1
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Ben Zion MY, Oppenheimer N. Compact Expansion of a Repulsive Suspension. PHYSICAL REVIEW LETTERS 2024; 132:238201. [PMID: 38905695 DOI: 10.1103/physrevlett.132.238201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 04/30/2024] [Indexed: 06/23/2024]
Abstract
Short-range repulsion governs the dynamics of matter from atoms to animals. Using theory, simulations, and experiments, we find that an ensemble of repulsive particles spreads compactly with a sharp boundary, in contrast to the diffusive spreading of Brownian particles. Starting from the pair interactions, at high densities, the many-body dynamics follow nonlinear diffusion with a self-similar expansion, growing as t^{1/4}; At longer times, thermal motion dominates with the classic t^{1/2} expansion. A logarithmic growth controlled by nearest-neighbor interactions connects the two self-similar regimes.
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Affiliation(s)
- Matan Yah Ben Zion
- School of Physics and Astronomy and the Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
- Department of Machine Learning and Natural Computing, Donders Institute for Brain, Cognition and Behavior, Thomas van Aquinostraat 4, Nijmegen, 6525GD, The Netherlands
| | - Naomi Oppenheimer
- School of Physics and Astronomy and the Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
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2
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Thermally active nanoparticle clusters enslaved by engineered domain wall traps. Nat Commun 2021; 12:5813. [PMID: 34608137 PMCID: PMC8490384 DOI: 10.1038/s41467-021-25931-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 09/09/2021] [Indexed: 11/08/2022] Open
Abstract
The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stiffness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiments and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.
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3
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Smith AM, Borkovec M, Trefalt G. Forces between solid surfaces in aqueous electrolyte solutions. Adv Colloid Interface Sci 2020; 275:102078. [PMID: 31837508 DOI: 10.1016/j.cis.2019.102078] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Revised: 10/11/2019] [Accepted: 11/18/2019] [Indexed: 11/15/2022]
Abstract
This review addresses experimental findings obtained with direct force measurements between two similar or dissimilar solid surfaces in aqueous electrolyte solutions. Interpretation of these measurements is mainly put forward in terms of the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). This theory invokes a superposition of attractive van der Waals forces and repulsive double layer forces. DLVO theory is shown to be extremely reliable, even in the case of multivalent ions. However, such a description is only successful, when appropriate surface charge densities, charge regulation characteristics, and ion pairing or complexation equilibria in solution are considered. Deviations from DLVO theory only manifest themselves at distances of typically below few nm. More long-ranged non-DLVO forces can be observed in some situations, particularly, in concentrated electrolyte solutions, in the presence of strongly adsorbed layers, or for hydrophobic surfaces. The latter forces probably originate from patch-charge surface heterogeneities, which can be induced by ion-ion correlation effects, charge fluctuations, or other types of surface heterogeneities.
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Affiliation(s)
- Alexander M Smith
- Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland
| | - Michal Borkovec
- Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland
| | - Gregor Trefalt
- Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland.
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4
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Trefalt G, Palberg T, Borkovec M. Forces between colloidal particles in aqueous solutions containing monovalent and multivalent ions. Curr Opin Colloid Interface Sci 2017. [DOI: 10.1016/j.cocis.2016.09.008] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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5
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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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6
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Zhang X, Zhang JS, Shi YZ, Zhu XL, Tan ZJ. Potential of mean force between like-charged nanoparticles: Many-body effect. Sci Rep 2016; 6:23434. [PMID: 26997415 PMCID: PMC4800448 DOI: 10.1038/srep23434] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2015] [Accepted: 03/07/2016] [Indexed: 11/26/2022] Open
Abstract
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles.
