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Williamson JC, Weatherford EE, DenBeste MM, Riley KC, Yee EF, Rogers ST, Tibbetts CA. Off-Critical Wetting Layer Divergence at the Liquid / Vapor Interface of Binary Liquid Mixtures. J Chem Phys 2022; 157:084504. [DOI: 10.1063/5.0105690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Surface wetting phenomena impact chemistry, physics, biology, and engineering. The wetting behaviors of partially-miscible binary liquid systems are especially complex. Here we report evidence of universal behavior in the divergence of wetting layer growth at liquid-vapor interfaces of the cyclohexane + aniline, hexane + o-toluidine, and methanol + carbon disulfide systems. Layer growth on the micron scale was followed using visible light scattering from stirred samples. Layer thicknesses diverged with decreasing temperature when coexistence was approached from the one-phase region, but only for solutions richer in the higher density / higher surface tension component. The onset of divergence was <1 K above the bulk coexistence temperature; nearer the critical composition, the onset temperature was the critical temperature itself. All three systems showed identical divergent wetting properties after variable normalization. In contrast, no divergent wetting layer formation was seen in the benzene + 1,2-propanediol or water + phenol systems. The mathematical sign of the Hamaker constant correlates with the contrasting behaviors. Collectively, these results have implications for theoretical descriptions of adsorption layer growth and crossover behavior, for measurements of complete wetting temperatures, and for practical applications.
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Affiliation(s)
- J. Charles Williamson
- Department of Chemistry, Willamette University College of Arts and Sciences, United States of America
| | | | - Makayla M. DenBeste
- Willamette University College of Arts and Sciences, United States of America
| | - K. Caroline Riley
- Willamette University College of Arts and Sciences, United States of America
| | - Estella F. Yee
- National Synchrotron Light Source II, Brookhaven National Laboratory, United States of America
| | - Sawyer T. Rogers
- Willamette University College of Arts and Sciences, United States of America
| | - Clara A Tibbetts
- Colorado State University Department of Chemistry, United States of America
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Schoen M, Evans R, Gubbins KE, Rabe JP, Thommes M, Jackson G. Gerhard Findenegg (1938–2019). Mol Phys 2021. [DOI: 10.1080/00268976.2021.1953272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Martin Schoen
- Technische Universität Berlin, Fakultät für Mathematik und Naturwissenschaften, Berlin, Germany
| | - Robert Evans
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK
| | - Keith E. Gubbins
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, USA
| | - Jürgen P. Rabe
- Department of Physics & IRIS Adlershof, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Matthias Thommes
- Department of Chemical and Bioeengineering, Institute of Separation Science and Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, London, UK
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Borjan Z, Vasilyev OA, Upton PJ, Dietrich S. Critical energy-density profile near walls. Phys Rev E 2020; 102:022805. [PMID: 32942512 DOI: 10.1103/physreve.102.022805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 07/27/2020] [Indexed: 11/07/2022]
Abstract
We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is "wet." It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface.
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Affiliation(s)
- Z Borjan
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - O A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - P J Upton
- Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England, United Kingdom
| | - S Dietrich
- Max-Planck-Institut fr Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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Scoppola E, Watkins EB, Campbell RA, Konovalov O, Girard L, Dufrêche J, Ferru G, Fragneto G, Diat O. Solvent Extraction: Structure of the Liquid–Liquid Interface Containing a Diamide Ligand. Angew Chem Int Ed Engl 2016. [DOI: 10.1002/ange.201603395] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Ernesto Scoppola
- Institut Laue-Langevin 38000 Grenoble France
- Institut de Chimie Séparative de MarcouleUMR 5257 CEA/CNRS/ENSCM/Université Montpellier 30207 Bagnols-sur-Cèze France
| | - Erik B. Watkins
- Institut Laue-Langevin 38000 Grenoble France
- Materials Synthesis and Integrated DevicesLos Alamos National Laboratory Los Alamos NM 87545 USA
| | | | - Oleg Konovalov
- European Synchrotron Radiation Facility 38430 Grenoble France
| | - Luc Girard
- Institut de Chimie Séparative de MarcouleUMR 5257 CEA/CNRS/ENSCM/Université Montpellier 30207 Bagnols-sur-Cèze France
| | - Jean‐Francois Dufrêche
- Institut de Chimie Séparative de MarcouleUMR 5257 CEA/CNRS/ENSCM/Université Montpellier 30207 Bagnols-sur-Cèze France
| | | | | | - Olivier Diat
- Institut de Chimie Séparative de MarcouleUMR 5257 CEA/CNRS/ENSCM/Université Montpellier 30207 Bagnols-sur-Cèze France
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Scoppola E, Watkins EB, Campbell RA, Konovalov O, Girard L, Dufrêche JF, Ferru G, Fragneto G, Diat O. Solvent Extraction: Structure of the Liquid-Liquid Interface Containing a Diamide Ligand. Angew Chem Int Ed Engl 2016; 55:9326-30. [PMID: 27320727 DOI: 10.1002/anie.201603395] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Indexed: 11/09/2022]
Abstract
Knowledge of the (supra)molecular structure of an interface that contains amphiphilic ligand molecules is necessary for a full understanding of ion transfer during solvent extraction. Even if molecular dynamics already yield some insight in the molecular configurations in solution, hardly any experimental data giving access to distributions of both extractant molecules and ions at the liquid-liquid interface exist. Here, the combined application of X-ray and neutron reflectivity measurements represents a key milestone in the deduction of the interfacial structure and potential with respect to two different lipophilic ligands. Indeed, we show for the first time that hard trivalent cations can be repelled or attracted by the extractant-enriched interface according to the nature of the ligand.
