Surface tension and energy of a classical liquid-vapour interface

Lekner, John; Henderson, J. R.

doi:10.1080/00268977700101771

Cited by 68 publications

(72 citation statements)

References 25 publications

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“…3. These terms, which are based on those employed by Lekner and Henderson [58], asymptotically agree with the hyperbolic tangent expression of Vrabec et al [25]. From the liquid and vapour densities ρ ′ and ρ ′′ of the fit to Eq.…”

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confidence: 58%

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Excess equimolar radius of liquid drops

et al. 2012

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The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from that defined with the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analysed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated-shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter σ. In these simulations, the magnitudes of the excess equimolar radius and the Tolman length are shown to be smaller than σ/2. Other methodical approaches, from which mutually contradicting findings have been reported, are critically discussed, outlining possible sources of inaccuracy.

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confidence: 58%

“…(23) is equivalent to the Kirkwood-Buff [57] mechanical route expression for the surface tension [58]. The higherorder terms therefore presumably capture the deviation between the mechanical and variational routes due to fluctuations or, equivalently, the contribution of nonequilibrium configurations to γ.…”

Section: The Variational Routementioning

confidence: 99%

Excess equimolar radius of liquid drops

et al. 2012

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“…These leading order contributions were also derived early on for planar interfaces by Lekner and Henderson. 56 It is also useful to realise that even though the mechanical work ⟨∆U⟩ fully characterizes the tension for planar and cylindrical interfaces, this does not preclude the existence of a higher-order entropic contribution. The dependence on a difference between ⟨Ua⟩ and ⟨U⟩⟨a⟩ suggests that the computation of the separate energetic and entropic contributions to the surface tension will require good statistics in order to obtain reliable results.…”

Section: B Interfacial Energies and Entropiesmentioning

confidence: 99%

Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water

Lau

Ford

Hunt

et al. 2015

The Journal of Chemical Physics

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The test-area (TA) perturbation approach has been gaining popularity as a methodology for the direct computation of the interfacial tension in molecular simulation. Though originally implemented for planar interfaces, the TA approach has also been used to analyze the interfacial properties of curved liquid interfaces. Here, we provide an interpretation of the TA method taking the view that it corresponds to the change in free energy under a transformation of the spatial metric for an affine distortion. By expressing the change in configurational energy of a molecular configuration as a Taylor expansion in the distortion parameter, compact relations are derived for the interfacial tension and its energetic and entropic components for three different geometries: planar, cylindrical, and spherical fluid interfaces. While the tensions of the planar and cylindrical geometries are characterized by first-order changes in the energy, that of the spherical interface depends on second-order contributions. We show that a greater statistical uncertainty is to be expected when calculating the thermodynamic properties of a spherical interface than for the planar and cylindrical cases, and the evaluation of the separate entropic and energetic contributions poses a greater computational challenge than the tension itself. The methodology is employed to determine the vapour-liquid interfacial tension of TIP4P/2005 water at 293 K by molecular dynamics simulation for planar, cylindrical, and spherical geometries. A weak peak in the curvature dependence of the tension is observed in the case of cylindrical threads of condensed liquid at a radius of about 8 Å, below which the tension is found to decrease again. In the case of spherical drops, a marked decrease in the tension from the planar limit is found for radii below ∼15 Å; there is no indication of a maximum in the tension with increasing curvature. The vapour-liquid interfacial tension tends towards the planar limit for large system sizes for both the cylindrical and spherical cases. Estimates of the entropic and energetic contributions are also evaluated for the planar and cylindrical geometries and their magnitudes are in line with the expectations of our simple analysis. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

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“…The leading term, ⌬F 1 = ͗⌬U͘, corresponds to the mechanical work involved in changing the area of the interface, which can be directly associated with the so-called virial expression for the tension 28 ͑expressed in terms of averages of the appropriate components ␣ of the virial, ͗x ␣ ͑dU / dx ␣ ͒͘, at the Hookean linear-response level͒. The corresponding entropic contribution due to the deformation is 28 …”

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“…In the case of a planar interface, it is well known that the interfacial tension can be obtained formally from the virial expression, 1,28 i.e., entirely from the leading-order contribution of Eq. ͑5͒.…”

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Communications: Evidence for the role of fluctuations in the thermodynamics of nanoscale drops and the implications in computations of the surface tension

Sampayo

Malijevský

Müller

et al. 2010

The Journal of Chemical Physics

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Test area deformations are used to analyse vapour-liquid interfaces of Lennard-Jones particles by molecular dynamics simulation. For planar vapour-liquid interfaces the change in free energy is captured by the average of the corresponding change in energy, the leading-order contribution. This is consistent with the commonly used mechanical (pressure tensor) route for the surface tension. By contrast for liquid drops one finds a large second-order contribution associated with fluctuations in energy. Both the first-and second-order terms make comparable contributions, invalidating the mechanical relation for the surface tension of small drops. The latter is seen to increase above the planar value for drop radii of ∼ 8 particle diameters, followed by an apparent weak maximum and slow decay to the planar limit, consistent with a small negative Tolman length.

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Surface tension and energy of a classical liquid-vapour interface

Cited by 68 publications

References 25 publications

Excess equimolar radius of liquid drops

Excess equimolar radius of liquid drops

Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water

Communications: Evidence for the role of fluctuations in the thermodynamics of nanoscale drops and the implications in computations of the surface tension

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