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Affiliation(s)
- Xi Zhang
- Center for Theoretical Physics and Key Laboratory of Artificial Micro &Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jin-Si Zhang
- Center for Theoretical Physics and Key Laboratory of Artificial Micro &Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Ya-Zhou Shi
- Center for Theoretical Physics and Key Laboratory of Artificial Micro &Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xiao-Long Zhu
- Department of Physics, School of Physics &Information Engineering, Jianghan University, Wuhan 430056, China
| | - Zhi-Jie Tan
- Center for Theoretical Physics and Key Laboratory of Artificial Micro &Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
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7
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Mattos TG, Harnau L, Dietrich S. Three-body critical Casimir forces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042304. [PMID: 25974488 DOI: 10.1103/physreve.91.042304] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2015] [Indexed: 06/04/2023]
Abstract
Within mean-field theory we calculate universal scaling functions associated with critical Casimir forces for a system consisting of three parallel cylindrical colloids immersed in a near-critical binary liquid mixture. For several geometrical arrangements and boundary conditions at the surfaces of the colloids we study the force between two colloidal particles in the direction normal to their axes, analyzing the influence of the presence of a third particle on that force. Upon changing temperature or the relative positions of the particles we observe interesting features such as a change of sign of this force caused by the presence of the third particle. We determine the three-body component of the forces acting on one of the colloids by subtracting the pairwise forces from the total force. The three-body contribution to the total critical Casimir force turns out to be more pronounced for small surface-to-surface distances between the colloids as well as for temperatures close to criticality. Moreover, we compare our results with similar ones for other physical systems such as three atoms interacting via van der Waals forces.
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Affiliation(s)
- T G Mattos
- Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Av. Amazonas 7675, 30510-000 Belo Horizonte, Brazil; Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany; and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - L Harnau
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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8
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Park BJ, Lee B, Yu T. Pairwise interactions of colloids in two-dimensional geometric confinement. SOFT MATTER 2014; 10:9675-9680. [PMID: 25363564 DOI: 10.1039/c4sm01823k] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present the pairwise interaction behaviour of colloids confined to two-dimensional (2D) colloidal cages using optical laser tweezers. A single probe particle inside hexagonal cage particles at a planar oil-water interface is allowed to diffuse freely and the spring constant is extracted from its trajectories. To evaluate the effect of multibody interactions, the pair interactions between the probe particle and each cage particle are directly measured by using optical tweezers. Based on pairwise additivity, Monte Carlo simulations are used to compare the values of the spring constant obtained from experiments and simulations. We find that the multibody interactions negligibly occur and thus the particle interactions confined to such colloidal cages are highly pairwise. This work demonstrates that the use of the pairwise assumption in numerical simulations is rational when interparticle repulsive interactions are sufficiently strong, such as the particle interactions at fluid-fluid interfaces.
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Affiliation(s)
- Bum Jun Park
- Department of Chemical Engineering, Kyung Hee University, Yongin, 446-701, South Korea.
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9
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Du D, Biswal SL. Micro-mutual-dipolar model for rapid calculation of forces between paramagnetic colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033310. [PMID: 25314567 DOI: 10.1103/physreve.90.033310] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2014] [Indexed: 06/04/2023]
Abstract
Typically, the force between paramagnetic particles in a uniform magnetic field is calculated using either dipole-based models or the Maxwell stress tensor combined with Laplace's equation for magnetostatics. Dipole-based models are fast but involve many assumptions, leading to inaccuracies in determining forces for clusters of particles. The Maxwell stress tensor yields an exact force calculation, but solving Laplace's equation is very time consuming. Here, we present a more elaborate dipole-based model: the micro-mutual-dipolar model. Our model has a time complexity that is similar to that of other dipole-based models but is much more accurate especially when used to calculate the force of small aggregates. Using this model, we calculate the force between two paramagnetic spheres in a uniform magnetic field and a circular rotational magnetic field and compare our results with those of other models. The forces for three-particle and ten-particle systems dispersed in two-dimensional (2D) space are examined using the same model. We also apply this model to calculate the force between two paramagnetic disks dispersed in 2D space. The micro-mutual-dipolar model is demonstrated to be useful for force calculations in dynamic simulations of small clusters of particles for which both accuracy and efficiency are desirable.
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Affiliation(s)
- Di Du
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
| | - Sibani Lisa Biswal
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
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10
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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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11
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Du D, Toffoletto F, Biswal SL. Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:043306. [PMID: 24827363 DOI: 10.1103/physreve.89.043306] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2013] [Indexed: 06/03/2023]
Abstract
Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.
