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Sarapas JM, Martin TB, Chremos A, Douglas JF, Beers KL. Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features. Proc Natl Acad Sci U S A 2020; 117:5168-5175. [PMID: 32094183 PMCID: PMC7071916 DOI: 10.1073/pnas.1916362117] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.
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Affiliation(s)
- Joel M Sarapas
- Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
| | - Tyler B Martin
- Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
| | - Alexandros Chremos
- Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
| | - Jack F Douglas
- Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
| | - Kathryn L Beers
- Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
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2
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González-Tovar E, Lozada-Cassou M. Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration. Adv Colloid Interface Sci 2019; 270:54-72. [PMID: 31181349 DOI: 10.1016/j.cis.2019.05.009] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Revised: 05/23/2019] [Accepted: 05/24/2019] [Indexed: 10/26/2022]
Abstract
In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.
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3
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Neville F, Moreno-Atanasio R. Influence of Shell Thickness on the Colloidal Stability of Magnetic Core-Shell Particle Suspensions. Front Chem 2018; 6:201. [PMID: 29922646 PMCID: PMC5996203 DOI: 10.3389/fchem.2018.00201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 05/15/2018] [Indexed: 01/01/2023] Open
Abstract
We present a Discrete Element study of the behavior of magnetic core-shell particles in which the properties of the core and the shell are explicitly defined. Particle cores were considered to be made of pure iron and thus possessed ferromagnetic properties, while particle shells were considered to be made of silica. Core sizes ranged between 0.5 and 4.0 μm with the actual particle size of the core-shell particles in the range between 0.6 and 21 μm. The magnetic cores were considered to have a magnetization of one tenth of the saturation magnetization of iron. This study aimed to understand how the thickness of the shell hinders the formation of particle chains. Chain formation was studied with different shell thicknesses and particle sizes in the presence and absence of an electrical double layer force in order to investigate the effect of surface charge density on the magnetic core-shell particle interactions. For core sizes of 0.5 and 4.0 μm the relative shell thicknesses needed to hinder the aggregation process were approximately 0.4 and 0.6 respectively, indicating that larger core sizes are detrimental to be used in applications in which no flocculation is needed. In addition, the presence of an electrical double layer, for values of surface charge density of less than 20 mC/m2, could stop the contact between particles without hindering their vertical alignment. Only when the shell thickness was considerably larger, was the electrical double layer able to contribute to the full disruption of the magnetic flocculation process.
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Affiliation(s)
- Frances Neville
- School of Environmental and Life Sciences, University of Newcastle, Callaghan, NSW, Australia
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4
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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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5
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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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6
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Everts JC, Boon N, van Roij R. Density-induced reentrant melting of colloidal Wigner crystals. Phys Chem Chem Phys 2016; 18:5211-8. [PMID: 26814798 DOI: 10.1039/c5cp07943h] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By using projections of the colloid–ion mixture to a system of (soft) repulsive spheres and the one-component plasma, we explain the experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density.
