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Chakraborty P, Mitra S, Kim AR, Zhao B, Mitra SK. Density Functional Theory Approach to Interpret Elastowetting of Hydrogels. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:7168-7177. [PMID: 38498935 DOI: 10.1021/acs.langmuir.4c00327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/20/2024]
Abstract
Sessile hydrogel drops on rigid surfaces exhibit a wetting/contact morphology intermediate between liquid drops and glass spheres. Using density functional theory, we reveal the contact forces acting between a hydrogel and a rigid glass surface. We show that while transitioning from liquid-like to solid-like hydrogels, there exists a critical hydrogel elasticity that enables a switch from attractive-to-repulsive interaction with the underlying rigid glass surface. Our theoretical model is validated by experimental observations of sessile polyacrylamide hydrogels of varying elasticity on glass surfaces. Further, the proposed model successfully approaches Young's law in the pure liquid limit and work of adhesion in the glassy limit. Lastly, we show a modified contact angle relation, taking into account the hydrogel elasticity to explain the features of a distinct hydrogel foot.
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Affiliation(s)
- Priyam Chakraborty
- Micro & Nano-scale Transport Laboratory, Surface Science and Bio-nanomaterials Laboratory Group, Department of Chemical Engineering Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Surjyasish Mitra
- Micro & Nano-scale Transport Laboratory, Department of Mechanical and Mechatronics Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - A-Reum Kim
- Micro & Nano-scale Transport Laboratory, Surface Science and Bio-nanomaterials Laboratory Group, Department of Chemical Engineering Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Boxin Zhao
- Surface Science and Bio-nanomaterials Laboratory Group, Department of Chemical Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Sushanta K Mitra
- Micro & Nano-scale Transport Laboratory, Department of Mechanical and Mechatronics Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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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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Squarcini A, Malgaretti P. Inhomogeneous surface tension of chemically active fluid interfaces. J Chem Phys 2020; 153:234903. [PMID: 33353340 DOI: 10.1063/5.0025989] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach, we derive closed-form expressions for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-monotonous dependence of the surface tension on the spatial separation between the peaks of the density of the suspended phase. Our results also predict the local value of the surface tension in the case in which the density of the suspended phase is not homogeneous along the interface.
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Affiliation(s)
- Alessio Squarcini
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
| | - Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
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Romero-Enrique JM, Squarcini A, Parry AO, Goldbart PM. Curvature corrections to the nonlocal interfacial model for short-ranged forces. Phys Rev E 2018; 97:062804. [PMID: 30011600 DOI: 10.1103/physreve.97.062804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Indexed: 11/07/2022]
Abstract
In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.
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Affiliation(s)
- José M Romero-Enrique
- Departamento de Física Atómica, Molecular y Nuclear, Área de Física Teórica, Universidad de Sevilla, Avenida de Reina Mercedes s/n, 41012 Seville, Spain
| | - Alessio Squarcini
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.,IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Paul M Goldbart
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, USA
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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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MacDowell LG. Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface. Phys Rev E 2017; 96:022801. [PMID: 28950477 DOI: 10.1103/physreve.96.022801] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2017] [Indexed: 11/07/2022]
Abstract
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.
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Affiliation(s)
- Luis G MacDowell
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense, Madrid 28040, Spain
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Hughes AP, Thiele U, Archer AJ. Influence of the fluid structure on the binding potential: Comparing liquid drop profiles from density functional theory with results from mesoscopic theory. J Chem Phys 2017; 146:064705. [DOI: 10.1063/1.4974832] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
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8
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Malijevský A, Parry AO. Influence of intermolecular forces at critical-point wedge filling. Phys Rev E 2016; 93:040801. [PMID: 27176242 DOI: 10.1103/physreve.93.040801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Indexed: 11/07/2022]
Abstract
We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or nonretarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated.
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Affiliation(s)
- Alexandr Malijevský
- Department of Physical Chemistry, Institute of Chemical Technology, Prague, 166 28 Praha 6, Czech Republic and Institute of Chemical Process Fundamentals, Academy of Sciences, 16502 Prague 6, Czech Republic
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, London SW7 2B7, United Kingdom
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Fernández EM, Chacón E, MacDowell LG, Tarazona P. Mesoscopic Hamiltonian for the fluctuations of adsorbed Lennard-Jones liquid films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062404. [PMID: 26172722 DOI: 10.1103/physreve.91.062404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2015] [Indexed: 06/04/2023]
Abstract
We use Monte Carlo simulations of a Lennard-Jones fluid adsorbed on a short-range planar wall substrate to study the fluctuations in the thickness of the wetting layer, and we get a quantitative and consistent characterization of their mesoscopic Hamiltonian, H[ξ]. We have observed important finite-size effects, which were hampering the analysis of previous results obtained with smaller systems. The results presented here support an appealing simple functional form for H[ξ], close but not exactly equal to the theoretical nonlocal proposal made on the basis a generic density-functional analysis by Parry and coworkers. We have analyzed systems under different wetting conditions, as a proof of principle for a method that provides a quantitative bridge between the molecular interactions and the phenomenology of wetting films at mesoscopic scales.