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Affiliation(s)
- Di Du
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
| | - Frank Toffoletto
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Sibani Lisa Biswal
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
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12
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Charged colloidal system: Small ion distribution and effective interaction. Colloids Surf A Physicochem Eng Asp 2014. [DOI: 10.1016/j.colsurfa.2012.09.056] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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13
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Naji A, Kanduč M, Forsman J, Podgornik R. Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond. J Chem Phys 2013; 139:150901. [DOI: 10.1063/1.4824681] [Citation(s) in RCA: 133] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Trefalt G, Szilagyi I, Borkovec M. Poisson-Boltzmann description of interaction forces and aggregation rates involving charged colloidal particles in asymmetric electrolytes. J Colloid Interface Sci 2013; 406:111-20. [PMID: 23827478 DOI: 10.1016/j.jcis.2013.05.071] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2013] [Revised: 05/08/2013] [Accepted: 05/25/2013] [Indexed: 11/17/2022]
Abstract
Forces and aggregation rates involving spherical particles are studied numerically within the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) for asymmetric and mixed electrolytes. Thereby, the double layer interactions are treated at the Debye-Hückel (DH) and Poisson-Boltzmann (PB) levels. The DH model is applicable for weakly charged systems, and effects of ion valence enter only implicitly through the ionic strength. The PB model is necessary for more highly charged systems, and depends on the actual ionic composition. One finds that forces in asymmetric electrolytes at fixed ionic strength weaken when the valence of the counterions is increased or when the valence of the coions is decreased. In symmetric electrolytes, the effect of counterions is more important than the one of the coions. For weakly charged systems, the critical coagulation concentration (CCC) decreases with the square of the valence in symmetric electrolytes, while this decrease is weaker in asymmetric ones. With increasing charge density, the dependence of the CCC on the valence becomes stronger, but the classical Schulze-Hardy decrease with the sixths power of the valence is only recovered for unrealistically high charge densities. Mixtures of electrolytes are treated within the same framework, and one observes that already small amounts of multivalent ions affect the system considerably. An empirical mixing rule is proposed to describe the calculated CCCs.
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Affiliation(s)
- Gregor Trefalt
- Department of Inorganic and Analytical Chemistry, University of Geneva, Geneva, Switzerland
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15
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Juniper MPN, Besseling R, Aarts DGAL, Dullens RPA. Acousto-optically generated potential energy landscapes: potential mapping using colloids under flow. OPTICS EXPRESS 2012; 20:28707-28716. [PMID: 23263108 DOI: 10.1364/oe.20.028707] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Optical potential energy landscapes created using acousto-optical deflectors are characterized via solvent-driven colloidal particles. The full potential energy of both single optical traps and complex landscapes composed of multiple overlapping traps are determined using a simple force balance argument. The potential of a single trap is shown to be well described by a Gaussian trap with stiffness found to be consistent with those obtained by a thermal equilibrium method. We also obtain directly the depth of the well, which (as with stiffness) varies with laser power. Finally, various complex systems ranging from double-well potentials to random landscapes are generated from individually controlled optical traps. Predictions of these landscapes as a sum of single Gaussian wells are shown to be a good description of experimental results, offering the potential for fully controlled design of optical landscapes, constructed from single optical traps.
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Affiliation(s)
- Michael P N Juniper
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK.
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16
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Kreuter C, Siems U, Henseler P, Nielaba P, Leiderer P, Erbe A. Stochastic transport of particles across single barriers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464120. [PMID: 23114426 DOI: 10.1088/0953-8984/24/46/464120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Transport phenomena of interacting particles are of high interest for many applications in biology and mesoscopic systems. Here we present measurements on colloidal particles, which are confined in narrow channels on a substrate and interact with a barrier, which impedes the motion along the channel. The substrate of the particle is tilted in order for the particles to be driven towards the barrier and, if the energy gained by the tilt is large enough, surpass the barrier by thermal activation. We therefore study the influence of this barrier as well as the influence of particle interaction on the particle transport through such systems. All experiments are supported with Brownian dynamics simulations in order to complement the experiments with tests of a large range of parameter space which cannot be accessed in experiments.