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Affiliation(s)
- J. C. Everts
- Institute for Theoretical Physics
- Center for Extreme Matter and Emergent Phenomena
- Utrecht University
- 3584 CE Utrecht
- The Netherlands
| | - N. Boon
- Division of Physical Chemistry
- Lund University
- Lund SE-221 00
- Sweden
| | - R. van Roij
- Institute for Theoretical Physics
- Center for Extreme Matter and Emergent Phenomena
- Utrecht University
- 3584 CE Utrecht
- The Netherlands
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7
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Rotenberg B, Bernard O, Hansen JP. Salt-induced effective interactions and phase separation of an ultrasoft model of polyelectrolytes. Mol Phys 2014. [DOI: 10.1080/00268976.2014.898106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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8
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Budkov YA, Frolov AI, Kiselev MG, Brilliantov NV. Surface-induced liquid-gas transition in salt-free solutions of model charged colloids. J Chem Phys 2013; 139:194901. [DOI: 10.1063/1.4828435] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Manzanilla-Granados HM, Lozada-Cassou M. Modified Colloidal Primitive Model as a Homogeneous Surface Charge Distribution: ζ-Potential. J Phys Chem B 2013; 117:11812-29. [DOI: 10.1021/jp403313k] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Héctor M. Manzanilla-Granados
- Escuela
Superior de Computo, Instituto Politécnico Nacional, U. P. Adolfo López
Mateos, Ciudad de México, 07738, México
| | - Marcelo Lozada-Cassou
- Programa
de Ingeniería Molecular, Instituto Mexicano del Petróleo, Col. San
Bartolo Atepehuacan C.P., Ciudad de Mexico, 07730, México
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10
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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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11
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Bhuiyan LB, Vlachy V, Outhwaite CW. Understanding polyelectrolyte solutions: Macroion condensation with emphasis on the presence of neutral co-solutes. INT REV PHYS CHEM 2010. [DOI: 10.1080/01442350110078842] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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12
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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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13
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Ishikawa M, Kitano R. Colloidal gas-liquid condensation of polystyrene latex particles with intermediate kappa a values (5 to 160, a >> kappa(-1)). LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:2438-2444. [PMID: 20141205 DOI: 10.1021/la9029084] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Polystyrene latex particles showed gas-liquid condensation under the conditions of large particle radius (a >> kappa(-1)) and intermediate kappa a, where kappa is the Debye-Hückel parameter and a is the particle radius. The particles were dissolved in deionized water containing ethanol from 0 to 77 vol %, settled to the bottom of the glass plate within 1 h, and then laterally moved toward the center of a cell over a 20 h period in reaching a state of equilibrium condensation. All of the suspensions that were 1 and 3 microm in diameter and 0.01-0.20 vol % in concentration realized similar gas-liquid condensation with clear gas-liquid boundaries. In 50 vol % ethanol solvent, additional ethanol was added to enhance the sedimentation force so as to restrict the particles in a monoparticle layer thickness. The coexistence of gas-liquid-solid (crystalline solid) was microscopically recognized from the periphery to the center of the condensates. A phase diagram of the gas-liquid condensation was created as a function of KCl concentration at a particle diameter of 3 microm, 0.10 vol % concentration, and 50:50 water/ethanol solvent at room temperature. The miscibility gap was observed in the concentration range from 1 to 250 microM. There was an upper limit of salt concentration where the phase separation disappeared, showing nearly critical behavior of macroscopic density fluctuation from 250 microM to 1 mM. These results add new experimental evidence to the existence of colloidal gas-liquid condensation and specify conditions of like-charge attraction between particles.
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Affiliation(s)
- Masamichi Ishikawa
- Department of Innovative and Engineered Materials, Tokyo Institute of Technology, 4259 Midori-ku, Nagatsuta-cho, Yokohama, Kanagawa 226-8502, Japan.
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14
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Colla TE, Levin Y, Trizac E. A self-consistent renormalized jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions. J Chem Phys 2009; 131:074115. [DOI: 10.1063/1.3211305] [Citation(s) in RCA: 35] [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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15
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Bordi F, Sennato S, Truzzolillo D. Polyelectrolyte-induced aggregation of liposomes: a new cluster phase with interesting applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:203102. [PMID: 21825508 DOI: 10.1088/0953-8984/21/20/203102] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Different charged colloidal particles have been shown to be able to self-assemble, when mixed in an aqueous solvent with oppositely charged linear polyelectrolytes, forming long-lived finite-size mesoscopic aggregates. On increasing the polyelectrolyte content, with the progressive reduction of the net charge of the primary polyelectrolyte-decorated particles, larger and larger clusters are observed. Close to the isoelectric point, where the charge of the adsorbed polyelectrolytes neutralizes the original charge of the particles' surface, the aggregates reach their maximum size, while beyond this point any further increase of the polyelectrolyte-particle charge ratio causes the formation of aggregates whose size is progressively reduced. This re-entrant condensation behavior is accompanied by a significant overcharging. Overcharging, or charge inversion, occurs when more polyelectrolyte chains adsorb on a particle than are needed to neutralize its original charge so that, eventually, the sign of the net charge of the polymer-decorated particle is inverted. The stability of the finite-size long-lived clusters that this aggregation process yields results from a fine balance between long-range repulsive and short-range attractive interactions, both of electrostatic nature. For the latter, besides the ubiquitous dispersion forces, whose supply becomes relevant only at high ionic strength, the main contribution appears due to the non-uniform correlated distribution of the charge on the surface of the polyelectrolyte-decorated particles ('charge-patch' attraction). The interesting phenomenology shown by these system has a high potential for biotechnological applications, particularly when the primary colloidal particles are bio-compatible lipid vesicles. Possible applications of these systems as multi-compartment vectors for the simultaneous intra-cellular delivery of different pharmacologically active substances will be briefly discussed.
