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Yadav M, Singh Y. Depletion potential, correlation functions and demixing transition in model colloid-polymer mixtures. J Colloid Interface Sci 2024; 675:1100-1107. [PMID: 39047528 DOI: 10.1016/j.jcis.2024.07.053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2024] [Revised: 07/03/2024] [Accepted: 07/06/2024] [Indexed: 07/27/2024]
Abstract
We describe a theoretical framework to calculate depletion potential between colloid particles induced by non-adsorbing ideal polymer chains (s-species) and correlation functions in a coarse-grained one-component system of colloids (c-species). A Padé approximant is used to express the depletion potential as a pair potential with many-body contributions subsumed in it. The depletion potential and correlation functions of c-species are calculated using a self-consistent procedure. Results for several values of size ratio q=σsσc (σs and σc are, respectively diameters of the polymer chain and a colloid particle) and packing fractions of s- and c-species are reported. The spinodal curve and critical point of demixing transition are determined for several values of q. Calculated values are compared with values found from other theories and simulations.
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Affiliation(s)
- Mamta Yadav
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
| | - Yashwant Singh
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India.
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2
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Yadav M, Singh Y. Coarse-grained Hamiltonian and effective one component theory of colloidal suspensions. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
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3
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Maeritz M, Oettel M. Droplet condensation in the lattice gas with density functional theory. Phys Rev E 2021; 104:034127. [PMID: 34654142 DOI: 10.1103/physreve.104.034127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/16/2021] [Indexed: 06/13/2023]
Abstract
A density functional for the lattice gas with next-neighbor attractions (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. The density functional is constructed via an auxiliary model with hard lattice gas particles and lattice polymers to incorporate the attractions. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density ρ[over ¯] in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential μ(ρ[over ¯]) are seen upon lowering the temperature away from the critical temperature [oscillations in μ(ρ[over ¯]) in the slab portion and spiky undulations in μ(ρ[over ¯]) in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension R_{s} in the droplet region]. This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension γ(R_{s}) gave a dominant contribution ∝1/R_{s}^{2}, although the consistency of γ(R_{s}) with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution ∝lnR_{s}/R_{s}^{2} in γ(R_{s}). The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.
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Affiliation(s)
- M Maeritz
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
| | - M Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
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4
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Maeritz M, Oettel M. Density functional for the lattice gas from fundamental measure theory. Phys Rev E 2021; 104:024124. [PMID: 34525668 DOI: 10.1103/physreve.104.024124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 06/11/2021] [Indexed: 06/13/2023]
Abstract
We construct a density functional for the lattice gas or Ising model on square and cubic lattices based on lattice fundamental measure theory. To treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.
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Affiliation(s)
- M Maeritz
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
| | - M Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
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5
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Egorov SA. Phase behavior of colloid-polymer mixtures in planar, spherical, and cylindrical confinement: A density functional theory study. J Chem Phys 2021; 154:184902. [PMID: 34241015 DOI: 10.1063/5.0048709] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Asakura-Oosawa (AO) model of colloid-polymer mixtures has been extensively studied over the past several decades both via computer simulations and Density Functional Theory (DFT). At this point, its structural and thermodynamic properties both in the bulk and in contact with flat structureless walls are well understood. At the same time, the phase behavior of AO mixtures in spherical cavities and cylindrical pores, while thoroughly investigated by simulations, has not received a comparably detailed DFT treatment. In this paper, we use the DFT results for the AO model in the bulk and under planar confinement as a point of reference for studying its thermodynamic and structural properties in cavities and pores. The accuracy of the DFT approach is assessed by comparing its predictions with the available extensive simulation data; good overall agreement is generally found with some notable exceptions in the vicinity of wetting and drying transitions. The deviations of the phase behavior in confinement from the bulk phase diagram are analyzed using the Kelvin equation, which is seen to work reasonably well under moderate confinement, i.e., for sufficiently large radii of confining cavities and pores.
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Affiliation(s)
- Sergei A Egorov
- Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, USA
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6
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Yadav M, Singh Y. The solvent mediated interaction potential between solute particles: theory and applications. SOFT MATTER 2020; 16:9780-9788. [PMID: 33001128 DOI: 10.1039/d0sm01168a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this paper we develop a theory to calculate the solvent mediated interaction potential between solute particles dispersed in a solvent. The potential is a functional of the instantaneous distribution of solute particles and is expressed in terms of the solute-solvent direct pair correlation function and the density-density correlation function of the bulk solvent. The dependence of the direct pair correlation function on multi-point correlations of the solute distribution is simplified with a mean field approximation. A self consistent approach is developed to calculate the effective potential between solute particles, the solute-solvent and the solute-solute correlation functions. The significance of the solvent fluctuations on the range of the effective potential is elucidated. The theory is applied to calculate equilibrium properties of the Asakura-Oosawa (AO) model for several values of solute and solvent densities and for several values of the particles size ratio. The results give a quantitative description of many-body effect on the effective potential and on the pair correlation functions.
