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Aguirre-Manzo LA, González-Mozuelos P. A self-consistent Ornstein-Zernike jellium for highly charged colloids (microgels) in suspensions with added salt. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:275101. [PMID: 34047280 DOI: 10.1088/1361-648x/abfe95] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 05/06/2021] [Indexed: 06/12/2023]
Abstract
This work discusses a jellium scheme, built within the framework of the multicomponent Ornstein-Zernike (OZ) equation, which is capable of describing the collective structure of suspensions of highly charged colloids with added salt, even in the presence of finite-size multivalent microions. This approach uses a suitable approximation to decouple the microion-microion correlations from the macroion-microion profiles, which in combination with the methodology from the dressed ion theory (DIT) gives a full account of the electrostatic effective potential among the colloids. The main advantages of the present contribution reside in its ability to manage the short-range potentials and non-linear correlations among the microions, as well as its realistic characterization of the ionic clouds surrounding each macroion. The structure factors predicted by this jellium scheme are contrasted with previously reported experimental results for microgel suspensions with monovalent salts (2019Phys. Rev. E100032602), thus validating its high accuracy in these situations. The present theoretical analysis is then extended to microgel suspensions with multivalent salts, which reveals the prominent influence of the counterion valence on the makeup of the effective potentials. Although the induced differences may be difficult to identify through the mesoscopic structure, our results suggest that the microgel collapsing transition may be used to enhance these distinct effects, thus giving a feasible experimental probe for these phenomena.
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Affiliation(s)
- L A Aguirre-Manzo
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
| | - P González-Mozuelos
- Departamento de Física, Cinvestav del I. P. N., Av. Instituto Politécnico Nacional 2508, Ciudad de México, C. P. 07360, Mexico
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2
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Bareigts G, Labbez C. Jellium and cell model for titratable colloids with continuous size distribution. J Chem Phys 2019; 149:244903. [PMID: 30599741 DOI: 10.1063/1.5066074] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results.
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Affiliation(s)
- Guillaume Bareigts
- ICB UMR 6303 CNRS, University of Bourgogne Franche-Comté, FR-21000 Dijon, France
| | - Christophe Labbez
- ICB UMR 6303 CNRS, University of Bourgogne Franche-Comté, FR-21000 Dijon, France
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3
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Banchio AJ, Heinen M, Holmqvist P, Nägele G. Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles. J Chem Phys 2018; 148:134902. [PMID: 29626910 DOI: 10.1063/1.5017969] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.
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Affiliation(s)
- Adolfo J Banchio
- Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, Córdoba, Argentina
| | - Marco Heinen
- División de Ciencias e Ingenierías, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Peter Holmqvist
- Division of Physical Chemistry, Lund University, Lund SE-221 00, Sweden
| | - Gerhard Nägele
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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4
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Weight BM, Denton AR. Structure and stability of charged colloid-nanoparticle mixtures. J Chem Phys 2018; 148:114904. [DOI: 10.1063/1.5004443] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Braden M. Weight
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
| | - Alan R. Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
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5
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Denton AR. Effective electrostatic interactions in colloid-nanoparticle mixtures. Phys Rev E 2017; 96:062610. [PMID: 29347449 DOI: 10.1103/physreve.96.062610] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Indexed: 06/07/2023]
Abstract
Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.
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Affiliation(s)
- Alan R Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
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6
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Goehring L, Li J, Kiatkirakajorn PC. Drying paint: from micro-scale dynamics to mechanical instabilities. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160161. [PMID: 28373384 PMCID: PMC5379044 DOI: 10.1098/rsta.2016.0161] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 01/12/2017] [Indexed: 05/24/2023]
Abstract
Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly concentrated into a solid, displaying a range of mechanical instabilities in response to highly variable internal pressures. Here we summarize the current appreciation of this process by pairing an advection-diffusion model of particle motion with a Poisson-Boltzmann cell model of inter-particle interactions, to predict the concentration gradients in a drying colloidal film. We then test these predictions with osmotic compression experiments on colloidal silica, and small-angle X-ray scattering experiments on silica dispersions drying in Hele-Shaw cells. Finally, we use the details of the microscopic physics at play in these dispersions to explore how two macroscopic mechanical instabilities-shear-banding and fracture-can be controlled.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
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Affiliation(s)
- Lucas Goehring
- School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Joaquim Li
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
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7
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Bareigts G, Labbez C. Effective pair potential between charged nanoparticles at high volume fractions. Phys Chem Chem Phys 2017; 19:4787-4792. [PMID: 28133670 DOI: 10.1039/c6cp08056a] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Simulations of charged colloidal dispersions are technically challenging. One possible workaround consists in reducing the system to the colloids only, whose interactions are described through an effective pair potential, wf. Still, the determination of wf is difficult mainly because it depends on the colloidal density, ϕ. Here we propose to calculate wf from simulations of a pair of colloids placed in a cubic box with periodic boundary conditions. The variation in ϕ is mimicked by an appropriate change in the concentration of counterions neutralized by an homogeneous background charge. The method is tested at the level of the primitive model. A good description of the structure of the colloidal dispersion is obtained in the low and high coupling regimes, even at high ϕ (≈30%). Furthermore, the method can easily be used in popular molecular simulation program packages and extended to non-spherical objects.
