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Te Vrugt M, Topp L, Wittkowski R, Heuer A. Microscopic derivation of the thin film equation using the Mori-Zwanzig formalism. J Chem Phys 2024; 161:094904. [PMID: 39225531 DOI: 10.1063/5.0217535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2024] [Accepted: 07/19/2024] [Indexed: 09/04/2024] Open
Abstract
The hydrodynamics of thin films is typically described using macroscopic models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for mobility and free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers.
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Affiliation(s)
- Michael Te Vrugt
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Leon Topp
- Institute of Physical Chemistry, Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institute of Theoretical Physics, Center for Soft Nanoscience, Universität Münster, 48149 Münster, Germany
| | - Andreas Heuer
- Institute of Physical Chemistry, Universität Münster, 48149 Münster, Germany
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2
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Rehner P, Aasen A, Wilhelmsen Ø. Tolman lengths and rigidity constants from free-energy functionals—General expressions and comparison of theories. J Chem Phys 2019; 151:244710. [DOI: 10.1063/1.5135288] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Rehner
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - A. Aasen
- Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
- SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Ø. Wilhelmsen
- Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
- SINTEF Energy Research, NO-7465 Trondheim, Norway
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3
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Mu X, Frank F, Riviere B, Alpak FO, Chapman WG. Mass-Conserved Density Gradient Theory Model for Nucleation Process. Ind Eng Chem Res 2018. [DOI: 10.1021/acs.iecr.8b03389] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaoqun Mu
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
| | - Florian Frank
- Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg 91054, Erlangen, Germany
| | - Beatrice Riviere
- Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, United States
| | - Faruk O. Alpak
- Shell International Exploration and Production Inc., Houston, Texas 77082, United States
| | - Walter G. Chapman
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
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4
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Aasen A, Blokhuis EM, Wilhelmsen Ø. Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples. J Chem Phys 2018; 148:204702. [PMID: 29865818 DOI: 10.1063/1.5026747] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The curvature dependence of the surface tension can be described by the Tolman length (first-order correction) and the rigidity constants (second-order corrections) through the Helfrich expansion. We present and explain the general theory for this dependence for multicomponent fluids and calculate the Tolman length and rigidity constants for a hexane-heptane mixture by use of square gradient theory. We show that the Tolman length of multicomponent fluids is independent of the choice of dividing surface and present simple formulae that capture the change in the rigidity constants for different choices of dividing surface. For multicomponent fluids, the Tolman length, the rigidity constants, and the accuracy of the Helfrich expansion depend on the choice of path in composition and pressure space along which droplets and bubbles are considered. For the hexane-heptane mixture, we find that the most accurate choice of path is the direction of constant liquid-phase composition. For this path, the Tolman length and rigidity constants are nearly linear in the mole fraction of the liquid phase, and the Helfrich expansion represents the surface tension of hexane-heptane droplets and bubbles within 0.1% down to radii of 3 nm. The presented framework is applicable to a wide range of fluid mixtures and can be used to accurately represent the surface tension of nanoscopic bubbles and droplets.
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Affiliation(s)
- Ailo Aasen
- Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Edgar M Blokhuis
- Colloid and Interface Science, Leiden Institute of Chemistry, 2300 RA Leiden, The Netherlands
| | - Øivind Wilhelmsen
- Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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5
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Rehner P, Gross J. Surface tension of droplets and Tolman lengths of real substances and mixtures from density functional theory. J Chem Phys 2018; 148:164703. [DOI: 10.1063/1.5020421] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Philipp Rehner
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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6
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Wilhelmsen Ø, Trinh TT, Lervik A. Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties. Phys Rev E 2018; 97:012126. [PMID: 29448485 DOI: 10.1103/physreve.97.012126] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2015] [Indexed: 11/07/2022]
Abstract
Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.
