Like-charged Colloidal Particles Research Articles

Lattice Induced Short-Range Attraction between Like-Charged Colloidal Particles.

We perform experiments and computer simulations to study the effective interactions between like-charged colloidal tracers moving in a two-dimensional fluctuating background of colloidal crystal. By a counting method that properly accounts for the configurational degeneracy of tracer pairs, we extract the relative probability of finding a tracer pair in neighboring triangular cells formed by background particles. We find that this probability at the nearest neighbor cell is remarkably greater than those at cells with larger separations, implying an effective attraction between the tracers. This effective attraction weakens sharply as the background lattice constant increases. Furthermore, we clarify that the lattice-mediated effective attraction originates from the minimization of free energy increase from deformation of the crystalline background due to the presence of diffusing tracers.

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge.

Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a “critical” value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the “critical” particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the “critical” particle charge based on the Lindemann melting law.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution.

Over the past few decades, the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in aqueous solution. Examples include nucleic acids and colloidal particles in the bulk solution and under confinement, and biological liquid-liquid phase separation. This observation is at odds with the intuitive expectation of an interparticle repulsion that decays monotonically with distance. Although attraction between like-charged particles can be rationalized theoretically in the strong-coupling regime, e.g., in the presence of multivalent counterions, recurring accounts of long-range attraction in aqueous solution containing monovalent ions at low ionic strength have posed an open conundrum. Here, we show that the behavior of molecular water at an interface-traditionally disregarded in the continuum electrostatics picture-provides a mechanism to explain the attraction between like-charged objects in a broad spectrum of experiments. This basic principle will have important ramifications in the ongoing quest to better understand intermolecular interactions in solution.

Reentrant crystallization of like-charged colloidal particles in an electrolyte solution: Relationship between the shape of the phase diagram and the effective potential of colloidal particles

The reentrant crystallization of like-charged colloidal particles in electrolyte solutions was studied to clarify the relationship between the shape of the phase diagram and the particle-particle effective potential. Coexisting densities were calculated at various electrolyte concentrations using the thermodynamic perturbation expansion method with effective one-component models. The effective potentials were obtained using an integral equation theory for liquids. Some model effective potentials were examined. The calculated results indicated that the reentrant behaviors of various acidic protein solutions observed in the experiments required not only the nonmonotonic dependence of the short-range attraction on the electrolyte concentration, but also the absence of a long repulsive tail.

Theory of Surface Forces in Multivalent Electrolytes.

Aqueous electrolyte solutions containing multivalent ions exhibit various intriguing properties, including attraction between like-charged colloidal particles, which results from strong ion–ion correlations. In contrast, the classical Derjaguin–Landau–Verwey–Overbeek theory of colloidal stability, based on the Poisson–Boltzmann mean-field theory, always predicts a repulsive electrostatic contribution to the disjoining pressure. Here, we formulate a general theory of surface forces, which predicts that the contribution to the disjoining pressure resulting from ion–ion correlations is always attractive and can readily dominate over entropic-induced repulsions for solutions containing multivalent ions, leading to the phenomenon of like-charge attraction. Ion-specific short-range hydration interactions, as well as surface charge regulation, are shown to play an important role at smaller separation distances but do not fundamentally change these trends. The theory is able to predict the experimentally observed strong cohesive forces reported in cement pastes, which result from strong ion–ion correlations involving the divalent calcium ion.

Field-induced dipolar attraction between like-charged colloids.

The field induced anisotropic interactions between like-charged colloidal particles is studied using direct numerical simulations, where the polarization of the electric double layer is explicitly computed under external AC electric fields. These interactions are found to depend on the magnitude E0 and frequency ω of the applied field, as well as the zeta potential, the Debye length, and the relative orientation of the particles. We also determined the range of E0 and ω over which a dipolar attraction is induced between a pair of like-charged colloids. Finally, we performed simulations for systems of six and twelve colloidal particles to study the stability of pear-chain-like configurations.

2SDP-05 アクチンモノマーの会合と多価カチオンが媒介する同符号コロイド粒子間実効引力(生体分子機械の動作機構を周りの水から眺めてみる,シンポジウム,第52回日本生物物理学会年会(2014年度))

2SDP-05 アクチンモノマーの会合と多価カチオンが媒介する同符号コロイド粒子間実効引力(生体分子機械の動作機構を周りの水から眺めてみる,シンポジウム,第52回日本生物物理学会年会(2014年度))

Coarse-Graining Intermolecular Interactions in Dispersions of Highly Charged Colloids

Effective pair potentials between charged colloids, obtained from Monte Carlo simulations of two single colloids in a closed cell at the primitive model level, are shown to reproduce accurately the structure of aqueous salt-free colloidal dispersions, as determined from full primitive model simulations by Linse et al. (Linse, P.; Lobaskin, V. Electrostatic Attraction and Phase Separation in Solutions of Like-Charged Colloidal Particles. Phys. Rev. Lett.1999, 83, 4208). Excellent agreement is obtained even when ion-ion correlations are important and is in principle not limited to spherical particles, providing a potential route to coarse-grained colloidal interactions in more complex systems.