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Affiliation(s)
- Guillaume Bareigts
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, Université de Bourgogne Franche-Comté, FR-21000 Dijon, France.
| | - Christophe Labbez
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, Université de Bourgogne Franche-Comté, FR-21000 Dijon, France.
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8
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García de Soria MI, Álvarez CE, Trizac E. Renormalized jellium model for colloidal mixtures. Phys Rev E 2016; 94:042609. [PMID: 27841649 DOI: 10.1103/physreve.94.042609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 11/07/2022]
Abstract
In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge, and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from one species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corresponding predictions are compared to the results of Monte Carlo simulations of binary mixtures, where Coulombic interactions are accounted for exactly, at the primitive model level (structureless solvent with fixed dielectric permittivity). An excellent agreement is found.
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Affiliation(s)
| | - Carlos E Álvarez
- Facultad de Ciencias Naturales y Matemáticas, Universidad del Rosario, Calle 12C No. 6-25, Bogotá, Colombia
| | - Emmanuel Trizac
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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9
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Everts JC, van der Linden MN, van Blaaderen A, van Roij R. Alternating strings and clusters in suspensions of charged colloids. SOFT MATTER 2016; 12:6610-6620. [PMID: 27439990 DOI: 10.1039/c6sm01283c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.
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Affiliation(s)
- J C Everts
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
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10
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Gapinski J, Nägele G, Patkowski A. Freezing lines of colloidal Yukawa spheres. II. Local structure and characteristic lengths. J Chem Phys 2014; 141:124505. [DOI: 10.1063/1.4895965] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jacek Gapinski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
| | - Gerhard Nägele
- Institute of Complex Systems (ICS-3), Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Adam Patkowski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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11
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Heinen M, Palberg T, Löwen H. Coupling between bulk- and surface chemistry in suspensions of charged colloids. J Chem Phys 2014; 140:124904. [DOI: 10.1063/1.4869338] [Citation(s) in RCA: 21] [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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12
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Heinen M, Allahyarov E, Löwen H. Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions. J Comput Chem 2013; 35:275-89. [DOI: 10.1002/jcc.23446] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Revised: 09/03/2013] [Accepted: 09/09/2013] [Indexed: 12/24/2022]
Affiliation(s)
- Marco Heinen
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
| | - Elshad Allahyarov
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
- Theoretical Department; Joint Institute for High Temperatures, Russian Academy of Sciences (IVTAN); 13/19 Izhorskaya street Moscow 125412 Russia
| | - Hartmut Löwen
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
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13
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Chung JK, Denton AR. Effective electrostatic interactions in mixtures of charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022306. [PMID: 24032832 DOI: 10.1103/physreve.88.022306] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2013] [Revised: 07/09/2013] [Indexed: 06/02/2023]
Abstract
We present a theory of effective electrostatic interactions in polydisperse suspensions of charged macroions, generalizing to mixtures a theory previously developed for monodisperse suspensions. Combining linear response theory with a random phase approximation for microion correlations, we coarse grain the microion degrees of freedom to derive general expressions for effective macroion-macroion pair potentials and a one-body volume energy. For model mixtures of charged hard-sphere colloids, we give explicit analytical expressions. The resulting effective pair potentials have the same general form as predicted by linearized Poisson-Boltzmann theory, but consistently incorporate dependence on macroion density and excluded volume via the Debye screening constant. The volume energy, which depends on the average macroion density, contributes to the free energy and so can influence thermodynamic properties of deionized suspensions. To validate the theory, we compute radial distribution functions of binary mixtures of oppositely charged colloidal macroions from molecular dynamics simulations of the coarse-grained model (with implicit microions), taking effective pair potentials as input. Our results agree closely with corresponding results from more computationally intensive Monte Carlo simulations of the primitive model (with explicit microions). Simulations of a mixture with large size and charge asymmetries indicate that charged nanoparticles can enhance electrostatic screening of charged colloids. The theory presented here lays a foundation for future large-scale modeling of complex mixtures of charged colloids, nanoparticles, and polyelectrolytes.
