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Keita C, Hallez Y, Salmon JB. Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient. Phys Rev E 2021; 104:L062601. [PMID: 35030960 DOI: 10.1103/physreve.104.l062601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.
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Affiliation(s)
- Camille Keita
- CNRS, Solvay, LOF, UMR 5258, Université Bordeaux, F-33600 Pessac, France
| | - Yannick Hallez
- Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
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2
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Campos-Villalobos G, Boattini E, Filion L, Dijkstra M. Machine learning many-body potentials for colloidal systems. J Chem Phys 2021; 155:174902. [PMID: 34742191 DOI: 10.1063/5.0063377] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Simulations of colloidal suspensions consisting of mesoscopic particles and smaller species such as ions or depletants are computationally challenging as different length and time scales are involved. Here, we introduce a machine learning (ML) approach in which the degrees of freedom of the microscopic species are integrated out and the mesoscopic particles interact with effective many-body potentials, which we fit as a function of all colloid coordinates with a set of symmetry functions. We apply this approach to a colloid-polymer mixture. Remarkably, the ML potentials can be assumed to be effectively state-independent and can be used in direct-coexistence simulations. We show that our ML method reduces the computational cost by several orders of magnitude compared to a numerical evaluation and accurately describes the phase behavior and structure, even for state points where the effective potential is largely determined by many-body contributions.
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Affiliation(s)
- Gerardo Campos-Villalobos
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Emanuele Boattini
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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3
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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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4
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Everts JC, Ravnik M. Complex electric double layers in charged topological colloids. Sci Rep 2018; 8:14119. [PMID: 30237464 PMCID: PMC6147863 DOI: 10.1038/s41598-018-32550-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 09/10/2018] [Indexed: 11/09/2022] Open
Abstract
Charged surfaces in contact with liquids containing ions are accompanied in equilibrium by an electric double layer consisting of a layer of electric charge on the surface that is screened by a diffuse ion cloud in the bulk fluid. This screening cloud determines not only the interactions between charged colloidal particles or polyelectrolytes and their self-assembly into ordered structures, but it is also pivotal in understanding energy storage devices, such as electrochemical cells and supercapacitors. However, little is known to what spatial complexity the electric double layers can be designed. Here, we show that electric double layers of non-trivial topology and geometry -including tori, multi-tori and knots- can be realised in charged topological colloidal particles, using numerical modelling within a mean-field Poisson-Boltzmann theory. We show that the complexity of double layers -including geometry and topology- can be tuned by changing the Debye screening length of the medium, or by changing the shape and topology of the (colloidal) particle. More generally, this work is an attempt to introduce concepts of topology in the field of charged colloids, which could lead to novel exciting material design paradigms.
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Affiliation(s)
- Jeffrey C Everts
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
| | - Miha Ravnik
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.,Department of Condensed Matter Physics, Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
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5
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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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6
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Hallez Y, Meireles M. Modeling the Electrostatics of Hollow Shell Suspensions: Ion Distribution, Pair Interactions, and Many-Body Effects. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:10430-10444. [PMID: 27623196 DOI: 10.1021/acs.langmuir.6b02730] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.
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Affiliation(s)
- Yannick Hallez
- Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS , Toulouse 31000, France
| | - Martine Meireles
- Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS , Toulouse 31000, France
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7
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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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8
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Hallez Y, Diatta J, Meireles M. Quantitative assessment of the accuracy of the Poisson-Boltzmann cell model for salty suspensions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:6721-9. [PMID: 24834492 DOI: 10.1021/la501265k] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
The cell model is a ubiquitous, fast, and relatively easily implemented model used to estimate the osmotic pressure of a colloidal dispersion. It has been shown to yield accurate approximations of the pressure in dispersions with a low salt content. It is generally accepted that it performs well when long-ranged interactions are involved and the structure of the dispersion is solidlike. The aim of the present work is to determine quantitatively the error committed by assuming the pressure computed with the cell model is the real osmotic pressure of a dispersion. To this end, cell model pressures are compared to a correct estimation of the actual pressures obtained from Poisson-Boltzmann Brownian dynamics simulations including many-body electrostatics and the thermal motion of the colloids. The comparison is performed for various colloidal sizes and charges, salt contents, and volume fractions. It is demonstrated that the accuracy of the cell model predictions is a function of only the average intercolloid distance scaled by Debye's length κd̅ and the normalized colloidal charge. The cell model is accurate for κd̅ < 1 and not reliable for κd̅ > 5 independently of the colloidal charge. In the 1 < κd̅ < 5 range, covering a wide set of experimental conditions, the colloidal surface charge has a large influence on the error associated with the cell approximation. The results presented in this article should provide a useful reference to determine a priori if the cell model can be expected to predict accurately an equation of state for a given set of physicochemical parameters.