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Affiliation(s)
- Mamta Yadav
- Department of Physics, Banaras Hindu University, Varanasi-221005, India.
| | - Yashwant Singh
- Department of Physics, Banaras Hindu University, Varanasi-221005, India.
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7
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Vis M, Brouwer KJH, González García Á, Petukhov AV, Konovalov O, Tuinier R. Quantification of the Structure of Colloidal Gas-Liquid Interfaces. J Phys Chem Lett 2020; 11:8372-8377. [PMID: 32957778 PMCID: PMC7528408 DOI: 10.1021/acs.jpclett.0c02464] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 09/15/2020] [Indexed: 05/17/2023]
Abstract
We have quantified the structure of the colloidal gas-liquid interface using synchrotron X-ray reflectivity measurements on a model colloid-polymer mixture. The interfacial width shows mean-field scaling with the colloid density difference, and the density profiles appear to be monotonic. Furthermore, our measurements allow us to distinguish between different theoretical polymer descriptions commonly used to model colloid-polymer mixtures. Our results highlight the importance of capturing the correct polymer physics in obtaining a quantitative theoretical description of the colloidal gas-liquid interface.
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Affiliation(s)
- Mark Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Kelly J H Brouwer
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, 3508 TA Utrecht, The Netherlands
| | - Álvaro González García
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, 3508 TA Utrecht, The Netherlands
| | - Andrei V Petukhov
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, 3508 TA Utrecht, The Netherlands
| | - Oleg Konovalov
- European Synchroton Radiation Facility, 38000 Grenoble, France
| | - Remco Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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8
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Tschopp SM, Vuijk HD, Sharma A, Brader JM. Mean-field theory of inhomogeneous fluids. Phys Rev E 2020; 102:042140. [PMID: 33212746 DOI: 10.1103/physreve.102.042140] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 10/13/2020] [Indexed: 06/11/2023]
Abstract
The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.
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Affiliation(s)
- S M Tschopp
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
| | - H D Vuijk
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Deutschland
| | - A Sharma
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Deutschland
| | - J M Brader
- Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland
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9
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Enhancement of stratification of colloidal particles near a substrate induced by addition of non-adsorbing polymers. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.136705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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10
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Kobayashi H, Rohrbach PB, Scheichl R, Wilding NB, Jack RL. Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model. J Chem Phys 2019; 151:144108. [DOI: 10.1063/1.5120833] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Hideki Kobayashi
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paul B. Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert Scheichl
- Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Nigel B. Wilding
- H.H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Robert L. Jack
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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11
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Lin SC, Oettel M. Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional binary hard-disk mixtures. Phys Rev E 2018; 98:012608. [PMID: 30110806 DOI: 10.1103/physreve.98.012608] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Indexed: 06/08/2023]
Abstract
Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional binary hard-disk mixtures are determined for the whole range of size ratios q=smalldiameter/largediameter, assuming random disorder (lattice points or interstitial occupied by large or small disks at random) in the crystal phase. The fluid-crystal transitions are first order due to the assumption of a periodic unit cell in the density-functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard-sphere mixtures. For the nonadditive case, a broadening of the fluid-crystal coexistence region is found for small q, whereas for large q a vapor-fluid transition intervenes. In the additive case, we find a sequence of spindle-type, azeotropic, and eutectic phase diagrams upon lowering q from 1 to 0.6. The transition from azeotropic to eutectic is different from the three-dimensional case. Surface tensions in general become smaller (up to a factor 2) upon addition of a second species and they are rather small. The minimization of the functionals proceeds without restrictions and optimized graphics card routines are used.
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Affiliation(s)
- Shang-Chun Lin
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Martin Oettel
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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12
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Mortazavifar M, Oettel M. Phase diagrams for sticky rods in bulk and in a monolayer from a lattice free-energy functional for anisotropic particles with depletion attractions. Phys Rev E 2017; 96:032608. [PMID: 29347030 DOI: 10.1103/physreve.96.032608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Indexed: 06/07/2023]
Abstract
A density functional of fundamental measure type for a lattice model of anisotropic particles with hard-core repulsions and effective attractions is derived in the spirit of the Asakura-Oosawa model. Through polymeric lattice particles of various size and shape, effective attractions of different strength and range between the colloids can be generated. The functional is applied to the determination of phase diagrams for sticky rods of length L in two dimensions, in three dimensions, and in a monolayer system on a neutral substrate. In all cases, there is a competition between ordering and gas-liquid transitions. In two dimensions, this gives rise to a tricritical point, whereas in three dimensions, the isotropic-nematic transition crosses over smoothly to a gas-nematic liquid transition. The richest phase behavior is found for the monolayer system. For L=2, two stable critical points are found corresponding to a standard gas-liquid transition and a nematic liquid-liquid transition. For L=3, the gas-liquid transition becomes metastable.
