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Höfling F, Dietrich S. Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction. J Chem Phys 2024; 160:104107. [PMID: 38469908 DOI: 10.1063/5.0186955] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 02/15/2024] [Indexed: 03/13/2024] Open
Abstract
Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.
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Affiliation(s)
- F Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
- Zuse Institut Berlin, Takustr. 7, 14195 Berlin, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Planková B, Vinš V, Hrubý J. Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves. J Chem Phys 2017; 147:164702. [PMID: 29096481 DOI: 10.1063/1.5008612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.
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Affiliation(s)
- Barbora Planková
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
| | - Václav Vinš
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
| | - Jan Hrubý
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
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Boniello G, Blanc C, Fedorenko D, Medfai M, Mbarek NB, In M, Gross M, Stocco A, Nobili M. Brownian diffusion of a partially wetted colloid. NATURE MATERIALS 2015; 14:908-11. [PMID: 26147846 DOI: 10.1038/nmat4348] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2014] [Accepted: 06/03/2015] [Indexed: 05/21/2023]
Abstract
The dynamics of colloidal particles at interfaces between two fluids plays a central role in microrheology, encapsulation, emulsification, biofilm formation, water remediation and the interface-driven assembly of materials. Common intuition corroborated by hydrodynamic theories suggests that such dynamics is governed by a viscous force lower than that observed in the more viscous fluid. Here, we show experimentally that a particle straddling an air/water interface feels a large viscous drag that is unexpectedly larger than that measured in the bulk. We suggest that such a result arises from thermally activated fluctuations of the interface at the solid/air/liquid triple line and their coupling to the particle drag through the fluctuation-dissipation theorem. Our findings should inform approaches for improved control of the kinetically driven assembly of anisotropic particles with a large triple-line-length/particle-size ratio, and help to understand the formation and structure of such arrested materials.
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Affiliation(s)
- Giuseppe Boniello
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Christophe Blanc
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Denys Fedorenko
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Mayssa Medfai
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Nadia Ben Mbarek
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Martin In
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Michel Gross
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Antonio Stocco
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
| | - Maurizio Nobili
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34000 Montpellier, France
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Aoki K, Mitsui T. Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011602. [PMID: 23005425 DOI: 10.1103/physreve.86.011602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Indexed: 06/01/2023]
Abstract
We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few μm) and temporally (~20 s). The method also requires relatively weak light power (~0.5 mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements.
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Affiliation(s)
- Kenichiro Aoki
- Research and Education Center for Natural Sciences and Department of Physics, Hiyoshi, Keio University, Yokohama 223-8521, Japan.
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Segovia-López JG, Zamora A, Santiago JA. Effective Hamiltonian of liquid-vapor curved interfaces in mean field. J Chem Phys 2011; 135:064102. [PMID: 21842921 DOI: 10.1063/1.3617414] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand potential at the level of mean field approximation that depends on the density profile and the short-range interaction potential. By introducing the step-function approximation for the density profile, and using general geometric arguments, we expand the grand potential in powers of the principal curvatures of the surface and find consistency with the Helfrich phenomenological model in the second order approximation.
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Affiliation(s)
- José G Segovia-López
- División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Km 1 Carretera Cunduacán-Jalpa, Apartado Postal 24, 86690 Cunduacán, Tabasco, Mexico.
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Falk K, Mecke K. Capillary waves of compressible fluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:184103. [PMID: 21508481 DOI: 10.1088/0953-8984/23/18/184103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The interplay of thermal noise and molecular forces is responsible for surprising features of liquids on sub-micrometer lengths-in particular at interfaces. Not only does the surface tension depend on the size of an applied distortion and nanoscopic thin liquid films dewet faster than would be expected from hydrodynamics, but also the dispersion relation of capillary waves differ at the nanoscale from the familiar macroscopic behavior. Starting with the stochastic Navier-Stokes equation we study the coupling of capillary waves to acoustic surface waves which is possible in compressible fluids. We find propagating 'acoustic-capillary waves' at nanometer wavelengths where in incompressible fluids capillary waves are overdamped.
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Affiliation(s)
- Kerstin Falk
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Erlangen, Germany
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Aarts DGAL. The interface in demixed colloid-polymer systems: wetting, waves and droplets. SOFT MATTER 2006; 3:19-23. [PMID: 32680188 DOI: 10.1039/b608479f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Phase transitions in colloid-polymer mixtures have attracted a large amount of attention over the last 20 years (W. C. K. Poon, , 2002, , R859; R. Tuinier, J. Rieger and C. G. de Kruif, , 2003, , 1). By comparison, the interfacial tension between the coexisting phases has received little attention. Here, we show that the ultralow interfacial tension in fluid-fluid demixed colloid-polymer systems, which is roughly one million times smaller than in ordinary liquids, manifests itself in a wide variety of interface characteristics and processes. Discussed are the interfacial wetting behaviour close to a hard wall, the thermal capillary waves at the free interface and the process of droplet coalescence and breakup. These subjects can be studied in a single experiment by combining modern soft matter chemistry and laser scanning confocal microscopy. This combination allows a further exploration of a broad range of interface issues.
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Affiliation(s)
- Dirk G A L Aarts
- Van't Hoff Laboratory, Debye Research Institute, University of Utrecht, Padualaan 8, 3584 CH Utrecht, The Netherlands.
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Hiester T, Dietrich S, Mecke K. Microscopic theory for interface fluctuations in binary liquid mixtures. J Chem Phys 2006; 125:184701. [PMID: 17115773 DOI: 10.1063/1.2358341] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermally excited capillary waves at fluid interfaces in binary liquid mixtures exhibit simultaneously both density and composition fluctuations. Based on a density functional theory for inhomogeneous binary liquid mixtures we derive an effective wavelength dependent Hamiltonian for fluid interfaces in these systems beyond the standard capillary-wave model. Explicit expressions are obtained for the surface tension, the bending rigidities, and the coupling constants of compositional capillary waves in terms of the profiles of the two number densities characterizing the mixture. These results lead to predictions for grazing-incidence x-ray scattering experiments at such interfaces.
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Affiliation(s)
- Thorsten Hiester
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstrase 7, D-91058 Erlangen, Germany.
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