The leading order terms in a curvature expansion of 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 in an extensive investigation of curvature corrections for pure fluids and mixtures. Predictions from the full DFT are compared to two simpler theories: predictive DGT, which has a density and temperature dependent influence matrix derived from DFT, and DGT, where the influence parameter reproduces the surface tension 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 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.
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28 December 2019
Research Article|
December 27 2019
Tolman lengths and rigidity constants from free-energy functionals—General expressions and comparison of theories Available to Purchase
P. Rehner
;
1
Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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A. Aasen
;
A. Aasen
2
Department of Energy and Process Engineering, Norwegian University of Science and Technology
, NO-7491 Trondheim, Norway
3
SINTEF Energy Research
, NO-7465 Trondheim, Norway
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Ø. Wilhelmsen
Ø. Wilhelmsen
2
Department of Energy and Process Engineering, Norwegian University of Science and Technology
, NO-7491 Trondheim, Norway
3
SINTEF Energy Research
, NO-7465 Trondheim, Norway
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P. Rehner
1
A. Aasen
2,3
Ø. Wilhelmsen
2,3
1
Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
2
Department of Energy and Process Engineering, Norwegian University of Science and Technology
, NO-7491 Trondheim, Norway
3
SINTEF Energy Research
, NO-7465 Trondheim, Norway
J. Chem. Phys. 151, 244710 (2019)
Article history
Received:
November 05 2019
Accepted:
November 26 2019
Citation
P. Rehner, A. Aasen, Ø. Wilhelmsen; Tolman lengths and rigidity constants from free-energy functionals—General expressions and comparison of theories. J. Chem. Phys. 28 December 2019; 151 (24): 244710. https://doi.org/10.1063/1.5135288
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