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Affiliation(s)
- M Mortazavifar
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
| | - M Oettel
- Institut für Angewandte Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
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13
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Pérez-Ramírez A, Figueroa-Gerstenmaier S, Odriozola G. Colloid-polymer mixtures under slit confinement. J Chem Phys 2017; 146:104903. [DOI: 10.1063/1.4977831] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Allan Pérez-Ramírez
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana, Ave. San Pablo 180 Col. Reynosa, Ciudad de México 02200, Mexico
- Departamento de Ingenierías Química, Electrónica y Biomédica, División de Ciencias e Ingenierías, Universidad de Guanajuato, Campus León, Loma del Bosque 103, León 37150, Guanajuato, Mexico
| | - Susana Figueroa-Gerstenmaier
- Departamento de Ingenierías Química, Electrónica y Biomédica, División de Ciencias e Ingenierías, Universidad de Guanajuato, Campus León, Loma del Bosque 103, León 37150, Guanajuato, Mexico
| | - Gerardo Odriozola
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana, Ave. San Pablo 180 Col. Reynosa, Ciudad de México 02200, Mexico
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14
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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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15
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Yin H, Sibley DN, Thiele U, Archer AJ. Films, layers, and droplets: The effect of near-wall fluid structure on spreading dynamics. Phys Rev E 2017; 95:023104. [PMID: 28297907 DOI: 10.1103/physreve.95.023104] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Indexed: 06/06/2023]
Abstract
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.
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Affiliation(s)
- Hanyu Yin
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - David N Sibley
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 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), Westfälische Wilhelms-Universität, Corrensstr. 40, 48149 Münster, Germany
| | - Andrew J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
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16
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Mortazavifar M, Oettel M. A fundamental measure density functional for fluid and crystal phases of the Asakura-Oosawa model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244018. [PMID: 27116650 DOI: 10.1088/0953-8984/28/24/244018] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We investigate a density functional for the Asakura-Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory.
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Affiliation(s)
- Mostafa Mortazavifar
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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17
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Ouhajji S, Nylander T, Piculell L, Tuinier R, Linse P, Philipse AP. Depletion controlled surface deposition of uncharged colloidal spheres from stable bulk dispersions. SOFT MATTER 2016; 12:3963-3971. [PMID: 27025949 DOI: 10.1039/c5sm02892b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The competition between surface adsorption and bulk aggregation was investigated for silica colloids dispersed in cyclohexane in contact with hydrophobized silica substrates. Central to this study is that the colloids and surfaces have the same material and surface properties. Colloid-colloid and colloid-surface interactions were controlled by addition of polymers providing depletion interaction. Bulk instability was determined by turbidity and viscosity measurements and surface adsorption by ellipsometry measurements. At increasing polymer concentration, strong surface adsorption occurred at polymer concentrations below that required for bulk phase separation. Complementary Monte Carlo simulations with the use of a new weak depletion theory support quantitatively the experimental observation of the existence of an interval of interaction strength at which aggregation in bulk is negligible while surface adsorption is substantial.
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Affiliation(s)
- Samia Ouhajji
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH, The Netherlands.
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18
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Jover J, Galindo A, Jackson G, Müller EA, Haslam AJ. Fluid–fluid coexistence in an athermal colloid–polymer mixture: thermodynamic perturbation theory and continuum molecular-dynamics simulation. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1047425] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Julio Jover
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London, SW7 2AZ, United Kingdom
| | - Amparo Galindo
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London, SW7 2AZ, United Kingdom
| | - George Jackson
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London, SW7 2AZ, United Kingdom
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London, SW7 2AZ, United Kingdom
| | - Andrew J. Haslam
- Department of Chemical Engineering, Imperial College London , South Kensington Campus, London, SW7 2AZ, United Kingdom
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19
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Santos A, López de Haro M, Fiumara G, Saija F. The effective colloid interaction in the Asakura–Oosawa model. Assessment of non-pairwise terms from the virial expansion. J Chem Phys 2015; 142:224903. [DOI: 10.1063/1.4922031] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
| | - Giacomo Fiumara
- Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno D’Alcontres 31, I-98166 Messina, Italy
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno d’Alcontres, 37-98158 Messina, Italy
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20
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López de Haro M, Tejero CF, Santos A, Yuste SB, Fiumara G, Saija F. Virial coefficients and demixing in the Asakura–Oosawa model. J Chem Phys 2015; 142:014902. [DOI: 10.1063/1.4904891] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
| | - Carlos F. Tejero
- Facultad de Ciencias Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - Santos B. Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain
| | - Giacomo Fiumara
- Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno D’Alcontres 31, I-98166 Messina, Italy
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno d’Alcontres, 37-98158 Messina, Italy
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21
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Stewart MC, Evans R. Layering transitions and solvation forces in an asymmetrically confined fluid. J Chem Phys 2014; 140:134704. [DOI: 10.1063/1.4869868] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [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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Ashton DJ, Wilding NB. Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:031301. [PMID: 24730783 DOI: 10.1103/physreve.89.031301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2014] [Indexed: 06/03/2023]
Abstract
We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behavior.