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Affiliation(s)
- Ernesto Scoppola
- Institut Laue-Langevin, 38000, Grenoble, France.,Institut de Chimie Séparative de Marcoule, UMR 5257 CEA/CNRS/ENSCM/Université Montpellier, 30207, Bagnols-sur-Cèze, France
| | - Erik B Watkins
- Institut Laue-Langevin, 38000, Grenoble, France.,Materials Synthesis and Integrated Devices, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | | | - Oleg Konovalov
- European Synchrotron Radiation Facility, 38430, Grenoble, France
| | - Luc Girard
- Institut de Chimie Séparative de Marcoule, UMR 5257 CEA/CNRS/ENSCM/Université Montpellier, 30207, Bagnols-sur-Cèze, France
| | - Jean-Francois Dufrêche
- Institut de Chimie Séparative de Marcoule, UMR 5257 CEA/CNRS/ENSCM/Université Montpellier, 30207, Bagnols-sur-Cèze, France
| | | | | | - Olivier Diat
- Institut de Chimie Séparative de Marcoule, UMR 5257 CEA/CNRS/ENSCM/Université Montpellier, 30207, Bagnols-sur-Cèze, France.
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Scoppola E, Watkins E, Li Destri G, Porcar L, Campbell RA, Konovalov O, Fragneto G, Diat O. Structure of a liquid/liquid interface during solvent extraction combining X-ray and neutron reflectivity measurements. Phys Chem Chem Phys 2015; 17:15093-7. [PMID: 25993438 DOI: 10.1039/c5cp01809a] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We have resolved the molecular structure of a bulk oil/water interface that contains amphiphilic ligand molecules using a combination of X-ray and neutron reflectivity measurements for the first time. This new capability can greatly impact future work in the field of ion separation by phase transfer, i.e. liquid/liquid extraction.
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Affiliation(s)
- E Scoppola
- Institut Laue-Langevin, 71 avenue des Martyrs, F-38000 Grenoble, France
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Knecht B, Woermann D. Composition Dependence of the Liquid/Air Interfacial Tension of 2-Butoxyethanol/Water Mixtures at Temperatures below the Lower Critical Temperature. ACTA ACUST UNITED AC 2014. [DOI: 10.1002/bbpc.199500032] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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BOWERS JAMES, CLEMENTS PATRICIAJ, McLURE IANA. The structure of the liquid-vapour interface of n-hexane + perfluoro-n-hexane along the path of critical composition through the critical end-point by neutron reflectivity. Mol Phys 2010. [DOI: 10.1080/002689796173101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Yeh MC, Chen CM, Chen LJ. Effect of molecular structure on wetting behavior of water+amphiphile mixtures: A density functional approach. J Chem Phys 2008; 128:044719. [DOI: 10.1063/1.2832323] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Goodchild I, Collier L, Millar SL, Prokes I, Lord JCD, Butts CP, Bowers J, Webster JRP, Heenan RK. Structural studies of the phase, aggregation and surface behaviour of 1-alkyl-3-methylimidazolium halide + water mixtures. J Colloid Interface Sci 2007; 307:455-68. [PMID: 17222419 DOI: 10.1016/j.jcis.2006.11.034] [Citation(s) in RCA: 223] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2006] [Revised: 11/20/2006] [Accepted: 11/20/2006] [Indexed: 11/30/2022]
Abstract
The surface, phase and aggregation behaviour of mixtures of 1-alkyl-3-methylimidazolium halide, [C(n)mim]X, where n is the alkyl chain length, with water has been explored using a variety of methods. Critical micelle concentrations (cmc) and micelle structures have been determined for aqueous [C(n)mim]Br solutions for n=2, 4, 6, 8, and 10. Small-angle neutron scattering (SANS) measurements reveal that for the n=8 and 10 systems, at concentrations just above the cmc, small near-spherical aggregates exist, which, after initial growth, possess core radii (aggregation numbers) at intermediate concentrations of 10.5+/-0.5 Angstrom (22+/-2) and 13.2+/-0.5 Angstrom (40+/-3), respectively, for n=8 and n=10. Towards higher concentrations, the aggregates appear to grow, with the aggregates in the [C(10)mim]Br system becoming increasingly elongated (prolate) with increasing concentration. No evident aggregates are formed in the systems with n=2 and 4. In the n=6 system, it appears that oblate aggregates with radius approximately 9 Angstrom form at the cmc and that the radius increases with increasing concentration. For longer alkyl chain lengths, at high concentrations lyotropic mesophases form in some systems. The mesophase region for the [C(8)mim]Cl system has been explored across the composition range using X-ray diffraction and (2)H NMR spectroscopy. Both techniques suggest that a major hexagonal phase with lattice parameter of 29.5+/-0.5 Angstrom coexists with a minor lamellar phase (23.5+/-0.3 Angstrom) or possibly a second hexagonal phase (27.1+/-0.4 Angstrom). The area per adsorbed molecule at the surface of [C(8)mim]Br solutions has been measured as a function of concentration using neutron reflectometry. A minimum in the area per molecule behaviour is coincident with a minimum identified in the surface tension isotherm occurring close to the cmc. The data suggest depletion of [C(8)mim]Br from the surface region occurs at concentrations immediately above the cmc.