Phase separation in binary colloids with charge asymmetry

We report that binary dispersions of like-charged colloidal particles with large charge asymmetry but similar size exhibit phase separation into crystal and fluid phases under very low salt conditions. This is unexpected because the effective colloid-colloid pair interactions are accurately described by a Yukawa model which is stable to demixing. We show that colloid-ion interactions provide an energetic driving force for phase separation, which is initiated by crystallization of one species.

Fluctuation interactions of colloidal particles

For like-charged colloidal particles, two mechanisms of attraction between them survive when the interparticle distance is larger than the Debye screening length. One of them is the conventional van der Waals attraction and the second is the attraction mechanism mediated by thermal fluctuations of particle position. The latter is related to the effective variable mass (Euler mass) of the particles produced by the fluid motion. The strongest attraction potential (up to the value of the temperature T) corresponds to the case of uncharged particles and a relatively large Debye screening length. In this case, the third attraction mechanism is involved. It is mediated by thermal fluctuations of the fluid density.

Energetic and Entropic Forces Governing the Attraction between Polyelectrolyte-Grafted Colloids

The energetic and entropic interactions governing the attraction between like-charged colloidal particles grafted with oppositely charged polyelectrolyte chains in a monovalent electrolyte are investigated computationally. We employ coarse-grained models of the colloids with varying surface and polyelectrolyte charges and Monte Carlo simulations to compute the potential of mean force between two colloidal particles as a function of their separation distance. By categorizing the potentials as attractive or purely repulsive, we obtain the extent and location of the attractive-force regime within the two-dimensional parameter space comprised of the colloid surface and polyelectrolyte charge. The attractive regime is found to occupy the inside of a hyperbola in this charge space, whose shape and size is determined by a complex interplay between energetic and entropic interactions. In particular, we find that the strength of attraction at short distances is governed by a balance between favorable energetic and entropic terms arising from polymer-bridging interactions, unfavorable energies arising from the mutual repulsion of the colloid surfaces and polyelectrolyte chains, and unfavorable entropies arising from the overlap and crowding effects of chains confined between the colloid surfaces. A phenomenological model is proposed to explain the hyperbolic shape of the attractive regime and make useful predictions about changes in its shape and location for conditions not investigated in this study.

Bound pairs: Direct evidence for long-range attraction between like-charged colloids

We report observations of stable bound pairs in very dilute deionized aqueous suspensions of highly charged polystyrene colloidal particles, with monovalent counterions, using a confocal laser scanning microscope. Through an analysis of several thousands of time series of confocal images recorded deep inside the bulk suspension, we find that the measured pair-potential, U ( r ) has a long-range attractive component with well depths larger than the thermal energy. These observations provide direct and unequivocal evidence for the existence of long-range attraction in U ( r ) of like-charged colloidal particles.

Interaction between like-charged colloidal particles in aqueous electrolyte solution: Attractive component arising from solvent granularity

The potential of mean force (PMF) between like-charged colloidal particles immersed in aqueous electrolyte solution is studied using the integral equation theory. Solvent molecules are modeled as neutral hard spheres, and ions and colloidal particles are taken to be charged hard spheres. The Coulomb potentials for ion-ion, ioncolloidal particle, and colloidal particle-colloidal particle pairs are divided by the dielectric constant of water. This simple model is employed to account for the effects of solvent granularity neglected in the so-called primitive model. The van der Waals attraction between colloidal particles, which is an essential constituent of conventional DLVO theory, is omitted in the present model. Nevertheless, when the electrolyte concentration is sufficiently high, attractive regions appear in the PMF. I n particular, the interaction at small separations is significantly attractive and the contact of colloidal parti cles is stabilized. This interesting behavior arises from the effects of the translational motion of solvent molecules.

Ordering, dynamics and phase transitions in charged colloids

Among the various soft matter systems, charge stabilized colloidal dispersions have gained recognition as tremendously useful model condensed matter systems because of their structural ordering and the rich phase behavior. This paper is a review of the work done in the last few years related to structural ordering and phase transitions brought about by parameters such as pressure, surface charge density and salt concentration. The dynamics in colloidal crystals and dense suspensions is influenced by hydrodynamic interactions arising due to the intervening viscous fluid. Lattice dynamics of colloidal crystals presents a nice testing ground for theories of hydrodynamic interaction. Apart from reviewing the measurements of phonon dispersion curves in thin colloidal crystals, we present here recent dynamic light scattering results on bulk colloidal crystals. The dynamics in colloidal liquids and colloidal glasses are also covered. Though colloidal liquids of low charge density particles freeze into a homogenous crystalline or a glassy state, they remain inhomogeneous when the charge density is beyond a critical value. Recently, this inhomogeneous state is confirmed to be a gas–solid coexistence. This observation of gas–solid coexistence in highly charged colloids along with the earlier observations of vapor–liquid condensation and a reentrant transition have created a debate on the existence of long-range attraction in the effective pair potential U ( r ) of like-charged colloidal particles. U ( r ) was measured directly using optical microscopy. However, the limitations in using the optical microscopy technique for determining U ( r ) in dilute suspensions are discussed. These limitations can be circumvented by employing confocal microscopy. We present our recent observation of stable bound pairs in very dilute and highly charged colloidal suspensions using confocal microscopy and the existence of an attractive minimum in the measured U ( r ) of like-charged particles. These observations provide direct evidence for the existence of counter-ion mediated long-range attraction between like-charged colloids. The need for understanding the microscopic mechanism of counter-ion mediated attraction is highlighted.