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Affiliation(s)
- Douglas J Ashton
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Nigel B Wilding
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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23
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Kavre I, Kostevc G, Kralj S, Vilfan A, Babič D. Fabrication of magneto-responsive microgears based on magnetic nanoparticle embedded PDMS. RSC Adv 2014. [DOI: 10.1039/c4ra05602g] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
We present a new fabrication method based on photo- and soft-lithography, suitable for production of prism shaped magnetic microparticles.
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Affiliation(s)
- Ivna Kavre
- Faculty of Mathematics and Physics
- University of Ljubljana
- 1000 Ljubljana, Slovenia
| | - Gregor Kostevc
- Faculty of Mathematics and Physics
- University of Ljubljana
- 1000 Ljubljana, Slovenia
| | - Slavko Kralj
- Nanos Scientificae d.o.o. (Nanos Sci)
- 1000 Ljubljana, Slovenia
- Department for Material Synthesis
- Jožef Stefan Institute
- 1000 Ljubljana, Slovenia
| | - Andrej Vilfan
- Department of Condensed Matter Physics
- Jožef Stefan Institute
- 1000 Ljubljana, Slovenia
| | - Dušan Babič
- Faculty of Mathematics and Physics
- University of Ljubljana
- 1000 Ljubljana, Slovenia
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24
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Winkler A, Virnau P, Binder K, Winkler RG, Gompper G. Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: a multiparticle collision dynamics study. J Chem Phys 2013; 138:054901. [PMID: 23406143 DOI: 10.1063/1.4789267] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent fluid constant, while the colloid and polymer particle numbers are kept constant) and thus an initially homogeneous system is quenched deeply into the miscibility gap, where it is unstable. For various relative concentrations of colloids and polymers, the time evolution of the growing colloid-rich and polymer-rich domains are studied by molecular dynamics simulation, taking hydrodynamic effects mediated by the solvent into account via MPC. It is found that the domain size [script-l](d)(t) grows with time t as [script-l](d)(t) [proportionality] t(1/3) for stick and (at late stages) as [script-l](d)(t) [proportionality] t(2/3) for slip b.c., while break-up of percolating structures can cause a transient "arrest" of growth. While these findings apply for films that are 5-10 colloid diameters wide, for ultrathin films (1.5 colloid diameters wide) a regime with [script-l](d)(t) [proportionality] t(1/2) is also identified for rather shallow quenches.
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Affiliation(s)
- Alexander Winkler
- Insitut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55099 Mainz, Germany
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25
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Archer AJ, Evans R. Relationship between local molecular field theory and density functional theory for non-uniform liquids. J Chem Phys 2013; 138:014502. [PMID: 23298050 DOI: 10.1063/1.4771976] [Citation(s) in RCA: 16] [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 local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.
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Affiliation(s)
- A J Archer
- Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
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26
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Mohry TF, Maciołek A, Dietrich S. Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions. J Chem Phys 2012; 136:224902. [PMID: 22713068 DOI: 10.1063/1.4722883] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.
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Affiliation(s)
- T F Mohry
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.
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27
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Marzi D, Likos CN, Capone B. Coarse graining of star-polymer – colloid nanocomposites. J Chem Phys 2012; 137:014902. [DOI: 10.1063/1.4730751] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Vink RLC, Neuhaus T, Löwen H. Fluid phase separation inside a static periodic field: An effectively two-dimensional critical phenomenon. J Chem Phys 2011; 134:204907. [DOI: 10.1063/1.3582903] [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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29
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30
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Hopkins P, Schmidt M. Binary non-additive hard sphere mixtures: fluid demixing, asymptotic decay of correlations and free fluid interfaces. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:325108. [PMID: 21386490 DOI: 10.1088/0953-8984/22/32/325108] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, [Formula: see text], decay of the partial pair correlation functions, g(ij)(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g(ij)(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.