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17
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Ruh D, Tränkle B, Rohrbach A. Fast parallel interferometric 3D tracking of numerous optically trapped particles and their hydrodynamic interaction. OPTICS EXPRESS 2011; 19:21627-21642. [PMID: 22109012 DOI: 10.1364/oe.19.021627] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Multi-dimensional, correlated particle tracking is a key technology to reveal dynamic processes in living and synthetic soft matter systems. In this paper we present a new method for tracking micron-sized beads in parallel and in all three dimensions - faster and more precise than existing techniques. Using an acousto-optic deflector and two quadrant-photo-diodes, we can track numerous optically trapped beads at up to tens of kHz with a precision of a few nanometers by back-focal plane interferometry. By time-multiplexing the laser focus, we can calibrate individually all traps and all tracking signals in a few seconds and in 3D. We show 3D histograms and calibration constants for nine beads in a quadratic arrangement, although trapping and tracking is easily possible for more beads also in arbitrary 2D arrangements. As an application, we investigate the hydrodynamic coupling and diffusion anomalies of spheres trapped in a 3 × 3 arrangement.
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Affiliation(s)
- Dominic Ruh
- Laboratory for Bio- and Nano- Photonics, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges Köhler Allee 102, 79110 Freiburg, Germany
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18
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Frischknecht AL, Yethiraj A. Two- and three-body interactions among nanoparticles in a polymer melt. J Chem Phys 2011; 134:174901. [DOI: 10.1063/1.3585979] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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19
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Walker DA, Kowalczyk B, de la Cruz MO, Grzybowski BA. Electrostatics at the nanoscale. NANOSCALE 2011; 3:1316-44. [PMID: 21321754 DOI: 10.1039/c0nr00698j] [Citation(s) in RCA: 147] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Electrostatic forces are amongst the most versatile interactions to mediate the assembly of nanostructured materials. Depending on experimental conditions, these forces can be long- or short-ranged, can be either attractive or repulsive, and their directionality can be controlled by the shapes of the charged nano-objects. This Review is intended to serve as a primer for experimentalists curious about the fundamentals of nanoscale electrostatics and for theorists wishing to learn about recent experimental advances in the field. Accordingly, the first portion introduces the theoretical models of electrostatic double layers and derives electrostatic interaction potentials applicable to particles of different sizes and/or shapes and under different experimental conditions. This discussion is followed by the review of the key experimental systems in which electrostatic interactions are operative. Examples include electroactive and "switchable" nanoparticles, mixtures of charged nanoparticles, nanoparticle chains, sheets, coatings, crystals, and crystals-within-crystals. Applications of these and other structures in chemical sensing and amplification are also illustrated.
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Affiliation(s)
- David A Walker
- Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
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El Shawish S, Dobnikar J, Trizac E. Colloidal ionic complexes on periodic substrates: ground-state configurations and pattern switching. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041403. [PMID: 21599154 DOI: 10.1103/physreve.83.041403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2010] [Revised: 12/17/2010] [Indexed: 05/30/2023]
Abstract
We theoretically and numerically studied ordering of "colloidal ionic clusters" on periodic substrate potentials such as those generated by optical trapping. Each cluster consists of three charged spherical colloids: two negatively and one positively charged. The substrate is a square or rectangular array of traps, each confining one such cluster. By varying the lattice constant from large to small, the observed clusters are first rodlike and form ferro- and antiferrolike phases, then they bend into a bananalike shape, and finally they condense into a percolated structure. Remarkably, in a broad parameter range between single-cluster and percolated structures, we have found stable supercomplexes composed of six colloids forming grapelike or rocketlike structures. We investigated the possibility of macroscopic pattern switching by applying external electrical fields.
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Affiliation(s)
- Samir El Shawish
- Department of Theoretical Physics, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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Schapotschnikow P, Vlugt TJH. Understanding interactions between capped nanocrystals: Three-body and chain packing effects. J Chem Phys 2009; 131:124705. [DOI: 10.1063/1.3227043] [Citation(s) in RCA: 69] [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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Speidel M, Friedrich L, Rohrbach A. Interferometric 3D tracking of several particles in a scanning laser focus. OPTICS EXPRESS 2009; 17:1003-15. [PMID: 19158918 DOI: 10.1364/oe.17.001003] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
High-Speed tracking of several particles allows measuring dynamic long-range interactions relevant to biotechnology and colloidal physics. In this paper we extend the successful technique of 3D back-focal plane interferometry to oscillating laser beams and show that two or more particles can be trapped and tracked with a precision of a few nanometers in all three dimensions. The tracking rate of several kHz is only limited by the scan speed of the beam steering device. Several tests proof the linearity and orthogonality of our detection scheme, which is of interest to optical tweezing applications and various metrologies. As an example we show the position cross-correlations of three diffusing particles in a scanning line optical trap.
