Capillary waves as eigenmodes of the density correlation at liquid surfaces

Hernández‐Muñoz, Jose; Chacón, Enrique; Tarazona, P.

doi:10.1063/1.5020764

Cited by 11 publications

(26 citation statements)

References 38 publications

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“…In addition, it is now apparent that, even with a positive rigidity K, this approach is not a short-cut to the determination of the underlying microscopic observables G(z, z ; q) and S(z; q). In fact, the very opposite is true: One needs to know G(z, z ; q) in order to dene a rigidity, if we wish to extend capillary-wave theory [20]. In this paper, we shall show in fact that both G(z, z ; q) and S(z; q) contain information occurring at higher wave-vectors which cannot possibly be encapsulated using a rigidity, and which does not rely on the denition of an interface position h(x).…”

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confidence: 99%

The Goldstone mode and resonances in the fluid interfacial region

Parry

Rascón

2018

Nat. Phys.

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The development of a molecular theory of inhomogeneous uids and, in particular, of the liquid-gas interface has received enormous interest in recent years; however, long standing attempts to extend the concept of the surface tension in mesoscopic approaches by making it scale dependent, while apparently plausible, have failed to connect with simulation and experimental studies of of the interface which probe the detailed properties of density correlations. Here, we show that a fully microscopic theory of correlations in the interfacial region can be developed which overcomes many problems associated with simpler mesoscopic ideas. This theory originates from recognizing that the correlation function displays, in addition to a Goldstone mode, an unexpected hierarchy of resonances which constrain severely its structural properties. Indeed, this approach allows us to identify new classes of fully integrable models for which , quite surprisingly, the tension, density prole and correlation function function can all be determined analytically, revealing the microscopic structure of correlations in all generalised van der Waals theories. Interfaces, for example between liquids and gases or between solids and liquids, are ubiquitous in nature playing crucial roles across all of biology and in modern technologies from oil recovery to micro-uidics. The key ingredient in our understanding of them is the nature of the surface tension; the macroscopic energy cost of separating coexisting uid phases. Indeed, at large scales the interface behaves like a taut drum-skin with the surface tension acting always to minimize the exposed surface area. However, it has also long been recognized that the surface tension provides insight into the microscopic world since it arises directly from the imbalance between the attractive intermolecular forces either side of the interface. It was van der Waals who rst developed a microscopic theory which not only predicted the coexistence of liquid and gas phases but also the structure of the interface separating them, specically that the change from a high density liquid to a low density gas does not occur abruptly but smoothly over a molecular scale. The modern statistical mechanical theory of interfaces is based on a marriage between these large scale and microscopic approaches. However, this union has not always been easy and has been the subject of many controversies. Consider an interface situated near the z = 0 plane separating coexisting bulk liquid and gas phases below a critical temperature T c. Three microscopic quantities of particular importance are ρ(z), the equilibrium density prole, G(z, z ; q), the 2D Fourier transform of the density-density pair correlation function in the direction along the

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confidence: 99%

The Goldstone mode and resonances in the fluid interfacial region

Parry

Rascón

2018

Nat. Phys.

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“…Fig. 5 compares the approximations (25) and (26) for S(0; q) and G(0, 0; q) with those obtained from numerical solution of the Ornstein-Zernike equations (14) and (12) and again demonstrate their extraordinary accuracy and utility over the whole range of wave-vectors. For example, the approximate expression for G(0, 0; q)/G b (q), which recall is exact at low and high q, is only 1% inaccurate, at worst, and is barely indistinguishable from the exact numerical result.…”

Section: C) Trigonometricmentioning

confidence: 80%

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations

Parry

Rascón

2019

Phys. Rev. E

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In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave-vectors q. Here, we investigate this further by comparing approximations for the local structure factor and correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the correlation function and structure factor across the whole spectrum of wave-vectors, encapsulating the cross-over from the Goldstone mode divergence (at small q) to bulk-like behaviour (at larger q). As shown, these approximations are exact for some square-gradient model potentials, and never more than a few percent inaccurate for the others. Additionally, we show that they very accurately describe the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are near indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

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“…The Intrinsic Sampling Method (ISM) 25,26,37 is a practical implementation of many-body definitions based on percolation analysis. 38,39 As in our previous work 30 for the LJ surface, we have applied the method to 5000 MD configurations for each model. The algorithm is fully described in Ref.…”

Section: A the Intrinsic Sampling Methodsmentioning

confidence: 99%

“…directly from our MD simulations and consistently with the ISM definition used to get (11) and (13) for the BW prediction (14). In our previous work for the LJ surface, 30 we had defined G I (z, z ; q) as in (18), obtained it from MD simulations, and used it as an intuitively appealing proposal for G bg (z, z ; q). The theoretical derivation given here formalizes the concept and the convolution (20) provides the dependence of the non-CW correlation background with the system size, consistently with the density profile (8).…”

Section: Non-cw Contributions Beyond Bedeaux-weeks Theorymentioning

confidence: 99%

Density correlation in liquid surfaces: Bedeaux-Weeks high order terms and non capillary wave background

Hernández‐Muñoz

Chacón

Tarazona

2018

The Journal of Chemical Physics

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We present Molecular Dynamics (MD) simulations of liquid-vapor surfaces, and their Intrinsic Sampling Method analysis, to get a quantitative test for the theoretical prediction of the capillary wave (CW) effects on density correlation done by Bedeaux and Weeks (BW) in 1985. The results are contrasted with Wertheim's proposal which is the first term in BW series and are complemented with a (formally defined and computational accessible) proposal for the background of non-CW fluctuations. Our conclusion is that BW theory is both accurate and needed since it may differ significantly from Wertheim's proposal. We discuss the implications for the analysis of experimental X-ray surface diffraction data and MD simulations.

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Capillary waves as eigenmodes of the density correlation at liquid surfaces

Cited by 11 publications

References 38 publications

The Goldstone mode and resonances in the fluid interfacial region

The Goldstone mode and resonances in the fluid interfacial region

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations

Density correlation in liquid surfaces: Bedeaux-Weeks high order terms and non capillary wave background

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