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Affiliation(s)
- Ian Goodchild
- Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD, UK
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Whitmer JK, Kiselev SB, Law BM. Adsorption at the liquid-vapor surface of a binary liquid mixture. J Chem Phys 2005; 123:204720. [PMID: 16351306 DOI: 10.1063/1.2128705] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In a binary liquid mixture, the component possessing the lowest surface tension preferentially adsorbs at the liquid-vapor surface. In the past this adsorption behavior has been extensively investigated for critical binary liquid mixtures near the mixture's critical temperature T(c). In this fluctuation-dominated regime the adsorption is described by a universal function of the dimensionless depth zxi where xi is the bulk correlation length. Fewer studies have quantitatively examined adsorption for off-critical mixtures because, in this case, one must carefully account for both the bulk and surface crossover from the fluctuation-dominated regime (close to T(c)) to the mean-field dominated regime (far from T(c)). In this paper we compare extensive liquid-vapor ellipsometric adsorption measurements for the mixture aniline+cyclohexane at a variety of critical and noncritical compositions with the crossover theory of Kiselev and co-workers [J. Chem. Phys. 112, 3370 (2000)].
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Affiliation(s)
- J K Whitmer
- Department of Physics, Kansas State University, Manhattan, KS 66506-2601, USA
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Wu CK, Chen LJ. Observation of a sequence of wetting transitions in the binary water+ethylene glycol monobutyl ether mixture. J Chem Phys 2005; 123:084506. [PMID: 16164311 DOI: 10.1063/1.2008235] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A homemade pendant drop/bubble tensiometer was assembled and applied to perform the surface-interfacial tension measurements for the binary water+ethylene glycol monobutyl ether (C4E1) mixture over the temperature range from 50 to 128 degrees C at 10 bar. The symbol CiEj is the abbreviation of a nonionic polyoxyethylene alcohol CiH2i+1(OCH2CH2)jOH. The wetting behavior of the C4E1-rich phase at the interface separating the gas and the aqueous phases was systematically examined according to the wetting coefficient calculated from the experimental results of surface/interfacial tensions. It was found that the C4E1-rich phase exhibits a sequence of wetting transitions, nonwetting-->partial wetting-->complete wetting, at the gas-water interface in the water+C4E1 system along with increasing the temperature, consistent with the conjecture of Kahlweit and Busse [J. Chem. Phys. 91, 1339 (1989)]. In addition, the relationship of the mutual solubility and the interfacial tension of the interface separating the C4E1-rich phase and the aqueous phase is discussed.