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Affiliation(s)
- Michael Speidel
- Laboratory for Bio- and Nano- Photonics, Department of Microsystems Engineering-IMTEK, University of Freiburg, Georges Köhler Allee 102,79110 Freiburg, Germany
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Reilly MA, Rapp B, Hamilton PD, Shen AQ, Ravi N. Material Characterization of Porcine Lenticular Soluble Proteins. Biomacromolecules 2008; 9:1519-26. [DOI: 10.1021/bm701229t] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Matthew A. Reilly
- Department of Veterans Affairs, 915 North Grand Boulevard, St. Louis, Missouri 63106, and Department of Energy, Environmental, and Chemical Engineering, Department of Biomedical Engineering, Department of Mechanical and Aerospace Engineering, and Department of Ophthalmology and Visual Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
| | - Brian Rapp
- Department of Veterans Affairs, 915 North Grand Boulevard, St. Louis, Missouri 63106, and Department of Energy, Environmental, and Chemical Engineering, Department of Biomedical Engineering, Department of Mechanical and Aerospace Engineering, and Department of Ophthalmology and Visual Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
| | - Paul D. Hamilton
- Department of Veterans Affairs, 915 North Grand Boulevard, St. Louis, Missouri 63106, and Department of Energy, Environmental, and Chemical Engineering, Department of Biomedical Engineering, Department of Mechanical and Aerospace Engineering, and Department of Ophthalmology and Visual Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
| | - Amy Q. Shen
- Department of Veterans Affairs, 915 North Grand Boulevard, St. Louis, Missouri 63106, and Department of Energy, Environmental, and Chemical Engineering, Department of Biomedical Engineering, Department of Mechanical and Aerospace Engineering, and Department of Ophthalmology and Visual Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
| | - Nathan Ravi
- Department of Veterans Affairs, 915 North Grand Boulevard, St. Louis, Missouri 63106, and Department of Energy, Environmental, and Chemical Engineering, Department of Biomedical Engineering, Department of Mechanical and Aerospace Engineering, and Department of Ophthalmology and Visual Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, Missouri 63130
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Cahill BP, Papastavrou G, Koper GJM, Borkovec M. Adsorption of poly(amido amine) (PAMAM) dendrimers on silica: importance of electrostatic three-body attraction. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2008; 24:465-73. [PMID: 18072793 DOI: 10.1021/la7021352] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Adsorption of poly(amido amine) (PAMAM) dendrimers to silicon oxide surfaces was studied as a function of pH, ionic strength, and dendrimer generation. By combining optical reflectometry and atomic force microscopy (AFM), the adsorbed layers can be fully characterized and an unequivocal determination of the adsorbed mass becomes possible. For early stages, the adsorption process is transport limited and of first order with respect to the dendrimer solution concentration. For later stages, the surface saturates and the adsorbed dendrimers form loose but correlated liquidlike surface structures. This correlation is evidenced by a peak in the pair correlation function determined by AFM. The maximum adsorbed amount increases with increasing ionic strength and pH. The increase with the ionic strength is explained by the random sequential adsorption (RSA) model and electrostatic repulsion between the dendrimers. The adsorbing dendrimers interact by the repulsive screened Coulomb potential, whose range decreases with increasing ionic strength and thus leads to increasing adsorbed densities. The pH increase is interpreted as an effect of the substrate and is quantitatively explained by the extended three-body RSA model. This model stipulates the importance of a three-body interaction acting between two adsorbing dendrimers and the charged substrate. The presence of the charged substrate weakens the repulsion between the adsorbing dendrimers and thus leads to higher surface densities. This effect can be interpreted as an additional attractive three-body interaction, which acts in addition to the usual two-body repulsion and originates from the additional screening of the Coulomb repulsion by the counterions accumulating in the diffuse layer.