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Affiliation(s)
- Yannick Hallez
- Université de Toulouse, INPT, UPS, Laboratoire de Génie Chimique, 118 Route de Narbonne, F-31062 Toulouse, France
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9
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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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10
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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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11
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Pianegonda S, Trizac E, Levin Y. The renormalized jellium model for spherical and cylindrical colloids. J Chem Phys 2007; 126:014702. [PMID: 17212506 DOI: 10.1063/1.2387168] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rodlike colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is self-consistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a nontrivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressures calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the renormalized jellium model for theoretical and experimental purposes and provides an alternative to the Poisson-Boltzmann cell model since it is free of some of the intrinsic limitations of this approach.
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Affiliation(s)
- Salete Pianegonda
- Laboratoire de Physique Théorique et Modèles Statistiques [Unité Mixte de Recherche 8626 du CNRS], Bâtiment 100, Université de Paris-Sud, 91405 Orsay Cedex, France
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12
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Trizac E, Belloni L, Dobnikar J, von Grünberg HH, Castañeda-Priego R. Macroion virial contribution to the osmotic pressure in charge-stabilized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011401. [PMID: 17358144 DOI: 10.1103/physreve.75.011401] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2006] [Indexed: 05/14/2023]
Abstract
Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called one component model, where the microionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the microionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed.
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Affiliation(s)
- E Trizac
- NSF Center for Theoretical Biological Physics, UCSD, La Jolla, California 92093-0374 USA
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13
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Zoetekouw B, van Roij R. Nonlinear screening and gas-liquid separation in suspensions of charged colloids. PHYSICAL REVIEW LETTERS 2006; 97:258302. [PMID: 17280401 DOI: 10.1103/physrevlett.97.258302] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2006] [Indexed: 05/13/2023]
Abstract
We calculate phase diagrams of charged colloidal spheres (valency Z and radius a) in a 1:1 electrolyte from multicentered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z = 1 and as large as 10(4) we find a gas-liquid spinodal instability in the colloid-salt phase diagram provided Z lambdaB/a > or similar 24+/-1, where lambdaB is the Bjerrum length.
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Affiliation(s)
- Bas Zoetekouw
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584CE Utrecht, the Netherlands
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14
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Kim K, Nakayama Y, Yamamoto R. Direct numerical simulations of electrophoresis of charged colloids. PHYSICAL REVIEW LETTERS 2006; 96:208302. [PMID: 16803214 DOI: 10.1103/physrevlett.96.208302] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2006] [Indexed: 05/10/2023]
Abstract
We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier-Stokes equations so that the electrohydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters; however, our simulation predicts notable deviations in the case of dense dispersions.
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Affiliation(s)
- Kang Kim
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
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15
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Zoetekouw B, van Roij R. Volume terms for charged colloids: a grand-canonical treatment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:021403. [PMID: 16605335 DOI: 10.1103/physreve.73.021403] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2005] [Indexed: 05/08/2023]
Abstract
We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms that affect the phase behavior and the thermodynamic properties, such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.
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Affiliation(s)
- Bas Zoetekouw
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584CE Utrecht, The Netherlands
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16
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Kim K, Yamamoto R. Efficient Simulations of Charged Colloidal Dispersions: A Density Functional Approach. MACROMOL THEOR SIMUL 2005. [DOI: 10.1002/mats.200400068] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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17
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Hynninen AP, Dijkstra M, van Roij R. Effect of three-body interactions on the phase behavior of charge-stabilized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061407. [PMID: 15244568 DOI: 10.1103/physreve.69.061407] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2004] [Indexed: 05/24/2023]
Abstract
We study numerically the effect of attractive triplet interactions on the phase behavior of suspensions of highly charged colloidal particles at low salinity. In our computer simulations, we employ the pair and triplet potentials that were obtained from a numerical Poisson-Boltzmann study [Phys. Rev. E 66, 011402 (2002)]]. On the basis of free energy calculations, we determine the phase diagram of an aqueous suspension of identical spheres of diameter sigma=32 nm and charge Z=80 as a function of colloid concentration and salinity, both for the purely pairwise additive system and for the system with pair and triplet interactions. The main effect of including the triplet interactions is a destabilization of the body-centered-cubic (bcc) crystal phase in favor of the face-centered-cubic (fcc) crystal phase. As a consequence the phase diagram features the coexistence of a rather dilute fluid with an almost-close-packed fcc phase at low salinity and bcc-fcc coexistence with a big density jump at intermediate salinity. The triplet attractions do not affect the phase behavior at sufficiently high salinity; under these conditions the system is well described by the pairwise potential.
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Affiliation(s)
- A-P Hynninen
- Debye Institute, Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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18
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Tsonchev S, Coalson RD, Liu A, Beck TL. Flexible polyelectrolyte simulations at the Poisson–Boltzmann level: A comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods. J Chem Phys 2004; 120:9817-21. [PMID: 15267998 DOI: 10.1063/1.1701841] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.