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Affiliation(s)
- Paul Hopkins
- H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
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31
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Ruckenstein E, Berim GO. Symmetry breaking in confined fluids. Adv Colloid Interface Sci 2010; 154:56-76. [PMID: 20170894 DOI: 10.1016/j.cis.2010.01.008] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2009] [Accepted: 01/20/2010] [Indexed: 11/16/2022]
Abstract
The recent progress in the theoretical investigation of the symmetry breaking (the existence of a stable state of a system, in which the symmetry is lower than the symmetry of the system itself) for classical and quantum fluids is reviewed. The emphasis is on the conditions which cause symmetry breaking in the density distribution for one component fluids and binary mixtures confined in a closed nanoslit between identical solid walls. The existing studies have revealed that two kinds of symmetry breaking can occur in such systems. First, a one-dimensional symmetry breaking occurs only in the direction normal to the walls as a fluid density profile asymmetric with respect of the middle of the slit and uniform in any direction parallel to the walls. Second, a two-dimensional symmetry breaking occurs in the fluid density distribution which is nonuniform in one of the directions parallel to the walls and asymmetrical in the direction normal to the walls. It manifests through liquid bumps and bridges in the fluid density distribution. For one component fluids, conditions of existence of symmetry breaking are provided in terms of the average fluid density, strength of fluid-solid interactions, distance at which the solid wall generates a hard core repulsion, and temperature. In the case of binary mixtures, the occurrence of symmetry breaking also depends on the composition of the confined mixtures.
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Affiliation(s)
- Eli Ruckenstein
- Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260, USA.
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32
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Zausch J, Virnau P, Binder K, Horbach J, Vink RL. Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura–Oosawa model. J Chem Phys 2009; 130:064906. [DOI: 10.1063/1.3071197] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Rosch TW, Errington JR. Fluid phase behavior of a model colloid-polymer mixture: Influence of polymer size and interaction strength. J Chem Phys 2008; 129:164907. [DOI: 10.1063/1.3000011] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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34
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Fortini A, Bolhuis PG, Dijkstra M. Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures. J Chem Phys 2008; 128:024904. [DOI: 10.1063/1.2818562] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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de Miguel E, Almarza NG, Jackson G. Surface tension of the Widom-Rowlinson model. J Chem Phys 2007; 127:034707. [PMID: 17655455 DOI: 10.1063/1.2751153] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.
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Affiliation(s)
- E de Miguel
- Departamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva, Spain.
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36
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Reich H, Dijkstra M, van Roij R, Schmidt M. Entropic Wetting and the Free Isotropic−Nematic Interface of Hard Colloidal Platelets. J Phys Chem B 2007; 111:7825-35. [PMID: 17579390 DOI: 10.1021/jp068870b] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We study bulk and interfacial properties of a model suspension of hard colloidal platelets with continuous orientations and vanishing thickness using both density functional theory, based on either a second virial approach or fundamental measure theory (FMT), and Monte Carlo (MC) simulations. We calculate the bulk equation of state, bulk isotropic-nematic (IN) coexistence, and properties of the (planar) free IN interface and of adsorption at a planar hard wall, where we find complete wetting of the nematic phase at the isotropic-wall interface upon approaching bulk IN coexistence. We investigate in detail the asymptotic decay of correlations at large distances. In all cases, the results from FMT and MC agree quantitatively. Our findings are of direct relevance to understanding interfacial properties of dispersions of colloidal platelets.
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Affiliation(s)
- Hendrik Reich
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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37
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Archer AJ, Pini D, Evans R, Reatto L. Model colloidal fluid with competing interactions: Bulk and interfacial properties. J Chem Phys 2007; 126:014104. [PMID: 17212487 DOI: 10.1063/1.2405355] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter sigma, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, whereby the ultimate decay of correlation functions changes from monotonic to long wavelength damped oscillatory decay on crossing certain lines in the phase diagram or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters the authors find, within the DFT, a lambda line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a lambda line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>>sigma) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the lambda line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby lambda transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface.
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Affiliation(s)
- A J Archer
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom.
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38
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Lo Verso F, Vink RLC, Pini D, Reatto L. Critical behavior in colloid-polymer mixtures: theory and simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061407. [PMID: 16906827 DOI: 10.1103/physreve.73.061407] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2006] [Indexed: 05/11/2023]
Abstract
We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.
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Affiliation(s)
- F Lo Verso
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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39
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Forsman J, Woodward CE. Surface transition in athermal polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051803. [PMID: 16802959 DOI: 10.1103/physreve.73.051803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2006] [Indexed: 05/10/2023]
Abstract
According to a recently developed density functional theory, athermal polymer solutions, in which the solvent particles are smaller than the monomers, may undergo a bulk fluid-fluid phase separation, driven by excluded volume effects. In recent work, we showed that an inert surface immersed in the dilute polymer phase can, in principle, be wetted by the condensed phase. However, we show here that the "prewetting transition" we assumed in our earlier studies is in fact a different type of surface transition. Rather than completely wet the surface at coexistence, the condensed phase layer which forms in the presence of the dilute bulk remains globally stable (and is finite in width) even as the bulk coexistence conditions are approached. Hence, the adsorbed phase inhibits complete wetting of the surface by the dilute phase. The surface transition is first order for the systems we study here and, for longer polymers, the surface phase coexistence line meets the bulk coexistence curve nontangentially to give rise to a lower transition point. For short polymers, we find that the surface transition can occur for a supercritical bulk. We develop a simple one-component thermal model, which displays analogous behavior at an adsorbing surface and provides us with some insight into the qualitative mechanisms responsible.