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Affiliation(s)
- Brian P Cahill
- Department of Inorganic, Analytical, and Applied Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, 1211 Geneva, Switzerland
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26
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Vishnyakov VI, Dragan GS, Evtuhov VM. Nonlinear Poisson-Boltzmann equation in spherical symmetry. Phys Rev E 2007; 76:036402. [PMID: 17930346 DOI: 10.1103/physreve.76.036402] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2007] [Indexed: 11/07/2022]
Abstract
The Poisson-Boltzmann problem in spherical symmetry has been considered using the distribution of a self-consistent potential around a charged grain in a thermal collisional plasma as an example. The qualitative patterns of all possible solutions have been presented and a study of their asymptotics has been carried out. It has been demonstrated that for large potentials it is possible to neglect the curvature of the grain surface and to use the solution of the plane problem. It has also been demonstrated that the electrical interaction of the grains is possible only at distances smaller than eight screening lengths.
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Affiliation(s)
- V I Vishnyakov
- Mechnikov Odessa National University, Odessa 65082, Ukraine
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27
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Dyshlovenko PE. Two-dimensional colloidal crystal in nonlinear Poisson-Boltzmann model. COLLOID JOURNAL 2007. [DOI: 10.1134/s1061933x07010036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Kreer T, Horbach J, Chatterji A. Nonlinear effects in charge stabilized colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021401. [PMID: 17025419 DOI: 10.1103/physreve.74.021401] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2006] [Indexed: 05/12/2023]
Abstract
Molecular-dynamics simulations are used to study the effective interactions in charged stabilized colloidal suspensions. We focus on highly charged macroions in the limit of low salt concentrations. Within this regime, nonlinear corrections to Debye-Hückel (DH) theory have to be considered. For non-bulk-like systems, such as isolated pairs or triples of macroions, we show that nonlinear effects can become relevant, which cannot be described by the charge renormalization concept [S. Alexander, J. Chem. Phys. 80, 5776 (1984)]. For an isolated pair of macroions, we find an almost perfect qualitative agreement between our simulation data and DH theory. However, on a quantitative level, neither DH theory nor the charge renormalization concept can be confirmed in detail. This seems mainly to be related to the fact that for small ion concentrations, microionic layers can strongly overlap, whereas, simultaneously, excluded volume effects are less important. In the case of isolated triples, where we compare between coaxial and triangular geometries, we find attractive corrections to pairwise additivity in the limit of small macroion separations and salt concentrations. These triplet interactions arise if all three microionic layers around the macroions exhibit a significant overlap. In contrast to the case of two isolated colloids, the charge distribution around a macroion in a triple is found to be anisotropic.
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Affiliation(s)
- T Kreer
- Institut für Physik, Johannes-Gutenberg-Universität, 55099 Mainz, Germany
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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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Nonlinear screening on the charged surfaces with trivalent and tetravalent salt ions: Monte Carlo simulations. Colloids Surf A Physicochem Eng Asp 2006. [DOI: 10.1016/j.colsurfa.2005.08.009] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Amokrane S, Ayadim A, Malherbe JG. Structure of highly asymmetric hard-sphere mixtures: An efficient closure of the Ornstein-Zernike equations. J Chem Phys 2005; 123:174508. [PMID: 16375547 DOI: 10.1063/1.2102891] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model.
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Affiliation(s)
- S Amokrane
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et de Technologie Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France.
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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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Delville A. Influence of Confinement on the Electrostatic Interaction between Charged Colloids: a (N,V,T) Monte Carlo Study within Hyperspherical Geometry. J Phys Chem B 2005; 109:8164-70. [PMID: 16851954 DOI: 10.1021/jp044711l] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Monte Carlo simulations within closed hyperspherical geometry are used to analyze the ionic distribution around two confined charged colloids to determine the origin of the net attraction recently reported in the literature. A scaling procedure is used to compare our numerical results obtained with small ideal colloids with the conclusion of the measurements performed with large silica colloids. Although no electrostatic attraction is detected under confinement, our simulations exhibit a significant reduction of the electrostatic repulsion between charged colloids confined between two weakly charged walls. After rescaling to reproduce the electrostatic repulsion between large confined colloids, our numerical results are qualitatively consistent with the reported attraction because we reasonably expect a reduction of the electrostatic force between such confined colloids below the order of magnitude of their van der Waals attraction.
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Affiliation(s)
- A Delville
- CRMD, CNRS, 1B rue de la Férollerie, 45071 Orléans Cedex 02, France
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