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Affiliation(s)
- Øivind Wilhelmsen
- Department of Energy and Process Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway and SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Thuat T Trinh
- Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Anders Lervik
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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7
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Guo Z, Liu Y, Lohse D, Zhang X, Zhang X. Stability of micro-Cassie states on rough substrates. J Chem Phys 2015; 142:244704. [DOI: 10.1063/1.4922905] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhenjiang Guo
- State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
| | - Yawei Liu
- State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
| | - Detlef Lohse
- Physics of Fluids group, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Xuehua Zhang
- Physics of Fluids group, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, VIC 3001, Australia
| | - Xianren Zhang
- State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
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8
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Wilhelmsen Ø, Bedeaux D, Reguera D. Tolman length and rigidity constants of the Lennard-Jones fluid. J Chem Phys 2015; 142:064706. [DOI: 10.1063/1.4907588] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Øivind Wilhelmsen
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, Barcelona, Spain
| | - Dick Bedeaux
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - David Reguera
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, Barcelona, Spain
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9
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Guo Z, Liu Y, Zhang X. Constrained lattice density functional theory and its applications on vapor–liquid nucleations. Sci Bull (Beijing) 2015. [DOI: 10.1007/s11434-014-0702-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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10
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Li J, Liu Y, Jiang G, Zhang X. Vapour-to-liquid nucleation in cone pores. MOLECULAR SIMULATION 2015. [DOI: 10.1080/08927022.2014.1001990] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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11
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Guo Q, Liu Y, Jiang G, Zhang X. Cooperative effect in nucleation: Nanosized seed particles jointly nucleate vapor-liquid transitions. J Chem Phys 2013; 138:214701. [DOI: 10.1063/1.4807726] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Blokhuis EM, van Giessen AE. Density functional theory of a curved liquid-vapour interface: evaluation of the rigidity constants. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:225003. [PMID: 23640023 DOI: 10.1088/0953-8984/25/22/225003] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k in its description. New formulae for k and k in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface, and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules shows that k is negative with a value around minus 0.5-1.0 kBT and that k is positive with a value that is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R(2) replaces the rigidity constants and we determine the (universal) proportionality constants.
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Affiliation(s)
- Edgar M Blokhuis
- Colloid and Interface Science, Leiden Institute of Chemistry, Gorlaeus Laboratories, PO Box 9502, 2300 RA Leiden, The Netherlands.
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13
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Malijevský A, Jackson G. A perspective on the interfacial properties of nanoscopic liquid drops. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464121. [PMID: 23114181 DOI: 10.1088/0953-8984/24/46/464121] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The structural and interfacial properties of nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the macroscopic level and the microscopic level of density functional theory (DFT). With a novel analysis we show that a purely macroscopic (static) mechanical treatment can lead to a qualitatively reasonable description of the surface tension and the Tolman length of a liquid drop; the latter parameter, which characterizes the curvature dependence of the tension, is found to be negative and has a magnitude of about a half of the molecular dimension. A mechanical slant cannot, however, be considered satisfactory for small finite-size systems where fluctuation effects are significant. From the opposite perspective, a curvature expansion of the macroscopic thermodynamic properties (density and chemical potential) is then used to demonstrate that a purely thermodynamic approach of this type cannot in itself correctly account for the curvature correction of the surface tension of liquid drops. We emphasize that any approach, e.g., classical nucleation theory, which is based on a purely macroscopic viewpoint, does not lead to a reliable representation when the radius of the drop becomes microscopic. The description of the enhanced inhomogeneity exhibited by small drops (particularly in the dense interior) necessitates a treatment at the molecular level to account for finite-size and surface effects correctly. The so-called mechanical route, which corresponds to a molecular-level extension of the macroscopic theory of elasticity and is particularly popular in molecular dynamics simulation, also appears to be unreliable due to the inherent ambiguity in the definition of the microscopic pressure tensor, an observation which has been known for decades but is frequently ignored. The union of the theory of capillarity (developed in the nineteenth century by Gibbs and then promoted by Tolman) with a microscopic DFT treatment allows for a direct and unambiguous description of the interfacial properties of drops of arbitrary size; DFT provides all of the bulk and surface characteristics of the system that are required to uniquely define its thermodynamic properties. In this vein, we propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine drops of varying size. A comparison of the predictions of our DFT with recent simulation data based on a second-order fluctuation analysis (Sampayo et al 2010 J. Chem. Phys. 132 141101) reveals the consistency of the two treatments. This observation highlights the significance of fluctuation effects in small drops, which give rise to additional entropic (thermal non-mechanical) contributions, in contrast to what one observes in the case of planar interfaces which are governed by the laws of mechanical equilibrium. A small negative Tolman length (which is found to be about a tenth of the molecular diameter) and a non-monotonic behaviour of the surface tension with the drop radius are predicted for the LJ fluid. Finally, the limits of the validity of the Tolman approach, the effect of the range of the intermolecular potential, and the behaviour of bubbles are briefly discussed.
