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Hebbeker P, Linse P, Schneider S. Optimal Displacement Parameters in Monte Carlo Simulations. J Chem Theory Comput 2016; 12:1459-65. [DOI: 10.1021/acs.jctc.5b00797] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Pascal Hebbeker
- Institute
of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Per Linse
- Physical
Chemistry 1, Lund University, 221 00 Lund, Sweden
| | - Stefanie Schneider
- Institute
of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
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Denton AR. Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:364108. [PMID: 21386524 DOI: 10.1088/0953-8984/22/36/364108] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to colloidal suspensions and other soft materials.
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Affiliation(s)
- A R Denton
- Department of Physics, North Dakota State University, Fargo, ND 58108-6050, USA.
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Denton AR. Electroneutrality and phase behavior of colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051401. [PMID: 18233653 DOI: 10.1103/physreve.76.051401] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2007] [Revised: 09/14/2007] [Indexed: 05/25/2023]
Abstract
Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-Hückel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Lower-dimensional systems (e.g., monolayers, clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining the observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.
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Affiliation(s)
- A R Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566, USA.
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Semashko OV, Brodskaya EN. Simulation of the electrical double layer of a macroion with different counterion charges. COLLOID JOURNAL 2006. [DOI: 10.1134/s1061933x06050140] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Denton AR. Nonlinear screening and effective electrostatic interactions in charge-stabilized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:031404. [PMID: 15524523 DOI: 10.1103/physreve.70.031404] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2004] [Indexed: 05/24/2023]
Abstract
A nonlinear response theory is developed and applied to electrostatic interactions between spherical macroions, screened by surrounding microions, in charge-stabilized colloidal suspensions. The theory describes leading-order nonlinear response of the microions (counterions, salt ions) to the electrostatic potential of the macroions and predicts microion-induced effective many-body interactions between macroions. A linear response approximation [A.R. Denton, Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which contributes to the free energy. Nonlinear response generates effective many-body interactions and essential corrections to both the effective pair potential and the volume energy. By adopting a random-phase approximation (RPA) for the response functions, and thus neglecting microion correlations, practical expressions are derived for the effective pair and triplet potentials and for the volume energy. Nonlinear screening is found to weaken repulsive pair interactions, induce attractive triplet interactions, and modify the volume energy. Numerical results for monovalent microions are in good agreement with available ab initio simulation data and demonstrate that nonlinear effects grow with increasing macroion charge and concentration and with decreasing salt concentration. In the dilute limit of zero macroion concentration, leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear response theory, when combined with the RPA, is formally equivalent to the mean-field Poisson-Boltzmann theory and that the linear response approximation corresponds, within integral-equation theory, to a linearized hypernetted-chain closure.
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Affiliation(s)
- A R Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566, USA.
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6
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Tavares F, Bratko D, Prausnitz J. The role of salt–macroion van der Waals interactions in the colloid–colloid potential of mean force. Curr Opin Colloid Interface Sci 2004. [DOI: 10.1016/j.cocis.2004.05.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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7
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Jardat M, Durand-Vidal S, Da Mota N, Turq P. Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: Comparison between experiments, analytical calculations and numerical simulations. J Chem Phys 2004; 120:6268-73. [PMID: 15267514 DOI: 10.1063/1.1652427] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.
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Affiliation(s)
- M Jardat
- Laboratoire Liquides Ioniques et Interfaces Chargees, UMR CNRS 7612, boite postale 51, Universite P. et M. Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France.
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Anta JA, Lago S. Self-consistent effective interactions in charged colloidal suspensions. J Chem Phys 2002. [DOI: 10.1063/1.1479140] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hayashi Y, Ullner M, Linse P. A Monte Carlo study of solutions of oppositely charged polyelectrolytes. J Chem Phys 2002. [DOI: 10.1063/1.1460859] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Jardat M, Cartailler T, Turq P. Counterion and polyion dynamics in highly asymmetrical electrolyte solutions. J Chem Phys 2001. [DOI: 10.1063/1.1376425] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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12
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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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13
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Affiliation(s)
- Jurij Reščič
- Physical Chemisty 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Per Linse
- Physical Chemisty 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
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Monte Carlo Simulation of Solutions of Like-Charged Colloidal Particles. ACTA ACUST UNITED AC 2000. [DOI: 10.1007/978-3-642-57313-2_18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Abstract
Polyelectrolytes are electrolytes asymmetric both in charge and size. Their properties in solution are dominated by Coulombic forces, and without a detailed understanding of these interactions, no interpretation of experimental data is possible. This paper is a review of recent developments in the theory of highly asymmetric electrolytes of spherical shape resembling surfactant micelles. Three different models are discussed: (a) the cell model, which is focused on the small ion-macroion interaction; (b) the model that treats the solution as an effective one-component fluid of macroions; and (c) the isotropic model, where the solution is represented as a mixture of charged spheres. Traditionally, the electrostatic interactions are accounted for via the solution of the Poisson-Boltzmann equation. This theory, however, ignores the fluctuations around the most probable distribution and may yield poor results for systems with multivalent ions. This paper focuses on developments beyond the Poisson-Boltzmann theory; the results of computer simulations and integral equation theories represent the major part of the review.
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Affiliation(s)
- V Vlachy
- Faculty of Chemistry and Chemical Technology, University of Ljubljana, POB 537, 1001 Ljubljana, Slovenia.
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16
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Lobaskin V, Linse P. Simulation of an asymmetric electrolyte with charge asymmetry 60:1 using hard-sphere and soft-sphere models. J Chem Phys 1999. [DOI: 10.1063/1.479728] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Allahyarov E, D'Amico I, Löwen H. Effect of geometrical confinement on the interaction between charged colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3199-210. [PMID: 11970128 DOI: 10.1103/physreve.60.3199] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/1999] [Indexed: 04/18/2023]
Abstract
The effective interaction between charged colloidal particles confined between two planar like-charged walls is investigated using computer simulations of the primitive model describing asymmetric electrolytes. In detail, we calculate the effective force acting onto a single macroion and onto a macroion pair in the presence of slitlike confinement. For moderate Coulomb coupling, we find that this force is repulsive. Under strong-coupling conditions, however, the sign of the force depends on the distance to the plates and on the interparticle distance. In particular, the particle-plate interaction becomes strongly attractive for small distances which may explain the occurrence of colloidal crystalline layers near the plates observed in recent experiments.
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Affiliation(s)
- E Allahyarov
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, Düsseldorf, D-40225 Düsseldorf, Germany.
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