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Affiliation(s)
- F Bordi
- Dipartimento di Fisica, Università di Roma 'La Sapienza', Piazzale Aldo Moro 5, I-00185 Rome, Italy. CRS CNR-INFM 'SOFT', Università di Roma 'La Sapienza', Piazzale Aldo Moro 5, I-00185-Rome, Italy
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16
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Hynninen AP, Panagiotopoulos AZ. Simulations of phase transitions and free energies for ionic systems. Mol Phys 2008. [DOI: 10.1080/00268970802112160] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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17
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Torres A, Cuetos A, Dijkstra M, van Roij R. Breakdown of the Yukawa model in de-ionized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031402. [PMID: 18517376 DOI: 10.1103/physreve.77.031402] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2007] [Indexed: 05/26/2023]
Abstract
We study effective colloidal interactions in de-ionized colloidal mixtures through sedimentation-diffusion equilibrium. We derive a coarse-grained effective model (EM) and compare its density profiles with those of the computationally much more expensive primitive model (PM) of colloids and counterions in gravity. The EM, which contains not only standard pairwise screened-Coulomb interactions, but also explicit many-body effects by means of a so-called volume term, can quantitatively account for all observed sedimentation phenomena such as lifting of colloids to high altitudes, segregation into layers in mixtures, and floating of heavy colloids on top of lighter ones. Without the volume term there is no quantitative agreement between the PM and EM, even in the present high-temperature limit of interest, showing that de-ionized colloidal suspensions cannot be described by a pairwise Yukawa model.
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Affiliation(s)
- Aldemar Torres
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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18
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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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19
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Lu B, Denton AR. Phase separation of charge-stabilized colloids: a Gibbs ensemble Monte Carlo simulation study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061403. [PMID: 17677259 DOI: 10.1103/physreve.75.061403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2006] [Revised: 03/02/2007] [Indexed: 05/16/2023]
Abstract
The fluid phase behavior of charge-stabilized colloidal suspensions is explored by applying a variant of the Gibbs ensemble Monte Carlo simulation method to a coarse-grained one-component model with implicit microions and solvent. The simulations take as input linear-response approximations for the effective electrostatic interactions--a hard-sphere-Yukawa pair potential and a one-body volume energy. The conventional Gibbs ensemble trial moves are supplemented by exchange of (implicit) salt between coexisting phases, with acceptance probabilities influenced by the state dependence of the effective interactions. Compared with large-scale simulations of the primitive model, with explicit microions, our computationally practical simulations of the one-component model closely match the pressures and pair distribution functions at moderate electrostatic couplings. For macroion valences and couplings within the linear-response regime, deionized aqueous suspensions with monovalent microions exhibit separation into macroion-rich and macroion-poor fluid phases below a critical salt concentration. The resulting pressures and phase diagrams are in excellent agreement with predictions of a variational free energy theory based on the same model.
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Affiliation(s)
- Ben Lu
- Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566, USA
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20
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Ciach A, Góźdź WT, Stell G. Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051505. [PMID: 17677071 DOI: 10.1103/physreve.75.051505] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2006] [Indexed: 05/16/2023]
Abstract
The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.
