been shown to play an important role in the description of nucleation
processes. This work presents general and rigorous expressions to compute these quantities for any nonlocal
density functional theory (DFT). The expressions hold for pure fluids and mixtures, and reduce to the
known expressions from density gradient theory (DGT). The framework is applied to a Helmholtz energy
functional based on the perturbed chain polar statistical associating fluid theory (PCP-SAFT) and is used
for an extensive investigation of curvature corrections for pure fluids and mixtures. Predictions from the full
DFT are compared to two simpler theories: predictive density gradient theory (pDGT), that has a density
and temperature dependent influence matrix derived from DFT, and DGT, where the influence parameter
reproduces the surface tension as predicted from DFT. All models are based on the same equation of state
and predict similar Tolman lengths and spherical rigidities for small molecules, but the deviations between
DFT and DGT increase with chain length for the alkanes. For all components except water, we find that
DGT underpredicts the value of the Tolman length, but overpredicts the value of the spherical rigidity. An
important basis for the calculation is an accurate prediction of the planar surface tension. Therefore, further
work is required to accurately extract Tolman lengths and rigidities of alkanols, because DFT with PCP-SAFT
does not accurately predict surface tensions of these fluids.