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Affiliation(s)
- Jan Forsman
- Theoretical Chemistry, P.O. Box 124, 221 00 Lund, Sweden.
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40
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Fortini A, Schmidt M, Dijkstra M. Phase behavior and structure of model colloid-polymer mixtures confined between two parallel planar walls. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051502. [PMID: 16802938 DOI: 10.1103/physreve.73.051502] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2005] [Indexed: 05/10/2023]
Abstract
Using Gibbs ensemble Monte Carlo simulations and density functional theory we investigate the fluid-fluid demixing transition in inhomogeneous colloid-polymer mixtures confined between two parallel plates with separation distances between one and ten colloid diameters covering the complete range from quasi-two-dimensional to bulklike behavior. We use the Asakura-Oosawa-Vrij model in which colloid-colloid and colloid-polymer interactions are hard-sphere like, while the pair potential between polymers vanishes. Two different types of confinement induced by a pair of parallel walls are considered--namely, either through two hard walls or through two semipermeable walls that repel colloids but allow polymers to freely penetrate. For hard (semipermeable) walls we find that the capillary binodal is shifted towards higher (lower) polymer fugacities and lower (higher) colloid fugacities as compared to the bulk binodal; this implies capillary condensation (evaporation) of the colloidal liquid phase in the slit. A macroscopic treatment is provided by a symmetric Kelvin equation for general binary mixtures based on the proximity in chemical potentials of statepoints at capillary coexistence and the reference bulk coexistence. Results for capillary binodals compare well with those obtained from the classic version of the Kelvin equation due to [Evans and Marini Bettolo Marconi, J. Chem. Phys. 86, 7138 (1987)] and are quantitatively accurate away from the fluid-fluid critical point, even at small wall separations. However, the significant shift of the critical polymer fugacity towards higher values upon increasing confinement, as found in simulations, is not reproduced. For hard walls the density profiles of polymers and colloids inside the slit display oscillations due to packing effects for all statepoints. For semipermeable walls either similar structuring or flat profiles are found, depending on the statepoint considered.
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Affiliation(s)
- Andrea Fortini
- Soft Condensed Matter, Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
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41
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Dijkstra M, van Roij R, Roth R, Fortini A. Effect of many-body interactions on the bulk and interfacial phase behavior of a model colloid-polymer mixture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:041404. [PMID: 16711797 DOI: 10.1103/physreve.73.041404] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2005] [Revised: 02/27/2006] [Indexed: 05/09/2023]
Abstract
We study a model suspension of sterically stabilized colloidal particles and nonadsorbing ideal polymer coils, both in bulk and adsorbed against a planar hard wall. By integrating out the degrees of freedom of the polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. We employ an efficient Monte Carlo simulation scheme for this mixture based on the exact effective colloid Hamiltonian; i.e., it incorporates all many-body interactions. The many-body character of the polymer-mediated effective interactions between the colloids yields bulk phase behavior and adsorption phenomena that differ substantially from those found for pairwise simple fluids. We determine the phase behavior for size ratios q=sigma(p)/sigma(c)=1, 0.6, and 0.1, where sigma(c) and sigma(p) denote the diameters of the colloids and polymer coils, respectively. For q=1 and 0.6, we find both a fluid-solid and a stable colloidal gas-liquid transition with an anomalously large bulk liquid regime caused by the many-body interactions. We compare the phase diagrams obtained from simulations with the results of the free-volume approach and with direct simulations of the true binary mixture. Although we did not simulate the polymer coils explicitly, we are able to obtain the three partial structure factors and radial distribution functions. We compare our results with those obtained from density functional theory and the Percus-Yevick approximation. We find good agreement between all results for the structure. We also study the mixture in contact with a single hard wall for q=1. Upon approach of the gas-liquid binodal, we find far from the triple point, three layering transitions in the partial wetting regime.