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Affiliation(s)
- Alexandr Malijevský
- E Hála Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals of the ASCR, Prague 6, Czech Republic.
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14
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Liu Y, Men Y, Zhang X. Nucleation mechanism for vapor-to-liquid transition from substrates with nanoscale pores opened at one end. J Chem Phys 2012; 137:104701. [DOI: 10.1063/1.4749319] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Men Y, Zhang X. Physical basis for constrained lattice density functional theory. J Chem Phys 2012; 136:124704. [DOI: 10.1063/1.3698197] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Liu Y, Men Y, Zhang X. How nanoscale seed particles affect vapor-liquid nucleation. J Chem Phys 2011; 135:184701. [DOI: 10.1063/1.3658502] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Corti DS, Kerr KJ, Torabi K. On the interfacial thermodynamics of nanoscale droplets and bubbles. J Chem Phys 2011; 135:024701. [PMID: 21766963 DOI: 10.1063/1.3609274] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
We present a new self-consistent thermodynamic formalism for the interfacial properties of nanoscale embryos whose interiors do not exhibit bulklike behavior and are in complete equilibrium with the surrounding mother phase. In contrast to the standard Gibbsian analysis, whereby a bulk reference pressure based on the same temperature and chemical potentials of the mother phase is introduced, our approach naturally incorporates the normal pressure at the center of the embryo as an appropriate reference pressure. While the interfacial properties of small embryos that follow from the use of these two reference pressures are different, both methods yield by construction the same reversible work of embryo formation as well as consistency between their respective thermodynamic and mechanical routes to the surface tension. Hence, there is no a priori reason to select one method over another. Nevertheless, we argue, and demonstrate via a density-functional theory (with the local density approximation) analysis of embryo formation in the pure component Lennard-Jones fluid, that our new method generates more physically appealing trends. For example, within the new approach the surface tension at all locations of the dividing surface vanishes at the spinodal where the density profile spanning the embryo and mother phase becomes completely uniform (only the surface tension at the Gibbs surface of tension vanishes in the Gibbsian method at this same limit). Also, for bubbles, the location of the surface of tension now diverges at the spinodal, similar to the divergent behavior exhibited by the equimolar dividing surface (in the Gibbsian method, the location of the surface of tension vanishes instead). For droplets, the new method allows for the appearance of negative surface tensions (the Gibbsian method always yields positive tensions) when the normal pressures within the interior of the embryo become less than the bulk pressure of the surrounding vapor phase. Such a prediction, which is allowed by thermodynamics, is consistent with the interpretation that the mother phase's attempted compression of the droplet is counterbalanced by the negative surface tension, or free energy cost to decrease the interfacial area. Furthermore, for these same droplets, the surface of tension can no longer be meaningfully defined (the surface of tension always remains well defined in the Gibbsian method). Within the new method, the dividing surface at which the surface tension equals zero emerges as a new lengthscale, which has various thermodynamic analogs to and similar behavior as the surface of tension.
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Affiliation(s)
- David S Corti
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100, USA.