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Affiliation(s)
- A Ciach
- Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa, Poland
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21
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Behera RN, Gupta-Bhaya P. On attractive interaction of a colloid pair of like charge at infinite dilution. J Chem Phys 2007; 126:044908. [PMID: 17286510 DOI: 10.1063/1.2408417] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Numerical data on the potential of mean force W(r) at infinite dilution of a highly charged colloid pair embedded in a 1:1 electrolyte are reported. The authors obtain attractive minima (W<0) at short interparticle distance in these potential functions in hypernetted chain (HNC) approximation, as salt concentration is increased. These minima, however, disappear in all system sets studied when a self-consistent Zerah-Hansen (ZH) closure is used. The authors infer that the attractive minima obtained in a HNC closure are spurious and result from the neglect of bridge diagrams in HNC approximation. An expression of bridge function, which the ZH closure in effect incorporates in W(r) to remove attractive minima, is derived in terms of modification of correlation functions. Features of repulsive pair potentials obtained using the ZH closure, their dependence on particle charge and salt concentration, and their agreement with those of the Derajguin-Landau-Verwey-Overbeek theory are investigated.
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Affiliation(s)
- Raghu Nath Behera
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India.
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22
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23
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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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Fortini A, Hynninen AP, Dijkstra M. Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension. J Chem Phys 2006; 125:094502. [PMID: 16965092 DOI: 10.1063/1.2335453] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.
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Affiliation(s)
- Andrea Fortini
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands.
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Denton AR. Phase separation in charge-stabilized colloidal suspensions: influence of nonlinear screening. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:041407. [PMID: 16711800 DOI: 10.1103/physreve.73.041407] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2005] [Indexed: 05/09/2023]
Abstract
The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, Phys. Rev. E 70, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, Phys. Rev. E 59, 2010 (1999); P. B. Warren, J. Chem. Phys. 112, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of de-ionized suspensions.
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Affiliation(s)
- A R Denton
- Department of Physics, North Dakota State University, Fargo, ND 58105-5566, USA.
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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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Warren PB. Phase separation, interface properties, and charge density waves in a simplified model for a macroion suspension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:011411. [PMID: 16486144 DOI: 10.1103/physreve.73.011411] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Revised: 12/21/2005] [Indexed: 05/06/2023]
Abstract
A simplified density functional theory for a macroion suspension is examined, where the correlation free energy corresponds to the macroion self-energy, treated within a linearized or Debye-Hückel approximation. The model possesses a miscibility gap (liquid-liquid phase separation) at low ionic strength. Within the gap, density profiles, electrical structure, and surface tension are calculated for the interface between coexisting phases, using a variational approximation. Additionally, structure factors are calculated for the homogeneous system. As one approaches the critical points, the structure factors can diverge at a nonzero wave vector, signaling the onset of charge density wave phases. Although the quantitative results should be treated with care, the results may be indicative of the rich phenomenology that can arise in asymmetric charged systems.
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Affiliation(s)
- Patrick B Warren
- Unilever R&D Port Sunlight, Bebington, Wirral, CH63 3JW, United Kingdom
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28
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Zinn SY, Fisher * ME. Interfacial tensions near critical endpoints: experimental checks of EdGF theory. Mol Phys 2005. [DOI: 10.1080/00268970500151338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Aqua JN, Banerjee S, Fisher ME. Criticality in charge-asymmetric hard-sphere ionic fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:041501. [PMID: 16383379 DOI: 10.1103/physreve.72.041501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2005] [Indexed: 05/05/2023]
Abstract
Phase separation and criticality are analyzed in z:1 charge-asymmetric ionic fluids of equisized hard spheres by generalizing the Debye-Hückel approach combined with ionic association, cluster solvation by charged ions, and hard-core interactions, following lines developed by Fisher and Levin for the 1:1 case (i.e., the restricted primitive model). Explicit analytical calculations for 2:1 and 3:1 systems account for ionic association into dimers, trimers, and tetramers and subsequent multipolar cluster solvation. The reduced critical temperatures, Tc* (normalized by z), decrease with charge asymmetry, while the critical densities increase rapidly with . The results compare favorably with simulations and represent a distinct improvement over all current theories such as the mean spherical approximation, symmetric Poisson-Boltzmann theory, etc. For z not equal to 1, the interphase Galvani (or absolute electrostatic) potential difference, Deltaphi(T), between coexisting liquid and vapor phases is calculated and found to vanish as absolute value (T-Tc) beta when T-->Tc-with, since our approximations are classical, beta = (1/2). Above Tc, the compressibility maxima and so-called k-inflection loci (which aid the fast and accurate determination of the critical parameters) are found to exhibit a strong z dependence.