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Affiliation(s)
- Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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42
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Henderson JR. Geometric thermodynamic fields and the generalized ensemble in colloidal physics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:010402. [PMID: 16486109 DOI: 10.1103/physreve.73.010402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Revised: 12/15/2005] [Indexed: 05/06/2023]
Abstract
The statistical geometry of hard-sphere mixtures, as defined by Speedy and Reiss, is found to lead to a sum rule that is identical in form to the fundamental equation of the generalized ensemble. This leads one to conjecture the specific form of a set of thermodynamic fields entirely defined by ensemble averages of geometric properties of the configurations. The potential for a direct physical understanding of these quantities is discussed and it is noted that they could, therefore, be of crucial significance to our future understanding of colloidal physics. In the presence of an ideal wall, an analogous sum rule is obtained in terms of interfacial geometric properties (the available surface area for insertions at the wall). For this case, which generalizes beyond hard-sphere models, there exists an obvious physical interpretation involving complete wetting at the ideal wall.
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Affiliation(s)
- J R Henderson
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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43
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Bryk P. Wetting in mixtures of colloids and excluded-volume polymers from density-functional theory. J Chem Phys 2005; 123:234907. [PMID: 16392949 DOI: 10.1063/1.2129261] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We use a microscopic density-functional theory based on Wertheim's [J. Chem. Phys. 87, 7323 (1987)] first-order thermodynamic perturbation theory to study the wetting behavior of athermal mixtures of colloids and excluded-volume polymers. In opposition to the wetting behavior of the Asakura-Oosawa-Vrij [J. Chem. Phys. 22, 1255 (1954); Pure Appl. Chem. 48, 471 (1976)] model we find the polymer-rich phase to wet a hard wall. The wetting transition is of the first order and is accompanied by the prewetting transition. We do not find any hints for the layering transitions in the partial wetting regime. Our results resemble the wetting behavior in athermal polymer solutions. We point out that an accurate, monomer-resolved theory for colloid-polymer mixtures should incorporate the correct scaling behavior in the dilute polymer regime and an accurate description of the reference system.
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Affiliation(s)
- Paweł Bryk
- Department for the Modeling of Physico-Chemical Processes, Maria Curie-Skłodowska University, 20-031 Lublin, Poland.
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Vink RLC, Jusufi A, Dzubiella J, Likos CN. Bulk and interfacial properties in colloid-polymer mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:030401. [PMID: 16241402 DOI: 10.1103/physreve.72.030401] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2005] [Revised: 07/26/2005] [Indexed: 05/04/2023]
Abstract
Large-scale Monte Carlo simulations of a phase-separating colloid-polymer mixture are performed and compared to recent experiments. The approach is based on effective interaction potentials in which the central monomers of self-avoiding polymer chains are used as effective coordinates. By incorporating polymer nonideality together with soft colloid-polymer repulsion, the predicted binodal is in excellent agreement with recent experiments. In addition, the interfacial tension as well as the capillary length are in quantitative agreement with experimental results obtained at a number of points in the phase-coexistence region, without the use of any fit parameters.
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Affiliation(s)
- R L C Vink
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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Cuesta JA, Lafuente L, Schmidt M. Lattice density functional for colloid-polymer mixtures: comparison of two fundamental measure theories. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:031405. [PMID: 16241433 DOI: 10.1103/physreve.72.031405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2005] [Indexed: 05/05/2023]
Abstract
We consider a binary mixture of colloid and polymer particles with positions on a simple cubic lattice. Colloids exclude both colloids and polymers from nearest neighbor sites. Polymers are treated as effective particles that are mutually noninteracting, but exclude colloids from neighboring sites; this is a discrete version of the (continuum) Asakura-Oosawa-Vrij model. Two alternative density functionals are proposed and compared in detail. The first is based on multioccupancy in the zero-dimensional limit of the bare model, analogous to the corresponding continuum theory that reproduces the bulk fluid free energy of free volume theory. The second is based on mapping the polymers onto a multicomponent mixture of polymer clusters that are shown to behave as hard cores; the corresponding property of the extended model in strong confinement permits direct treatment with lattice fundamental measure theory. Both theories predict the same topology for the phase diagram with a continuous fluid-fcc freezing transition at low polymer fugacity and, upon crossing a tricritical point, a first-order freezing transition for high polymer fugacities with rapidly broadening density jump.
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Affiliation(s)
- José A Cuesta
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain
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Vink RLC, Schmidt M. Simulation and theory of fluid demixing and interfacial tension of mixtures of colloids and nonideal polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051406. [PMID: 16089534 DOI: 10.1103/physreve.71.051406] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2005] [Indexed: 05/03/2023]
Abstract
An extension of the Asakura-Oosawa-Vrij model of hard sphere colloids and nonadsorbing polymers is studied with grand canonical Monte Carlo simulations and density functional theory. Polymer nonideality is taken into account through a repulsive step-function pair potential between polymers. Simulation results validate previous theoretical findings for the shift of the bulk fluid demixing binodal upon increasing strength of polymer-polymer repulsion, indicating suppression of phase separation. For increasing strength of the polymer-polymer repulsion, simulation and theory consistently predict the interfacial tension of the free interface between the colloidal liquid and the colloidal gas phase to decrease significantly for fixed colloid density difference in the coexisting phases, and to increase for fixed polymer reservoir packing fraction.