Attractive interactions between like-charged colloidal particles at the air/water interface

In the past few years, measurements of the pair interaction potential have shown evidence of micrometer-range attractive interactions between colloidal particles trapped between glass plates. In these experiments it is believed that the glass walls play an important role in the observed attractions. Colloidal particles trapped at the air/water interface show the formation of different 2-D colloidal patterns such as foams, clusters, and chains, whose formation has been taken as evidence of micrometer-range attractive interaction. Here, we present measurements of the pair interaction potential between 0.5-μm colloidal particles at the air/water interface. Indeed, the pair potential shows an attractive secondary minimum at about 1.9 σ, where σ is the particle's diameter. Surprisingly, the position and depth of the secondary well are similar to those found in colloidal systems trapped between glass plates. However, we do not have a clear explanation on the origin of the attractive component of the interaction potential.

Effective pair potential between confined charged colloidal particles.

The pair correlation function g(r) between like-charged colloidal particles in quasi-two-dimensional geometries is measured by optical microscopy for a wide range of particle concentrations and various degrees of confinement. The effective pair potential u(r) is obtained by deconvoluting g(r) via Monte Carlo computer simulations. Our results confirm the existence of a long-range attractive component of u(r) and the appearance of an extra attractive term under stringent confinement.

Effective attractions between like-charged colloidal particles

We apply the Ornstein–Zernike equations together with the extended Zerah–Hansen approach, described in a previous paper [J. Chem. Phys. 109, 11074 (1998)], to determine the microstructure of a colloidal suspension at finite concentrations. Using these results as an input, the effective pair potential between two colloidal particles is also calculated following the general approach described in that paper. It is found that, for sufficiently large concentrations, this effective potential develops an attractive well with a minimum located at a distance of almost four macroparticle diameters. It is also shown that this attraction is generated by the inversion of the sign of the effective charged distribution surrounding each macroparticle involved in the electrostatic component of the effective pair potential.

Glass transition and dynamical heterogeneities in charged colloidal suspensions under pressure.

Constant-pressure Monte Carlo simulations have been performed to study the static and dynamical properties of a liquidlike ordered suspension of like-charged colloidal particles subjected to a sudden compression. We report for the first time a liquidlike ordered monodisperse suspension undergoing a glass transition at a very low volume fraction ( straight phi = 0.003) and existence of dynamical heterogeneities near the glass transition. Mobile particles have been identified using the non-Gaussian parameter for the self-part of the Van Hove correlation function, and they are found to form clusters. The pressure dependence of mean cluster size and the cluster-size distribution of the mobile particles are discussed.

Interparticle force between like-charged colloidal systems: a numerical study

We investigate numerically the interparticle force between like-charged colloidal systems confined by a cylinder. The interactions between colloidal particles are repulsive with smaller electrostatic coupling. On the contrary, the attractive interaction dominates with larger electrostatic coupling. These results clarify that the fluctuation effect beyond the Poisson–Boltzmann equation plays an important role, and the strength of the electrostatic coupling in an aqueous solution is an essential parameter to determine the effective potential between like-charged colloidal particles.

Electrostatic attraction and phase separation in solutions of like-charged colloidal particles

Asymmetric electrolytes consisting of highly charged spherical macroions and small ions representing an aqueous solution of ionic surfactant micelles have been studied at different macroion concentrations by means of Monte Carlo simulations. The model system comprises macroions with 60 elementary charges and either monovalent, divalent, or trivalent counterions interacting solely through hard-core and Coulomb forces. Thermodynamic and structural properties are examined, and the effects of the counterion valency are discussed. For the lowest electrostatic macroion–counterion coupling (monovalent counterions), the macroions are well separated and an effective repulsive potential is acting between them. At stronger electrostatic coupling (divalent counterions), the double-layer repulsion between the macroions is strongly reduced and at short separations the attractive force becomes comparable to the double-layer repulsion. At even stronger coupling (trivalent counterions), the attractive correlation force between the macroions dominates and causes the solution to separate into two fluid phases of highly different density of the electrolyte. Our results differ quantitatively from the mean-field Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, one of the cornerstones of colloid science, which predicts a purely repulsive electrostatic force among like-charged colloidal particles under all conditions. At the same time, our results are consistent with similar finding of an attraction of electrostatic origin between two similarly charged planar surfaces at sufficiently large electrostatic coupling. A detailed analysis of the counterion distribution in the neighborhood of two macroions close to each other has also been performed for divalent counterions. Finally, the effect of salt addition has also been examined.