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Affiliation(s)
- Jean-Noël Aqua
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 USA
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Fisher ME, Aqua JN, Banerjee S. How multivalency controls ionic criticality. PHYSICAL REVIEW LETTERS 2005; 95:135701. [PMID: 16197147 DOI: 10.1103/physrevlett.95.135701] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2005] [Indexed: 05/04/2023]
Abstract
To understand how multivalency affects criticality in z:1 ionic fluids, we report an ion-cluster association theory embodying ionic solvation and excluded volume for equisized hard-sphere models with z=1-3. In accord with simulation but contradicting integral equation and field theories, the reduced critical temperature falls when z increases while the density rho(c) rises steeply. These trends can be explained semiquantitatively by noting that 80%-90% of the ions near T(c) are bound in neutral or charged clusters, depleting the ionic strength. For z not equal 1, predicted interphase Galvani potentials vanish at T(c).
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Affiliation(s)
- Michael E Fisher
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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Bier M, Harnau L, Dietrich S. Free isotropic-nematic interfaces in fluids of charged platelike colloids. J Chem Phys 2005; 123:114906. [PMID: 16392596 DOI: 10.1063/1.2036975] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.
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Affiliation(s)
- Markus Bier
- Max-Planck Institut für Metallforschung, Stuttgart, Germany.
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Penfold J, Staples E, Ugazio S, Tucker I, Soubiran L, Hubbard J, Noro M, O'Malley B, Ferrante A, Ford G, Buron H. The Microstructure of Di-alkyl Chain Cationic/Nonionic Surfactant Mixtures: Observation of Coexisting Lamellar and Micellar Phases and Depletion Induced Phase Separation. J Phys Chem B 2005; 109:18107-16. [PMID: 16853326 DOI: 10.1021/jp0500788] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The evolution of the microstructure and composition occurring in the aqueous solutions of di-alkyl chain cationic/nonionic surfactant mixtures has been studied in detail using small angle neutron scattering, SANS. For all the systems studied we observe an evolution from a predominantly lamellar phase, for solutions rich in di-alkyl chain cationic surfactant, to mixed cationic/nonionic micelles, for solutions rich in the nonionic surfactant. At intermediate solution compositions there is a region of coexistence of lamellar and micellar phases, where the relative amounts change with solution composition. A number of different di-alkyl chain cationic surfactants, DHDAB, 2HT, DHTAC, DHTA methyl sulfate, and DISDA methyl sulfate, and nonionic surfactants, C12E12 and C12E23, are investigated. For these systems the differences in phase behavior is discussed, and for the mixture DHDAB/C12E12 a direct comparison with theoretical predictions of phase behavior is made. It is shown that the phase separation that can occur in these mixed systems is induced by a depletion force arising from the micellar component, and that the size and volume fraction of the micelles are critical factors.
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Affiliation(s)
- J Penfold
- ISIS Facility, CCLRC, Rutherford Appleton Laboratory, Chilton, Didcot, OXON, UK
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Denton AR, Schmidt M. Mixtures of charged colloid and neutral polymer: Influence of electrostatic interactions on demixing and interfacial tension. J Chem Phys 2005; 122:244911. [PMID: 16035820 DOI: 10.1063/1.1940055] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.
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Affiliation(s)
- Alan R Denton
- Department of Physics, North Dakota State University, Fargo, 58105-5566, USA.
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Abstract
A new dynamical definition of the effective colloidal charge, especially suitable for the Monte Carlo and Molecular-dynamics simulations, is proposed. It is shown that for aqueous colloidal suspensions containing monovalent counterions the "dynamical" effective charge agrees perfectly with the "statistical" effective charge calculated using the Alexander prescription. In the case of multivalent ions, the effective charge behaves in a qualitatively different way from the predictions of the Poisson-Boltzmann theory.
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Affiliation(s)
- Alexandre Diehl
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, CEP 60455-760, Fortaleza, CE, Brazil.
