Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.     

Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.     

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions.The counterions consist of two rigidly bonded point charges,each of valency Z.The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges.The system is analyzed by employing a self-consistent field theory,which treats the short and long range interactions of the counterions within different approximations.We find that in the weak coupling limit,the interactions are only repulsive.In the intermediate coupling regime,the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods,bridging contributes to the attractive interaction.In the strong coupling limit,the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces.Two minima can then appear in the force curve between surfaces.     

Long-range attraction between surfaces: existence and amplitude?

The possible occurrence of a long-range attraction between hydrophobic surfaces is fundamental for understanding the kinetics of protein folding or self-assembling structures, such as biological membranes, the stability of emulsions and inorganic dispersions. Direct force measurements have revealed the presence in water of a long-range attraction between macroscopic and hydrophobic surfaces. Nevertheless, the existence of this so-called ‘hydrophobic force’ for smaller objects is still under discussion. For macroscopic surfaces, it appears that electrostatic contributions due to surface heterogeneities and gas effects and/or bubble bridging have to be taken into account, but do they define an intrinsic ‘hydrophobic force’? For charged colloidal particles, theoretical predictions of electrostatic attraction and a phase separation when the counterions are multivalent, are partially confirmed by experiments, and recent experimental evidences of an attraction in a confined geometry put an exciting challenge for theoreticians.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.     

"Like-charge attraction" between anionic polyelectrolytes: molecular dynamics simulations

"Like-charge attraction" is a phenomenon found in many biological systems containing DNA or proteins, as well as in polyelectrolyte systems of industrial importance. "Like-charge attraction" between polyanions is observed in the presence of mobile multivalent cations. At a certain limiting concentration of cations, the negatively charged macroions cease to repel each other and even an attractive force between the anions is found. With classical molecular dynamics simulations it is possible to elucidate the processes that govern the attractive behavior with atomistic resolution. As an industrially relevant example we study the interaction of negatively charged carboxylate groups of sodium polyacrylate molecules with divalent cationic Ca2+ counterions. Here we show that Ca2+ ions initially associate with single chains of polyacrylates and strongly influence sodium ion distribution; shielded polyanions approach each other and eventually "stick" together (precipitate), contrary to the assumption that precipitation is initially induced by intermolecular Ca2+ bridging.     

Generalizations for the potential of mean force between two isolated colloidal particles from Monte Carlo simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin-Landau-Verwey-Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Gamma=z(2)l(B)/a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l(B)=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Gamma approximately 0.5 and, second, that onset of attraction occurs at Gamma approximately 1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.     

Proteins and polyelectrolytes: A charged relationship

We review the interaction of charged polymeric systems with proteins. In solutions of low ionic strength there are many examples of proteins attracted to polyelectrolytes even if both systems carry the same overall charge. This attractive interaction is widespread, having been observed for single polyelectrolyte chains as well as for polyelectrolytes grafted to surfaces (polyelectrolyte brushes) and charged polymeric networks. In all cases, adding salt weakens the interaction considerably. We discuss the suggestion that the attractive force at low salinity originates from the asymmetry of interaction between charged polymer segments and charged patches on the surface of the protein globule. This can be explained if the attractive force is mainly due to a counterion release force, i.e., the polyelectrolyte chains become the multivalent counterions for the patches of opposite charge localized on the surface of the proteins. We review a selection of simple models that lead to semi-quantitative estimates of this force as the function of salt concentration.     

Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids

This paper presents Stokesian dynamics simulations of experiments involving one or two charged colloids near either a single charged wall or confined between parallel charged walls. Equilibrium particle-particle and particle-wall interactions are interpreted from dynamic particle trajectories in simulations involving (1) a single particle levitated above a wall, (2) two particles below a wall, and (3) two particles confined between two parallel walls. By specifying only repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials and including multibody hydrodynamics, we successfully recover expected potentials in some cases, while anomalous attraction is observed in other cases. Attraction inferred in the latter simulations displays quantitative agreement with literature measurements when particle dynamics are interpreted using reported analyses. Because anomalous attraction is reproduced in simulations using only electrostatic repulsive DLVO potentials, our results reveal the one-dimensional analyses to be invalid for configurations that are inherently multidimensional via multibody hydrodynamics. Parameters related to experimental sampling of particle dynamics are also found to be critical for obtaining accurate potentials. We explain the anomalous attraction in each experiment using effective potentials, which can be employed in an a priori fashion to assist the confident design of future experiments involving interfacial and confined colloids. Ultimately, our findings reveal the importance of dimensionality and multibody hydrodynamics for understanding nonequilibrium dynamics of colloids near surfaces.     

Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.     

Electrostatic surface interactions in mixtures of symmetric and asymmetric electrolytes: a Monte Carlo study

Canonical Monte Carlo simulations of the interaction between a uniformly charged spherical particle and a discretely charged planar surface in solutions of symmetric and asymmetric electrolytes were performed. To assess the nature of the interactions, the force exerted on the colloidal particle perpendicular to the planar surface was calculated. Attractive minima in the interaction force between the similarly charged surfaces reveal the occurrence of two phenomena: long-range attraction of electrostatic origin and short-range attraction due to depletion effects. The degree of electrostatic coupling determines the magnitude and range of like-charge attraction between the two surfaces.     