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Affiliation(s)
- Chih-Kang Wu
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617 Republic of China
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Wu CK, Chen LJ. Wetting behavior of mixtures of water and nonionic polyoxyethylene alcohol. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2005; 21:6883-90. [PMID: 16008400 DOI: 10.1021/la050691i] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Five binary water + C4Ej mixtures, water + n-C4E0, water + 2-C4E0, water + iso-C4E0, water + n-C4E1, and water + iso-C4E1, were chosen to perform the surface/interfacial tension measurements over the experimental temperature range from 10 to 85 degrees C at the normal pressure by using a homemade pendent drop/bubble tensiometer. The symbol CiEj is the abbreviation of a nonionic polyoxyethylene alcohol CiH(2i+1)(OCH2CH2)jOH. The wetting behavior of the CiEj-rich phase at the interface separating gas and the aqueous phase is systematically examined according to the wetting coefficient resulting from the experimental data of surface/interfacial tensions measurements. For those systems with a lower critical solution temperature, for example, water + n-C6E2, water + n-C4E1, and water + iso-C4E1, a wetting transition from partial wetting to nonwetting is always observed when the system is brought to close to its lower critical solution temperature. On the other hand, to start with a partial wetting CiEj-rich phase, a wetting transition from partial wetting to complete wetting is always observed when the system is driven to approach its upper critical solution temperature. The effect of hydrophobicity of CiEj on the wetting behavior of the CiEj-rich phase at the interface separating gas and the aqueous phase was carefully investigated by using five sets of mixtures: (1) water + n-C4E0, water + n-C5E0, and water + n-C6E0; (2) water + 2-C4E0 and water + 2-C5E0; (3) water + 2-C4E0 and water + n-C4E0; (4) water + n-C4E1, water + n-C5E1, and water + n-C6E1; (5) water + n-C4E0 and water + n-C4E1. The CiEj-rich phase would tend to drive away from complete wetting (or nonwetting) to partial wetting with an increase in the hydrophobicity of CiEj in the binary water + CiEj system. All the wetting behavior observed in the water + CiEj mixtures is consistent with the prediction of the critical point wetting theory of Cahn.
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Affiliation(s)
- Chih-Kang Wu
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China
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Rother G, Woywod D, Schoen M, Findenegg GH. Confinement effect on the adsorption from a binary liquid system near liquid/liquid phase separation. J Chem Phys 2004; 120:11864-73. [PMID: 15268220 DOI: 10.1063/1.1755667] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The preferential adsorption of one component of a binary system at the inner surfaces of mesoporous silica glasses was studied in a wide composition range at temperatures close to liquid/liquid phase separation. Confinement effects on the adsorption were investigated by using three controlled-pore glass (CPG-10) materials of different mean pore size (10 to 50 nm). For the experimental system (2-butoxyethanol+water), which exhibits an upper miscibility gap, strong preferential adsorption of water occurs, as the coexistence curve is approached at bulk compositions, at which water is the minority component. In this strong adsorption regime the area-related surface excess amount of adsorbed water decreases with decreasing pore width, while the shift in the volume-related mean composition of the pore liquid shows an opposite trend, i.e., greatest deviation from bulk composition occurring in the most narrow pores. A simple mean-field lattice model of a liquid mixture confined by parallel walls is adopted to rationalize these experimental findings. This model reproduces the main findings of the confinement effect on the adsorption near liquid/liquid phase separation.
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Affiliation(s)
- Gernot Rother
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 112, D-10623 Berlin, Germany
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Yeh MC, Lin PC, Chen LJ. Effect of Molecular Structure on Wetting Behavior at the Air−Liquid Interface of Water + Alcohol Mixtures. J Phys Chem B 2004. [DOI: 10.1021/jp0380531] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ming-Chih Yeh
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China
| | - Ping-Chang Lin
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China
| | - Li-Jen Chen
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China
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Howse JR, Manzanares-Papayanopoulos E, McLure IA, Bowers J, Steitz R, Findenegg GH. Critical adsorption and boundary layer structure of 2-butoxyethanol+D2O mixtures at a hydrophilic silica surface. J Chem Phys 2002. [DOI: 10.1063/1.1463398] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schulz J, Bowers J, Findenegg GH. Crossover from Preferential Adsorption to Depletion: Aqueous Systems of Short-Chain CnEm Amphiphiles at Liquid/Liquid Interfaces. J Phys Chem B 2001. [DOI: 10.1021/jp010616q] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jens Schulz
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 112, D-10623 Berlin, Germany
| | - James Bowers
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 112, D-10623 Berlin, Germany
| | - Gerhard H. Findenegg
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 112, D-10623 Berlin, Germany
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Borjan Z, Upton PJ. Local-functional theory of critical adsorption. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:065102. [PMID: 11415157 DOI: 10.1103/physreve.63.065102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2000] [Indexed: 05/23/2023]
Abstract
Local-functional methods are applied to critical adsorption in three-dimensional Ising-like systems. The universal order-parameter-profile scaling functions, P(+/-)(x), along the critical isochore (+) and phase boundary (-), are calculated along with their associated universal amplitudes. Good agreement is found with the results of Monte Carlo simulations. General properties of P(+/-)(x) for small and large scaled distance, x, are elucidated. An order-parameter scaling function, P(c)(x), for critical adsorption along the critical isotherm is introduced and calculated.
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Affiliation(s)
- Z Borjan
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Ave., Bristol BS8 1TL, England
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Smith DS, Law BM. Ellipsometric study of critical adsorption and measurement of universal surface integrals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2727-2745. [PMID: 9965387 DOI: 10.1103/physreve.54.2727] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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