Effects of the dielectric discontinuity on the counterion distribution in a colloidal suspension

Santos, Alexandre Pereira dos; Bakhshandeh, Amin; Levin, Yan

doi:10.1063/1.3615940

Cited by 57 publications

(94 citation statements)

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“…For most colloidal suspensions of practical interest ǫ w /ǫ c ≫ 1. In this limit it is possible to show that the exact Green function for the interaction between two counterions is [13],(1) The terms in Eq. 1 are respectively the electrostatic potential produced by an ion located at r ′ , image charge located at the inversion point a 2 r ′2 r ′ inside the colloid, and the counter-image charge spread uniformly from the inversion point up to the center of the colloidal particle [14,15], ψ c (r, r ′ ) = 1 ǫ w a log rr ′ − r · r ′ a 2 − r · r ′ + a 4 − 2a 2 (r · r ′ ) + r 2 r ′2 .…”

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Weak and Strong Coupling Theories for Polarizable Colloids and Nanoparticles

2011

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A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nano-particles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far-field. All the results are compared with the Monte Carlo simulations, showing an excellent agreement between the theory and the simulations.PACS numbers: 64.70.pv, 61.20.Qg, 82.45.Gj Colloidal suspensions are of great practical interest for biology, chemistry, and physics. The subject has a long history going back more than a hundred years. In spite of the intense effort, many interesting phenomena which are found in colloidal science have not been fully elucidated. For example, it is well known that the stability of a hydrophobic colloidal suspension depends specifically on the electrolyte present in suspension. Addition of multivalent counterions results in a rapid precipitation of colloidal particles. What is more surprising is that even for monovalent counterions, stability of colloidal suspensions depend strongly on the precise nature of the counterions. Thus, as one goes along the halogen series, the critical coagulation concentrations of positive colloidal particles can decrease by as much as an order of magnitude, when anion is changed from fluoride to iodide [1]. Another interesting phenomenon found in suspensions with multivalent ions is the reversal of electrophoretic mobility [2,3], or equivalently charge reversal [4][5][6][7]. Under some conditions, it is also possible to observe like-charge attraction between the colloidal particles of the same sign of charge [8][9][10][11][12]. Many of these interesting phenomena are the consequence of strong electrostatic correlations between the counterions. The role of electrostatic correlations has been studied using simple models of colloidal suspensions which neglect particle polarizability. The standard Poisson-Boltzmann equation (PB) -used extensively in colloidal science -fails to account for the induced charge at the particle-solvent interface, predicting that the counterion density should remain unaffected by the colloidal polarizability. In this Letter, we will show that the induced colloidal charge significantly modifies the ionic density distribution even for monovalent counterions. The theory developed in this Letter allows us to accurately predict the counterion density distribution both in the weak (monovalent counterions) and strong (multivalent counterions) coupling limits.We will use the primitive model of colloidal suspension in which colloidal particles are represented by hard spheres of radius a and dielectric constant ǫ c with the ...

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“…1 can be used to obtain the counterion density distributions using Monte Carlo (MC) as was shown in Ref. [13], and is a much faster alternative to simulations based on expansion in Legendre polynomials [16].…”

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Weak and Strong Coupling Theories for Polarizable Colloids and Nanoparticles

2011

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“…The presence of charge induces a surface charge on the dielectric interface. For a point charge located a distance r from the center of the dielectric sphere, the potential generated by the induced surface charge can be represented by the sum of a point charge of magnitude q K = ∆q(R/r) located at a distance r K = R 2 /r from the center of the sphere and a line charge stretching from the center of the sphere to r K with a linear charge density [3,4,5,6]…”

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“…In the limit that ε ′ ≫ ε or ε ′ ≪ ε, the expressions for the Green's function and ion self energy can be written in closed form [3,4,6]. The self energy in this case is exactly given by…”

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Depletion forces due to image charges near dielectric discontinuities

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2015

Current Opinion in Colloid & Interface Science

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The depletion force is an effective inter-particle attractive interaction that is entropically driven by the exclusion of co-solvent molecules. For large co-solvents, such as polymers, the exclusion is primarily driven by excluded volume interactions. However, the exclusion of co-solvents, such as electrolytes, can be caused by other mechanisms. In this review, we summarize the literature on interparticle depletion forces that arise from repulsive image-charge forces between low-dielectric particles and electrolytes. In particular, we emphasize the results from a variational perturbation theory for describing the salting-out behavior observed in moderately concentrated salt solutions. The theory predicts an unscreened force with a range given by the Bjerrum length and a magnitude proportional to the osmotic pressure of the salt solution. The force becomes significant at the same salt concentration where salting-out behavior is typically observed.

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“…The polarization due to interfaces remains a technical difficulty for particle-based computer simulations, and its algorithm development has attracted up-to-date attention [9][10][11][12]. Direct numerical solutions of the Poisson's equation with finite element methods [13] are intensive for Monte Carlo (MC) and molecular dynamics (MD) simulations (for a survey of electrostatic algorithm in sim- * Electronic address: xuzl@sjtu.edu.cn ulations, see [14]), and analytical solutions are only available for simple geometries such as one spherical interface or cylindrical interface where harmonics series expansions or methods of image charges [15][16][17][18][19] can be employed.…”

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Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

2013

Phys. Rev. E

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Electrostatic polarization is important in many nano-/micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving an convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining could reduce the number of image charges to around a dozen, by 1-2 orders of magnitude. We use the algorithm to investigate the interaction force between likely charged spheres in different dielectric environments. We find the size and charge asymmetry leads to an attraction between like charges, in agreement with existing results. Furthermore, we study three-body interaction and find in the presence of an external interface, the interaction force depends on the curvature of the interface, and behavior a non-monotonic electrostatic force.

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Effects of the dielectric discontinuity on the counterion distribution in a colloidal suspension

Cited by 57 publications

References 33 publications

Weak and Strong Coupling Theories for Polarizable Colloids and Nanoparticles

Weak and Strong Coupling Theories for Polarizable Colloids and Nanoparticles

Depletion forces due to image charges near dielectric discontinuities

Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

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