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Affiliation(s)
- R L C Vink
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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Fortini A, Dijkstra M, Schmidt M, Wessels PPF. Wall-fluid and liquid-gas interfaces of model colloid-polymer mixtures by simulation and theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051403. [PMID: 16089531 DOI: 10.1103/physreve.71.051403] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2004] [Indexed: 05/03/2023]
Abstract
We perform a study of the interfacial properties of a model suspension of hard sphere colloids with diameter sigma(c) and nonadsorbing ideal polymer coils with diameter sigma(p) . For the mixture in contact with a planar hard wall, we obtain from simulations the wall-fluid interfacial free energy, gamma(wf) , for size ratios q =sigma(p)/sigma(c) =0.6 and 1, using thermodynamic integration, and study the (excess) adsorption of colloids, Gamma(c) , and of polymers, Gamma(p) , at the hard wall. The interfacial tension of the free liquid-gas interface, gamma(lg) , is obtained following three different routes in simulations: (i) from studying the system size dependence of the interfacial width according to the predictions of capillary wave theory, (ii) from the probability distribution of the colloid density at coexistence in the grand canonical ensemble, and (iii) for state points where the colloidal liquid wets the wall completely, from Young's equation relating gamma(lg) to the difference of wall-liquid and wall-gas interfacial tensions, gamma(wl)-gamma(wg) . In addition, we calculate gamma(wf) ,Gamma(c) , and Gamma(p) using density functional theory and a scaled particle theory based on free volume theory. Good agreement is found between the simulation results and those from density functional theory, while the results from scaled particle theory quantitatively deviate but reproduce some essential features. Simulation results for gamma(lg) obtained from the three different routes are all in good agreement. Density functional theory predicts gamma(lg) with good accuracy for high polymer reservoir packing fractions, but yields deviations from the simulation results close to the critical point.
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Affiliation(s)
- Andrea Fortini
- Soft Condensed Matter, Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
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Moncho-Jordá A, Dzubiella J, Hansen JP, Louis AA. Density-functional study of interfacial properties of colloid-polymer mixtures. J Phys Chem B 2005; 109:6640-9. [PMID: 16851746 DOI: 10.1021/jp045841x] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Interfacial properties of colloid-polymer mixtures are examined within an effective one-component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer-induced depletion forces. Restriction is made to zero-, one-, and two-body effective potentials, and a free energy functional is used that treats colloid excluded volume correlations within Rosenfeld's fundamental measure theory, and depletion-induced attraction within first-order perturbation theory. This functional allows a consistent treatment of both ideal and interacting polymers. The theory is applied to surface properties near a hard wall, to the depletion interaction between two walls, and to the fluid-fluid interface of demixed colloid-polymer mixtures. The results of the present theory compare well with predictions of a fully two-component representation of mixtures of colloids and ideal polymers (the Asakura-Oosawa model) and allow a systematic investigation of the effects of polymer-polymer interactions on interfacial properties. In particular, the wall surface tension is found to be significantly larger for interacting than for ideal polymers, whereas the opposite trend is predicted for the fluid-fluid interfacial tension.
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Affiliation(s)
- A Moncho-Jordá
- Departamento de Física Aplicada, Universidad de Granada, Facultad de Ciencias, Campus Fuentenueva S/N, 18071 Granada, Spain.
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Vink RLC, Horbach J, Binder K. Capillary waves in a colloid-polymer interface. J Chem Phys 2005; 122:134905. [PMID: 15847500 DOI: 10.1063/1.1866072] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L x L x D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector-dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed.
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Affiliation(s)
- R L C Vink
- Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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Forsman J, Woodward CE. Prewetting and layering in athermal polymer solutions. PHYSICAL REVIEW LETTERS 2005; 94:118301. [PMID: 15903894 DOI: 10.1103/physrevlett.94.118301] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2004] [Indexed: 05/02/2023]
Abstract
Coexistence conditions for prewetting and layering at a hard surface in additive hard sphere polymer solutions, where the solvent particles are smaller than the monomers, have been calculated by density functional methods. Various chain lengths and pressures have been investigated. An unexpected finding is that prewetting in these systems may proceed below the bulk critical pressure. We rationalize this behavior in terms of local properties of the pressure tensor. For longer chains, a different behavior is observed where the systems display a lower wetting pressure, i.e., a low pressure bound for surface wetting.
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Affiliation(s)
- Jan Forsman
- Theoretical Chemistry, P.O. Box 124, 221 00 Lund, Sweden
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