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Wang GF, Lai SK. Domains of phase separation in a charged colloidal dispersion driven by electrolytes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:051402. [PMID: 15600613 DOI: 10.1103/physreve.70.051402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2004] [Revised: 07/06/2004] [Indexed: 05/24/2023]
Abstract
We put forth the idea of treating coexisting phases as a composite system and express its free energy as the average of its constitutent free energies weighted by their respective volume proportions. As a result, the theoretical study of charged colloidal phase separation in the presence of electrolytes reduces to optimizing solely the entities pertaining to colloids and small ions. As concrete illustrations, we demarcated the boundaries of coexisting phases for the simplest colloidal dispersion driven by salts at moderate to high concentrations and compared the results with those obtained in the usual manner to numerically show the robust efficiency of the present theory. Also, for a charged colloidal dispersion at very low ionic strength, we crosshatched both the homogeneous one phase and coexisting phases, and used the domains of coexisting phases to interpret an anomalous "transition" of phase diagrams exhibited in dilute colloidal dispersions induced by salts on dilution.
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Affiliation(s)
- G F Wang
- Complex Liquids Laboratory, Department of Physics, National Central University, Chungli 320, Taiwan, Republic of China
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36
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Wang H, Denton AR. Effective electrostatic interactions in suspensions of polyelectrolyte brush-coated colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:041404. [PMID: 15600405 DOI: 10.1103/physreve.70.041404] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2004] [Indexed: 05/24/2023]
Abstract
Effective electrostatic interactions between colloidal particles, coated with polyelectrolyte brushes and suspended in an electrolyte solvent, are described via linear-response theory. The inner cores of the macroions are modeled as hard spheres, the outer brushes as spherical shells of continuously distributed charge, the microions (counterions and salt ions) as point charges, and the solvent as a dielectric continuum. The multicomponent mixture of macroions and microions is formally mapped onto an equivalent one-component suspension by integrating out from the partition function the microion degrees of freedom. Applying second-order perturbation theory and a random-phase approximation, analytical expressions are derived for the effective pair interaction and a one-body volume energy, which is a natural by-product of the one-component reduction. The combination of an inner core and an outer shell, respectively impenetrable and penetrable to microions, allows the interactions between macroions to be tuned by varying the core diameter and brush thickness. In the limiting cases of vanishing core diameter and vanishing shell thickness, the interactions reduce to those derived previously for star polyelectrolytes and charged colloids, respectively.
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Affiliation(s)
- H Wang
- Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566, USA.
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37
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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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38
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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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39
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Barbosa MC, Deserno M, Holm C, Messina R. Screening of spherical colloids beyond mean field: a local density functional approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051401. [PMID: 15244818 DOI: 10.1103/physreve.69.051401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2003] [Indexed: 05/24/2023]
Abstract
We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-Hückel-hole-cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the one-component plasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by its zero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations and give the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simpler zero temperature limit yield better results than the Poisson-Boltzmann theory.
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Affiliation(s)
- Marcia C Barbosa
- Instituto de Física, UFRGS, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil.
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Trizac E, Levin Y. Renormalized jellium model for charge-stabilized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:031403. [PMID: 15089290 DOI: 10.1103/physreve.69.031403] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2003] [Indexed: 05/24/2023]
Abstract
We introduce a renormalized jellium model to calculate the equation of state for charged colloidal suspensions. An almost perfect agreement with Monte Carlo simulations is found. Our self-consistent approach naturally allows to define the effective charge of particles at finite colloidal density. Although this quantity may differ significantly from its counterpart obtained from the standard Poisson-Boltzmann cell approach, the osmotic pressures for both models are in good agreement. We argue that by construction, the effective charge obtained using the jellium approximation is more appropriate to the study of colloidal interactions. We also discuss a possibility of a fluid-fluid critical point and show how our equation of state can be used to shed light on the surprising results found in recent sedimentation experiments.