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18
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Ghosh S, Ghosh SK. Density functional theory of size-dependent surface tension of Lennard-Jones fluid droplets using a double well type Helmholtz free energy functional. J Chem Phys 2011; 135:124710. [DOI: 10.1063/1.3633475] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Zhou D, Zeng M, Mi J, Zhong C. Theoretical Study of Phase Transition, Surface Tension, and Nucleation Rate Predictions for Argon. J Phys Chem B 2010; 115:57-63. [PMID: 21162588 DOI: 10.1021/jp104969c] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Di Zhou
- Laboratory of Computational Chemistry, Department of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
| | - Ming Zeng
- Laboratory of Computational Chemistry, Department of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
| | - Jianguo Mi
- Laboratory of Computational Chemistry, Department of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
| | - Chongli Zhong
- Laboratory of Computational Chemistry, Department of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
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20
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Uline MJ, Torabi K, Corti DS. Homogeneous nucleation and growth in simple fluids. II. Scaling behavior, instabilities, and the (n,v) order parameter. J Chem Phys 2010; 133:174512. [DOI: 10.1063/1.3499314] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Sampayo JG, Malijevský A, Müller EA, de Miguel E, Jackson G. Communications: Evidence for the role of fluctuations in the thermodynamics of nanoscale drops and the implications in computations of the surface tension. J Chem Phys 2010; 132:141101. [DOI: 10.1063/1.3376612] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Verkouteren RM, Verkouteren JR. Inkjet metrology: high-accuracy mass measurements of microdroplets produced by a drop-on-demand dispenser. Anal Chem 2009; 81:8577-84. [PMID: 19824716 PMCID: PMC2762308 DOI: 10.1021/ac901563j] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2009] [Accepted: 08/31/2009] [Indexed: 12/04/2022]
Abstract
We describe gravimetric methods for measuring the mass of droplets generated by a drop-on-demand (DOD) microdispenser. Droplets are deposited, either continuously at a known frequency or as a burst of known number, into a cylinder positioned on a submicrogram balance. Mass measurements are acquired precisely by computer, and results are corrected for evaporation. Capabilities are demonstrated using isobutyl alcohol droplets. For ejection rates greater than 100 Hz, the repeatability of droplet mass measurements was 0.2%, while the combined relative standard uncertainty (u(c)) was 0.9%. When bursts of droplets were dispensed, the limit of quantitation was 72 microg (1490 droplets) with u(c) = 1.0%. Individual droplet size in a burst was evaluated by high-speed videography. Diameters were consistent from the tenth droplet onward, and the mass of an individual droplet was best estimated by the average droplet mass with a combined uncertainty of about 1%. Diameters of the first several droplets were anomalous, but their contribution was accounted for when dispensing bursts. Above the limits of quantitation, the gravimetric methods provided statistically equivalent results and permit detailed study of operational factors that influence droplet mass during dispensing, including the development of reliable microassays and standard materials using DOD technologies.
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Affiliation(s)
- R Michael Verkouteren
- Surface and Microanalysis Research Division, Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
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Jiang T, Wu J. Cluster formation and bulk phase behavior of colloidal dispersions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021401. [PMID: 19792118 DOI: 10.1103/physreve.80.021401] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2009] [Revised: 06/22/2009] [Indexed: 05/28/2023]
Abstract
We investigated cluster formation in model colloids where the interparticle potential beyond the collision diameter includes a short-ranged attraction and a longer-ranged repulsion. The structure and thermodynamic properties of the model system can be accurately described by the first-order mean-spherical approximation (FMSA) and a perturbation theory for bulk phases and by a nonlocal density-functional theory (DFT) for stable/metastable clusters. In corroboration with recent experiments and molecular simulations, we predicted that the bulk to cluster transition may occur at both one-phase and two-phase regions of the colloidal phase diagram. While formation of colloidal clusters appears uncorrelated with the bulk phase transitions, the local phenomena may nevertheless play an important role in the dynamics of stable colloids and the kinetics of colloidal phase transitions.
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Affiliation(s)
- Tao Jiang
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521-0444, USA
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24
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Men Y, Yan Q, Jiang G, Zhang X, Wang W. Nucleation and hysteresis of vapor-liquid phase transitions in confined spaces: effects of fluid-wall interaction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051602. [PMID: 19518462 DOI: 10.1103/physreve.79.051602] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2008] [Revised: 02/24/2009] [Indexed: 05/27/2023]
Abstract
In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, w , in this work, we have classified w into three regions ( w>0.9 , 0.1< or =w< or =0.9 , and w<0.1 ), which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.
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Affiliation(s)
- Yumei Men
- Division of Molecular and Materials Simulation, Key Laboratory for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China
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25
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Li Z, Wu J. Formation of lamellar structures from spherical particles. J Chem Phys 2009; 130:165102. [DOI: 10.1063/1.3118681] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Wu J. Solvation of a Spherical Cavity in Simple Liquids: Interpolating between the Limits. J Phys Chem B 2009; 113:6813-8. [DOI: 10.1021/jp9016163] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521
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