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Affiliation(s)
- Eva M Fernández
- Departamento de Física Fundamental, Universidad Nacional de Educación Distancia, Madrid, Spain and Instituto de Ciencia de Materiales de Madrid, CSIC, 28049, Madrid, Spain
| | - Enrique Chacón
- Instituto de Ciencia de Materiales de Madrid, CSIC, 28049, Madrid, Spain and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autońoma de Madrid, Madrid, 28049, Spain
| | - Luis G MacDowell
- Departamento de Química Física, Universidad Complutense de Madrid, 28040, Madrid, Spain
| | - Pedro Tarazona
- Departamento de Física Teórica de la Materia Condensada, Condensed Matter Physics Center IFIMAC and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, 28049, Spain
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Hughes AP, Thiele U, Archer AJ. Liquid drops on a surface: Using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling. J Chem Phys 2015; 142:074702. [DOI: 10.1063/1.4907732] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Affiliation(s)
- Adam P. Hughes
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Uwe Thiele
- Westfälische Wilhelms-Universität Münster, Institut für Theorestische Physik, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
- Center of Nonlinear Science (CeNoS), Westfälische Wilhelms Universität Münster, Corrensstr. 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation (CMTC), University of Münster, Corrensstr. 40, 48149 Münster, Germany
| | - Andrew J. Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
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Rodríguez-Rivas Á, Galván J, Romero-Enrique JM. Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau-Ginzburg model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:035101. [PMID: 25437528 DOI: 10.1088/0953-8984/27/3/035101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We study the interfacial phenomenology of a fluid in contact with a one-dimensional array of infinitely long grooves of sinusoidal section, characterized by the periodicity length L and amplitude A. The system is modelled by the Landau-Ginzburg-Wilson functional, with fluid-substrate couplings which control the wettability of the substrate. We investigate the filling and wetting phenomena within the mean-field approximation, and compare with the predictions of the macroscopic and interfacial Hamiltonian theories. For large values of L and under bulk coexistence conditions, we observe first-order filling transitions between dry (D) and partially filled (F) interfacial states, and wetting transitions between partially filled F and completely wet (W) interfacial states of the same order as for the flat substrate. Depending on the order of the wetting transition, the transition temperature is either shifted towards lower temperatures for first-order wetting or it coincides with the wetting temperature on the flat substrate for continuous wetting. On the other hand, if the groove height is of order of the correlation length, only wetting transitions between D and W states are observed under bulk coexistence conditions. For this case, the transition temperature shift obeys approximately Wenzel's phenomenological law if the substrate favors first-order wetting, but it remains unshifted for continuous wetting. The borderline between the small and large L regimes correspond to a D - F - W triple point if wetting is first-order, and a D - F critical point for continuous wetting. Beyond bulk coexistence conditions, filling and first-order wetting transitions continue into off-coexistence filling and prewetting lines, which end up at critical points. Our findings show that the macroscopic theory only describes accurately the filling transition close to bulk coexistence and large L, while microscopic structure of the fluid is essential to understand wetting and filling away from bulk coexistence.
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Affiliation(s)
- Álvaro Rodríguez-Rivas
- Departamento de Física Atómica, Molecular y Nuclear, Area de Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
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MacDowell LG, Benet J, Katcho NA, Palanco JM. Disjoining pressure and the film-height-dependent surface tension of thin liquid films: new insight from capillary wave fluctuations. Adv Colloid Interface Sci 2014; 206:150-71. [PMID: 24351859 DOI: 10.1016/j.cis.2013.11.003] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2013] [Revised: 11/05/2013] [Accepted: 11/06/2013] [Indexed: 10/26/2022]
Abstract
In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.
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Indekeu JO, Koga K, Hooyberghs H, Parry AO. Renormalization group calculations for wetting transitions of infinite order and continuously varying order: local interface Hamiltonian approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022122. [PMID: 24032790 DOI: 10.1103/physreve.88.022122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2013] [Indexed: 06/02/2023]
Abstract
We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.
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Affiliation(s)
- J O Indekeu
- Institute for Theoretical Physics, KU Leuven, BE-3001 Leuven, Belgium
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MacDowell LG, Benet J, Katcho NA. Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid film. PHYSICAL REVIEW LETTERS 2013; 111:047802. [PMID: 23931407 DOI: 10.1103/physrevlett.111.047802] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2013] [Indexed: 06/02/2023]
Abstract
Our understanding of both structure and dynamics of adsorbed liquids heavily relies on the capillary wave Hamiltonian, but a thorough test of this model is still lacking. Here we study the capillary wave fluctuations of a liquid film with short-range forces adsorbed on a solid exhibiting van der Waals interactions. We show for the first time that the measured capillary wave spectrum right above the first order wetting transition provides an interface potential consistent with independent calculations from thermodynamic integration. However, the surface tension exhibits an oscillatory film thick dependence which reveals a hitherto unnoticed capillary wave broadening mechanism beyond mere interfacial displacements.
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Affiliation(s)
- Luis G MacDowell
- Departamento de Química Física, Facultad de Química, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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Koga K, Indekeu J, Widom B. Wetting transitions of continuously varying or infinite order from a mean-field density-functional theory. Mol Phys 2011. [DOI: 10.1080/00268976.2011.556095] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Koga K, Indekeu JO, Widom B. Infinite-order transitions in density-functional models of wetting. PHYSICAL REVIEW LETTERS 2010; 104:036101. [PMID: 20366660 DOI: 10.1103/physrevlett.104.036101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2009] [Indexed: 05/29/2023]
Abstract
A class of density-functional models for wetting transitions is defined. A necessary condition for the transitions to be of higher than first order is derived. A locus of wetting transitions in the plane of two model field variables is determined on which there are states of first-order and of higher-order, including infinite-order, transitions. The observed behavior is rationalized via a different but related, analytically soluble model.
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Affiliation(s)
- K Koga
- Department of Chemistry, Faculty of Science, Okayama University, Okayama 700-8530, Japan
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