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Affiliation(s)
- Jun Kyung Chung
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
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14
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Westermeier F, Fischer B, Roseker W, Grübel G, Nägele G, Heinen M. Structure and short-time dynamics in concentrated suspensions of charged colloids. J Chem Phys 2012; 137:114504. [DOI: 10.1063/1.4751544] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [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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Falcón-González JM, Castañeda-Priego R. Renormalized jellium mean-field approximation for binary mixtures of charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041401. [PMID: 21599152 DOI: 10.1103/physreve.83.041401] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2010] [Revised: 02/10/2011] [Indexed: 05/30/2023]
Abstract
In this work the renormalized jellium model of colloidal suspensions, originally proposed by Trizac and Levin [Phys. Rev. E 69, 031403 (2004)], is extended to study mechanisms of charge renormalization in binary mixtures of charged colloids. We here apply our recent reformulation that introduces the requirement of self-consistency directly into the Poisson-Boltzmann equation, i.e., the background charge is explicitly replaced by the effective one, thus facilitating the whole charge renormalization scheme. We briefly discuss the reformulated model for monodisperse charged suspensions composed of either spheres or rods. In particular, we put emphasis on the effects of the surface charge variation, mixture composition, and particle size on the charge regulation of charge-stabilized colloidal suspensions.
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Affiliation(s)
- José Marcos Falcón-González
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico
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16
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Heinen M, Holmqvist P, Banchio AJ, Nägele G. Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment. J Chem Phys 2011; 134:044532. [DOI: 10.1063/1.3524309] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.2] [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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Lorenz NJ, Palberg T. Melting and freezing lines for a mixture of charged colloidal spheres with spindle-type phase diagram. J Chem Phys 2010; 133:104501. [DOI: 10.1063/1.3487523] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Allahyarov E, Löwen H. Nonadditivity in the effective interactions of binary charged colloidal suspensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424117. [PMID: 21715852 DOI: 10.1088/0953-8984/21/42/424117] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species A and B for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek (DLVO)) pair potential but the AB cross-interaction is different from the geometric mean of the two direct AA and BB interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then significantly negative and is then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO theory.
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Affiliation(s)
- E Allahyarov
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany. Department of Physics, Case Western Reserve University, Cleveland, OH 44106, USA. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
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19
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Eggen E, van Roij R. Poisson-Boltzmann cell model for heterogeneously charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041402. [PMID: 19905309 DOI: 10.1103/physreve.80.041402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2009] [Indexed: 05/28/2023]
Abstract
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquidlike with respect to translational degrees of freedom are also isotropic with respect to particle orientation.
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Affiliation(s)
- Eelco Eggen
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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20
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Wette P, Schöpe HJ, Palberg T. Enhanced crystal stability in a binary mixture of charged colloidal spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021407. [PMID: 19792124 DOI: 10.1103/physreve.80.021407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2009] [Revised: 06/25/2009] [Indexed: 05/28/2023]
Abstract
We report on the phase behavior of a binary charged sphere mixture of size ratio Gamma=0.68 and charge ratio Lambda approximately 1 as a function of composition p and number density n . For p=0.1-0.3 we observe freezing at densities well below the freezing densities of the pure components. At all compositions our data indicate the formation of substitutional alloy crystals of body centered cubic structure. No indications for compound formation were observed. Rather, our findings point at the first observation of an upper azeotrope. Measurements of the crystallization kinetics reveal a combined density and composition dependence of growth velocities and nucleation rate densities, with small but significant anomalies at p*=0.2 . These correlated deviations can be rationalized within classical theories of solidification and suggest an increased similarity between melt and solid for this particular composition.
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Affiliation(s)
- Patrick Wette
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
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21
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Gapinski J, Patkowski A, Banchio AJ, Buitenhuis J, Holmqvist P, Lettinga MP, Meier G, Nägele G. Structure and short-time dynamics in suspensions of charged silica spheres in the entire fluid regime. J Chem Phys 2009; 130:084503. [DOI: 10.1063/1.3078408] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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