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Affiliation(s)
- Emmanuel Trizac
- Laboratoire de Physique Théorique, UMR CNRS 8627, Université de Paris XI, Bâtiment 210, F-91405 Orsay Cedex, France
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41
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Tamashiro MN, Schiessel H. Where the linearized Poisson-Boltzmann cell model fails: the planar case as a prototype study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066106. [PMID: 14754268 DOI: 10.1103/physreve.68.066106] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2003] [Indexed: 05/24/2023]
Abstract
The linearized Poisson-Boltzmann (PB) approximation is investigated for the classical problem of two infinite, uniformly charged planes in electrochemical equilibrium with an infinite monovalent salt reservoir. At the nonlinear level, we obtain an explicit expression of the associated electrostatic contribution to the semi-grand-canonical potential. The linearized osmotic-pressure difference between the interplane region and the salt reservoir becomes negative in the low-temperature, large-separation, or high-surface charge limits, in disagreement with the exact (at mean-field level) nonlinear PB solution. We show that these artifacts--although thermodynamically consistent with quadratic expansions of the nonlinear functional--can be traced back to the nonfulfillment of the underlying assumptions of the linearization. Explicit comparison between the analytical expressions of the exact nonlinear solution and the corresponding linearized equations allows us to show that the linearized results are asymptotically exact in the weak-coupling and counterionic ideal-gas limits, but always fail otherwise, predicting negative osmotic-pressure differences. By taking appropriate limits of the full nonlinear PB solution, we provide asymptotic expressions for the semi-grand-canonical potential and the osmotic-pressure difference that involve only elementary functions, which cover the complementary region where the linearized theory breaks down.
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Affiliation(s)
- M N Tamashiro
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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42
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Bowen W, Williams PM, Wilson J. Quantifying extra interaction forces in charged colloidal dispersions from frontal ultrafiltration experiments. Colloids Surf A Physicochem Eng Asp 2003. [DOI: 10.1016/j.colsurfa.2003.07.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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43
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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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44
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Mohanty PS, Tata BVR. Charge and salt-driven reentrant order-disorder and gas-solid transitions in charged colloids. J Colloid Interface Sci 2003; 264:101-8. [PMID: 12885525 DOI: 10.1016/s0021-9797(03)00368-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Monte Carlo simulations have been performed for aqueous charged colloidal suspensions as a function of effective charge density (sigma) on the particles and salt concentration C(s). We vary the effective charge density in our simulations over a range where a reentrant solid-liquid transition in suspensions of silica and polymer latex particles has been reported by Yamanaka et al. (Phys. Rev. Lett. 80 (1998) 5806). We show that at low ionic strengths a homogeneous liquid-like ordered suspension undergoes crystallization upon increasing sigma. Further increase in sigma resulted once again in a disordered state, which is in agreement with experimental observations. In addition to this reentrant order-disorder transition, we observe an inhomogeneous-to-homogeneous transition in our simulations when salt is added to the disordered inhomogeneous state. This inhomogeneous-to-homogeneous disordered transition is analogous to the solid-gas transition of atomic systems and has not yet been observed in charged colloids. The reported experimental observations on charged colloidal suspensions are discussed in the light of present simulation results.
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Affiliation(s)
- P S Mohanty
- Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India
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Tamashiro MN, Schiessel H. Where the linearized Poisson–Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions. J Chem Phys 2003. [DOI: 10.1063/1.1579676] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kalikmanov VI. Soft depletion in binary fluids. PHYSICAL REVIEW E 2003; 68:010101. [PMID: 12935117 DOI: 10.1103/physreve.68.010101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2003] [Indexed: 11/07/2022]
Abstract
We show theoretically that a binary fluid characterized on a mesoscopic scale by purely repulsive short-range interactions without cores possesses an effective attraction between like particles. This "soft depletion effect" is a generic phenomenon driving a mixing-demixing transition in a binary system with pure repulsions.
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Affiliation(s)
- V I Kalikmanov
- Department of Applied Physics, Computational Physics Section, University of Delft, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
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SHINOHARA TADATOMI, SMALLEY MARTINV, SOGAMI IKUOS. Helmholtz free energy of a multilayer system of highly charged plates immersed in an electrolyte. Mol Phys 2003. [DOI: 10.1080/0026897031000112442] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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48
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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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Sear RP. The effects of added salt on the second virial coefficients of the complete proteome of E. coli. J Chem Phys 2003. [DOI: 10.1063/1.1544556] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Deserno M, Arnold A, Holm C. Attraction and Ionic Correlations between Charged Stiff Polyelectrolytes. Macromolecules 2003. [DOI: 10.1021/ma020923+] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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