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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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2
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MacDowell LG. Surface tension of bulky colloids, capillarity under gravity, and the microscopic origin of the Kardar-Parisi-Zhang equation. Phys Rev E 2023; 108:L022801. [PMID: 37723748 DOI: 10.1103/physreve.108.l022801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 07/26/2023] [Indexed: 09/20/2023]
Abstract
Experimental measurements of the surface tension of colloidal interfaces have long been in conflict with computer simulations. In this Letter we show that the surface tension of colloids as measured by surface fluctuations picks up a gravity-dependent contribution which removes the discrepancy. The presence of this term puts a strong constraint on the structure of the interface which allows one to identify corrections to the fundamental equation of equilibrium capillarity and deduce bottom up the microscopic origin of a growth model with close relation to the Kardar-Parisi-Zhang equation.
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Affiliation(s)
- Luis G MacDowell
- Departamento de Química-Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
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3
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Hantal G, Jedlovszky P, Sega M. Local structure of liquid/vapour interfaces approaching the critical point. SOFT MATTER 2023; 19:3773-3782. [PMID: 37098698 DOI: 10.1039/d3sm00176h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Investigating the structure of fluid interfaces at high temperatures is a particularly delicate task that requires effective ways of discriminating liquid from vapour and identifying the location of the liquid phase boundary, thereby allowing to distinguish intrinsic from capillary fluctuations. Several numerical approaches require introducing a coarse-graining length scale, often heuristically chosen to be the molecular size, to determine the location of the liquid phase boundary. Here, we propose an alternative rationale for choosing this coarse-graining length scale; we require the average position of the local liquid phase dividing surface to match its flat, macroscopic counterpart. We show that this approach provides additional insight into the structure of the liquid/vapour interface, suggesting the presence of another length scale beyond the bulk correlation one that plays an important role in determining the interface structure.
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Affiliation(s)
- György Hantal
- Institute of Physics and Materials Science, University of Natural Resources and Life Sciences, Peter Jordan Strasse 82, A-1190 Vienna, Austria
| | - Pál Jedlovszky
- Department of Chemistry, Eszterhazy Karoly University, Leanyka utca 6, H-3300 Eger, Hungary
| | - Marcello Sega
- Department of Chemical Engineering, University College London, London WC1E 7JE, UK.
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4
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Endres SC, Avila M, Mädler L. A discrete differential geometric formulation of multiphase surface interfaces for scalable multiphysics equilibrium simulations. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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5
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Luengo-Márquez J, Izquierdo-Ruiz F, MacDowell LG. Intermolecular forces at ice and water interfaces: premelting, surface freezing and regelation. J Chem Phys 2022; 157:044704. [DOI: 10.1063/5.0097378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Lifshitz theory we assess the role of van der Waals forces at interfaces of ice and water. The results are combined with measured structural forces from computer simulations to develop a quantitative model of the surface free energy of premelting films. This input is employed within the framework of wetting theory and allows us to predict qualitatively the behavior of quasi-liquid layer thickness as a function of ambient conditions. Our results emphasize the significance of vapor pressure. The ice vapor interface is shown to exhibit only incomplete premelting, but the situation can shift to a state of complete surface melting above water saturation. The results obtained serve also to assess the role of subsurface freezing at the water-vapor interface, and we show that intermolecular forces favor subsurface ice nucleation only in conditions of water undersaturation. We show ice regelation at ambient pressure may be explained as a process of capillary freezing, without the need to invoke the action of bulk pressure melting. Our results for van der Waals forces are exploited in order to gauge dispersion interactions in empirical point charge models of water.
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Affiliation(s)
| | | | - Luis G. MacDowell
- Dpto. de Quimica Fisica, Universidad Complutense de Madrid Facultad de Ciencias Químicas, Spain
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Zhang Y, Lockerby DA, Sprittles JE. Relaxation of Thermal Capillary Waves for Nanoscale Liquid Films on Anisotropic-Slip Substrates. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:8667-8676. [PMID: 34251820 DOI: 10.1021/acs.langmuir.1c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centered cubic lattice. This surface's anisotropy breaks the simple scalar proportionality between slip velocity and wall shear stress and requires the introduction of a slip-coefficient tensor. The Langevin equation can describe both the growth of capillary wave spectra and the relaxation of capillary wave correlations, with the former providing a time scale for the surface to reach thermal equilibrium. Temporal correlations of interfacial Fourier modes, measured at thermal equilibrium in MD, demonstrate that (i) larger slip lengths lead to a faster decay in wave correlations and (ii) unlike isotropic-slip substrates, the time correlations of waves on anisotropic-slip substrates are wave-direction-dependent. These findings emerge naturally from the proposed Langevin equation, which becomes wave-direction-dependent, agrees well with MD results, and allows us to produce experimentally verifiable predictions.
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Affiliation(s)
- Yixin Zhang
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
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Zhang Y, Sprittles JE, Lockerby DA. Nanoscale thin-film flows with thermal fluctuations and slip. Phys Rev E 2020; 102:053105. [PMID: 33327206 DOI: 10.1103/physreve.102.053105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 10/10/2020] [Indexed: 06/12/2023]
Abstract
The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long-wave approximation to fluctuating hydrodynamics. Analytically derived capillary spectra, which evolve in time, are found from the new SLEs and compared to molecular dynamics simulations. It is shown that thermal fluctuations lead to the generation and growth of surface waves, and slip accelerates this growth. SLEs developed here provide useful tools to study nanoscale film dewetting, nanofiber coating, and liquid transport using nanofibers.
