Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Bruot, Nicolas; Caupin, Frédéric

doi:10.1103/physrevlett.116.056102

Cited by 75 publications

(70 citation statements)

References 49 publications

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“…(1), the curvature dependent Tolman length, δ T (R s ) is often replaced by the Tolman length of the planar interface δ. In later works, 4, [9][10][11][12] it was shown that with this approximation, Eq. (1) is incapable of representing the surface tension of small droplets.…”

Section: Introductionmentioning

confidence: 95%

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

Rehner

Aasen

Wilhelmsen

2019

The Journal of Chemical Physics

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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.

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Section: Introductionmentioning

confidence: 95%

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

Rehner

Aasen

Wilhelmsen

2019

The Journal of Chemical Physics

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“…In the literature, there are conflicting reports on the dependence of the surface tension on curvature in water: Refs. [4,72,73] find that the bubble is free energetically favored over the droplet, while Refs. [74][75][76][77][78] arrive at the opposite conclusion.…”

Section: Appendix B: Volume Of the Largest Bubble As A Reaction Coordmentioning

confidence: 99%

Molecular mechanism for cavitation in water under tension

Menzl

González

Geiger

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.cavitation | water | negative pressure | bubble nucleation | liquid-vapor transition D ue to its pronounced cohesion, water remains stable under tension for long times. Experimentally, strongly negative pressures exceeding −120 MPa (1-6) can be sustained before the system decays into the vapor phase via cavitation, i.e., bubble nucleation. Recently, cavitation in water under tension has drawn research interest due to its importance in biological processes, like water transport in natural (7-10) and synthetic (11, 12) trees, spore propagation of ferns (13), and poration of cell membranes (14, 15). Furthermore, cavitation in water appears to be the driving force behind the sonocrystallization of ice (16,17), and preventing its occurrence remains a challenge in turbine and propeller design (18). Studying the onset of cavitation has also proven to be a valuable tool to locate the line of density maxima in metastable water (4), which contributes to the ongoing effort of explaining the origin of water's anomalies (6,19). Interest in the topic is magnified by the startling discrepancy arising when cavitation in water is investigated using different experimental methods. Although agreement between different methods is excellent in the high-temperature regime, where the liquid is unable to sustain large tension, a significantly higher degree of metastability is reached when studying cavitation in inclusions along an isochoric path (1-5) compared with other techniques (20, 21) at low temperatures (22).Due to the short time scale on which the transition takes place and the small volume of the critical bubble at experimentally feasible conditions, direct observation of cavitation at the microscopic level...

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“…The sign of the Tolman length for common fluids such as water and the Lennard-Jones (LJ) fluid has been discussed extensively in the literature. 3,[10][11][12][13] For the LJ fluid, there is now a consensus that the Tolman length is negative. 11,12 The sign will, however, depend on the specifics of the system studied; for example, Tröster and Binder 14 found a positive Tolman length from simulations of a 3D triplet spin Ising lattice model.…”

Section: Introductionmentioning

confidence: 99%

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

Aasen

Blokhuis

Wilhelmsen

2018

The Journal of Chemical Physics

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The curvature dependence of the surface tension can be described by the Tolman length (first-order correction) and the rigidity constants (second-order corrections) through the Helfrich expansion. We present and explain the general theory for this dependence for multicomponent fluids and calculate the Tolman length and rigidity constants for a hexane-heptane mixture by use of square gradient theory. We show that the Tolman length of multicomponent fluids is independent of the choice of dividing surface and present simple formulae that capture the change in the rigidity constants for different choices of dividing surface. For multicomponent fluids, the Tolman length, the rigidity constants, and the accuracy of the Helfrich expansion depend on the choice of path in composition and pressure space along which droplets and bubbles are considered. For the hexane-heptane mixture, we find that the most accurate choice of path is the direction of constant liquid-phase composition. For this path, the Tolman length and rigidity constants are nearly linear in the mole fraction of the liquid phase, and the Helfrich expansion represents the surface tension of hexane-heptane droplets and bubbles within 0.1% down to radii of 3 nm. The presented framework is applicable to a wide range of fluid mixtures and can be used to accurately represent the surface tension of nanoscopic bubbles and droplets.

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Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Cited by 75 publications

References 49 publications

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

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

Molecular mechanism for cavitation in water under tension

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

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