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Affiliation(s)
- Stefan Tsonchev
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
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19
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Dobnikar J, Chen Y, Rzehak R, von Grünberg HH. Many-body interactions and the melting of colloidal crystals. J Chem Phys 2003. [DOI: 10.1063/1.1595642] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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DUFRÊCHE JF, WHITE TO, HANSEN JP. Charged-stabilized colloidal suspensions: counterion condensation and phase diagrams. Mol Phys 2003. [DOI: 10.1080/0026897031000085100] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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21
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Quesada-Pérez M, Callejas-Fernández J, Hidalgo-Alvarez R. Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles. Adv Colloid Interface Sci 2002; 95:295-315. [PMID: 11843194 DOI: 10.1016/s0001-8686(01)00065-3] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.
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Affiliation(s)
- M Quesada-Pérez
- Departamento de Física, Universidad de Jaén, Escuela Universitaria Politécnica de Linares, Spain
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22
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Meyer S, Levitz P, Delville A. Influence of the Relative Orientation of Two Charged Anisotropic Colloidal Particles on Their Electrostatic Coupling: A (N,V,T) Monte Carlo Study. J Phys Chem B 2001. [DOI: 10.1021/jp011193v] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- S. Meyer
- CRMD, CNRS, 1b rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - P. Levitz
- CRMD, CNRS, 1b rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - A. Delville
- CRMD, CNRS, 1b rue de la Férollerie, 45071 Orléans Cedex 02, France
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23
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Meyer S, Levitz P, Delville A. A (N,V,T) Monte Carlo Study of the Long-range Electrostatic Coupling between a Large Collection of Charged Colloidal Platelets. J Phys Chem B 2001. [DOI: 10.1021/jp011439w] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- S. Meyer
- CRMD, CNRS, 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - P. Levitz
- CRMD, CNRS, 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - A. Delville
- CRMD, CNRS, 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
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24
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Dijkstra M. Computer simulations of charge and steric stabilised colloidal suspensions. Curr Opin Colloid Interface Sci 2001. [DOI: 10.1016/s1359-0294(01)00106-6] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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25
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Delville A, Levitz P. Direct Derivation of the Free Energy of Two Charged Lamellar Colloids from (N,V,T) Monte Carlo Simulations. J Phys Chem B 2000. [DOI: 10.1021/jp002625p] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- A. Delville
- CRMD, CNRS 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
| | - P. Levitz
- CRMD, CNRS 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
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26
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Delville A. Influence of Specific Site Binding on the Interactions between Charged Colloids: A ( N, V, T) Monte Carlo Study. J Phys Chem B 2000. [DOI: 10.1021/jp001090x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- A. Delville
- CRMD, CNRS, 1B rue de la Férollerie, 45071 Orléans, Cedex 02, France
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27
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Abstract
This review summarizes and assesses recent theoretical and experimental advances, with special emphasis on the effective interaction between charge-stabilized colloids, in the bulk or in confined geometries, and on the ambiguities of defining an effective charge of the colloidal particles. Some consideration is given to the often neglected discrete solvent effects.
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Affiliation(s)
- J P Hansen
- Department of Chemistry, Cambridge University, Cambridge CB2 1EW, United Kingdom.
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28
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Belloni L. Eccentric poisson-boltzmann cell model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:2493-2500. [PMID: 11088729 DOI: 10.1103/physreve.62.2493] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2000] [Indexed: 05/23/2023]
Abstract
We solve the nonlinear Poisson-Boltzmann equation around a charged colloidal sphere in an electrolyte that is confined in a cell. The colloid has an eccentric position inside the confining sphere. This models the situation in a highly concentrated charge-stabilized colloidal suspension, where a single colloid simultaneously interacts with the whole cage of neighboring colloids. We calculate the ion density profiles, the free energy, and the osmotic pressure as a function of the shifting position. We express the total force acting on the particle as a sum of pair contributions and compare the resulting pair interaction potential law with the standard Derjaguin-Landau-Verwey-Overbeck expression.
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29
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Quesada-Pérez M, Callejas-Fernández J, Hidalgo-Álvarez R. Renormalization processes in the charge density of polymer colloids. Colloids Surf A Physicochem Eng Asp 1999. [DOI: 10.1016/s0927-7757(99)00282-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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30
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Belloni L. Ionic condensation and charge renormalization in colloidal suspensions. Colloids Surf A Physicochem Eng Asp 1998. [DOI: 10.1016/s0927-7757(97)00281-1] [Citation(s) in RCA: 235] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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31
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Sumaru K, Matsuoka H, Yamaoka H, Wignall GD. Evaluation of the counterion distribution around spherical micelles in solution by small-angle neutron scattering. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:1744-1752. [PMID: 9964435 DOI: 10.1103/physreve.53.1744] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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32
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Gisler T, Schulz SF, Borkovec M, Sticher H, Schurtenberger P, D’Aguanno B, Klein R. Understanding colloidal charge renormalization from surface chemistry: Experiment and theory. J Chem Phys 1994. [DOI: 10.1063/1.467894] [Citation(s) in RCA: 137] [Impact Index Per Article: 4.6] [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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34
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Kalyuzhnyi Y, Vlachy V. Integral equation theory for highly asymmetric electrolyte solutions. Chem Phys Lett 1993. [DOI: 10.1016/0009-2614(93)85712-w] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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