Density functional theory for Yukawa fluids

We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.     

A theoretical investigation on the pH-induced switching of mixed polyelectrolyte brushes

A theoretical investigation on the pH-induced switching of mixed polyelectrolyte brushes was performed by using a molecular theory. The results indicate that the switching properties of mixed polyelectrolyte brushes are dependent on the pH values. At low pH, negatively charged chains adopt a compact conformation on the bottom of the brush while positively charged chains are highly stretched away from the surface. At high pH values, the inverse transformation takes place. The role of pH determining the polymer chains conformation and charge behavior of mixed polyelectrolyte brushes was analyzed. It is found that there exists a mechanism for reducing strong electrostatic repulsions： stretching of the chains. The H＋ and OH- units play a more important role as counterions of the charged polymers do. The collapse of the polyelectrolyte chains for different pH values could be attributed to the screening of the electrostatic interactions and the counterion-mediated attractive interaction along the chains.     

Influence of confinement on the electrostatic interaction between charged colloids: a (N,V,T) Monte Carlo study within hyperspherical geometry

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.     

Influence of the diffuse layer overcharging or undercharging on the stability of charged interfaces: a restricted grand canonical Monte Carlo study

We have applied a restricted grand canonical Monte Carlo procedure to describe, in the framework of the primitive model, the counterion exchange mechanism between diffuse layers of counterions surrounding segregated charged lamellae. The net charge transfer between the dense and dilute domains is shown to vary as a function of the valence of the neutralizing counterions: undercharging of the dense interlayer is detected in the presence of monovalent counterions and overcharging with divalent counterions. Furthermore, no net reduction of the swelling pressure is detected for monovalent counterions, while a large enhancement of the net interlamellar attraction is found for charged lamellae neutralized by divalent counterions.     

Strong attraction among the fully hydrophilic {Mo72Fe30} macroanions

We report the study on the unique driving forces of the self-assembly of fully hydrophilic, soluble {Mo72Fe30} macroanions into single-layer, vesicle-like "blackberry" structures in water and mixed solvents. The hydrophobic interaction that is responsible for the vesicle formation of amphiphilic surfactants does not contribute to the current blackberry formation because of the absence of hydrophobic moiety. The hydrogen bond, van der Waals force, and chemical interaction only play minor roles. Laser light scattering and conductance measurements on a series of {Mo72Fe30}/ethanol/H2O solutions show that a certain amount of negative charges are necessary for the self-assembly, clearly indicating the existence of long-range attraction between macroanions, presumably due to the small counterions in between. The experimental results suggest that the charges on macroanions play a dual effect: short-range electrostatic repulsion and long-range "like-charge attraction", which is the major source of attractive force between hydrophilic macroanions, while van der Waals force, hydrogen bonds, and temporary inter-{Mo72Fe30} Fe-O-Fe chemical linking may also have minor contributions.     

Interaction forces between colloidal particles in a solution of like-charged, adsorbing nanoparticles

We have measured the force between a weakly charged micron-sized colloidal particle and flat substrate in the presence of highly charged nanoparticles of the same sign under solution conditions such that the nanoparticles physically adsorb to the colloidal particle and substrate. The objective was to investigate the net effect on the force profile between the microparticle and flat substrate arising from both nanoparticle adsorption and nanoparticles in solution. The experiments used colloidal probe atomic force microscopy (CP-AFM) to measure the force profile between a relatively large (5 μm) colloidal probe glass particle and a planar glass substrate in aqueous solutions at varying concentrations of spherical nanoparticles. At very low nanoparticle concentrations, the primary effect was an increase in the electrostatic repulsion between the surfaces due to adsorption of the more highly charged nanoparticles. As the nanoparticle concentration is increased, a depletion attraction formed, followed by longer-range structural forces at the highest nanoparticle concentrations studied. These results suggest that, depending on their concentration, such nanoparticles can either stabilize a dispersion of weakly-charged colloidal particles or induce flocculation. This behavior is qualitatively different from that in nonadsorbing systems, where the initial effect is the development of an attractive depletion force.     

Direct surface force measurements of polyelectrolyte multilayer films containing nanocrystalline cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.     

Agglutination of like-charged red blood cells induced by binding of beta2-glycoprotein I to outer cell surface

Plasma protein-mediated attractive interaction between membranes of red blood cells (RBCs) and phospholipid vesicles was studied. It is shown that beta(2)-glycoprotein I (beta(2)-GPI) may induce RBC discocyte-echinocyte-spherocyte shape transformation and subsequent agglutination of RBCs. Based on the observed beta(2)-GPI-induced RBC cell shape transformation it is proposed that the hydrophobic portion of beta(2)-GPI molecule protrudes into the outer lipid layer of the RBC membrane and increases the area of this layer. It is also suggested that the observed agglutination of RBCs is at least partially driven by an attractive force which is of electrostatic origin and depends on the specific molecular shape and internal charge distribution of membrane-bound beta(2)-GPI molecules. The suggested beta(2)-GPI-induced attractive electrostatic interaction between like-charged RBC membrane surfaces is qualitatively explained by using a simple mathematical model within the functional density theory of the electric double layer, where the electrostatic attraction between the positively charged part of the first domains of bound beta(2)-GPI molecules and negatively charged glycocalyx of the adjacent RBC membrane is taken into account.