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Affiliation(s)
- Yixin Zhang
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
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Höfling F, Dietrich S. Finite-size corrections for the static structure factor of a liquid slab with open boundaries. J Chem Phys 2020; 153:054119. [PMID: 32770898 DOI: 10.1063/5.0017923] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures.
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Affiliation(s)
- F Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraβe 3, 70569 Stuttgart, Germany
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9
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Hilaire L, Siboulet B, Ledesma-Alonso R, Legendre D, Tordjeman P, Charton S, Dufrêche JF. Deformation of a Liquid Near an AFM Tip: Molecular Dynamics Approach. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:8993-9004. [PMID: 32643935 DOI: 10.1021/acs.langmuir.0c00023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The interaction between an atomic force microscopy (AFM) probe and a thin film of water deposited over a flat substrate is studied using molecular dynamics (MD). The effects of the film thickness and the probe radius on both the deformation height of the liquid interface and the distance of the jump to contact at which the liquid comes in direct contact with the probe are investigated. The dynamics of the surface deformation and the role of interface fluctuations are studied in detail. The systems considered belong to the thin-film regime described in a semianalytical model previously established by Ledesma-Alonso et al. (Langmuir 2013, 29, 7749-7757). MD simulations predict that for shallow films, both the distance at which the jump to contact occurs and the surface maximal deformation height increase steadily with the layer thickness regardless of the probe radius, which is in agreement with the previously proposed theoretical model. The deformation of the surface was shown to be unstable because of the strong effect of thermal fluctuations. For each of the considered systems, the film thickness was such that interface fluctuations induced the jump to contact. The comparison of the deformation obtained in MD with the profiles predicted by the continuous model points out the complementarity between the two approaches. The results of the molecular approach not only are consistent with those of the continuous model but also provide more information on the description of nanoscale phenomena. In particular, MD results point out the importance of fluctuations when it comes to the description of the particular dynamics of nanosystems involving soft interfaces. This shows the need to improve continuous models by complementing them with a molecular approach for a better accuracy.
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Affiliation(s)
- Lolita Hilaire
- CEA, DES, ISEC, DMRC, Univ Montpellier, Marcoule, France
| | | | - René Ledesma-Alonso
- Departamento de Ingeniería Industrial y Mecánica, Escuela de Ingeniería, Universidad de las Américas Puebla, Ex Hacienda Sta. Catarina Mártir S/N, San Andrés Cholula, Puebla 72810, Mexico
| | - Dominique Legendre
- Institut de Mécanique des Fluides de Toulouse (IMFT), INPT-CNRS, Université de Toulouse, Allée du Professeur Camille Soula, Toulouse 31400, France
| | - Philippe Tordjeman
- Institut de Mécanique des Fluides de Toulouse (IMFT), INPT-CNRS, Université de Toulouse, Allée du Professeur Camille Soula, Toulouse 31400, France
| | - Sophie Charton
- CEA, DES, ISEC, DMRC, Univ Montpellier, Marcoule, France
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10
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Parry AO, Rascón C. Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations. Phys Rev E 2019; 100:022803. [PMID: 31574699 DOI: 10.1103/physreve.100.022803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Indexed: 11/07/2022]
Abstract
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 [Nat. Phys. 15, 287 (2019)1745-247310.1038/s41567-018-0361-z]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small q) to bulklike behavior (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 describe very accurately 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 nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.
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Affiliation(s)
- A O Parry
- Department of Mathematics, Imperial College London, London SW7 2BZ, United Kingdom
| | - C Rascón
- GISC, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain.,ICMAT, Campus Cantoblanco UAM, 28049 Madrid, Spain
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11
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Zhang Y, Sprittles JE, Lockerby DA. Molecular simulation of thin liquid films: Thermal fluctuations and instability. Phys Rev E 2019; 100:023108. [PMID: 31574687 DOI: 10.1103/physreve.100.023108] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2019] [Indexed: 06/10/2023]
Abstract
The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the dynamics of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) can massively amplify the instability, (b) cause the fluctuation wavelength that is dominant to evolve in time (a single fastest-growing mode does not exist), and (c) decrease the critical wavelength so that classically stable films can be ruptured.
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Affiliation(s)
- Yixin Zhang
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
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12
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MacDowell LG, Llombart P, Benet J, Palanco JG, Guerrero-Martinez A. Nanocapillarity and Liquid Bridge-Mediated Force between Colloidal Nanoparticles. ACS OMEGA 2018; 3:112-123. [PMID: 31457880 PMCID: PMC6641340 DOI: 10.1021/acsomega.7b01650] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2017] [Accepted: 12/21/2017] [Indexed: 06/10/2023]
Abstract
In this work, we probe the concept of interface tension for ultrathin adsorbed liquid films on the nanoscale by studying the surface fluctuations of films down to the monolayer. Our results show that the spectrum of film height fluctuations of a liquid-vapor surface may be extended to ultrathin films provided we take into account the interactions of the substrate with the surface. Global fluctuations of the film height are described in terms of disjoining pressure, whereas surface deformations that are proportional to the interface area are accounted for by a film thickness-dependent surface tension. As a proof of concept, we model the capillary forces between colloidal nanoparticles held together by liquid bridges. Our results indicate that the classical equations for capillarity follow very precisely down to the nanoscale provided we account for the film height dependence of the surface tension.
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Affiliation(s)
- Luis G. MacDowell
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain
| | - Pablo Llombart
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain
| | - Jorge Benet
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain
| | - Jose G. Palanco
- Departamento
de Materiales y Producción Aeroespacial, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros 3, 28040 Madrid, Spain
| | - Andrés Guerrero-Martinez
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain
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