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.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Emulsifier-free emulsion polymerization produces highly charged, monodisperse particles for near infrared photonic crystals

We have developed emulsifier-free, emulsion polymerization recipes for the synthesis of highly charged, monodisperse latex particles of diameters between 500 and 1100 nm. These latexes consist of poly[styrene-(co-2-hydroxyethyl methacrylate)] spherical particles whose surfaces are functionalized with sulfate and carboxylic acid groups. These highly charged, monodisperse particles readily self-assemble into robust, three-dimensionally ordered crystalline colloidal array photonic crystals that Bragg diffract light in the near infrared spectral region. By altering the particle number density, the diffraction wavelength can be tuned from approximately 1000 to approximately 4000 nm.     

Evidence of hydration forces between proteins

Proteins are fundamental molecules in biology that are also involved in a wide range of industrial and biotechnological processes. Consequently, many works in the literature have been devoted to the study of protein–protein and protein–surface interactions in aqueous solutions. The results have been usually interpreted within the frame of the classical Derjaguin–Landau–Verwey–Overbeek (DLVO) theory for colloidal systems. However, against the DLVO predictions, striking evidence of repulsive forces between proteins at high salt concentrations has been observed in different works based on the analysis of the second virial coefficient or on the direct measurement of protein interaction with an atomic force microscope. Hydration forces due to the adsorption of hydrated cations onto the negatively charged protein surfaces have been invoked to rationalize this anomalous repulsion. The hydration forces between proteins provide protein-covered particles with a non-DLVO colloidal stability at high salt concentrations, as different studies in the literature has proven. This review summarizes the most relevant results published so far on the presence of hydration forces between proteins and protein-coated colloidal particles.     

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.     

Effective medium approximation and deposition of colloidal particles in fibrous and granular media

Laminar flow of fluids through fibrous and granular media and deposition of colloidal particles from a liquid suspension are two fundamental phenomena encountered in many industrial applications. An Effective Medium Approximation (EMA) is used to determine the fluid flow permeability and particle capture efficiency of random arrays of cylindrical and spherical collectors. The EMA assumes a model system in which a packing element (a single fiber in the fibrous medium and a single sphere in the granular medium) is surrounded by a fluid envelope and an effective-medium beyond the envelope. It integrates the important features of both the cell models and Brinkman's model. The Stokes equation and Brinkman equation are solved for the fluid envelope and effective medium regions, respectively, to obtain the permeability and close-to-surface velocity field around the collectors. The convective diffusion equation is then solved to determine the particle deposition rate. The analytical expressions for the permeability and particle deposition rate are derived for all possible cases of random packing of uniform and non-uniform cylinders and spheres. Effects of various system properties and operating conditions on deposition of colloidal particles are investigated. The physical or chemical conditions include the properties which affect the magnitude of double layer interaction: the electrolyte concentration and surface potentials, and the property which affects the van der Waals interaction: the Hamaker constant. It was found that the effects of the above properties is much more significant when the surface interactions play more important roles in the particle deposition process, or when the height of the total interaction energy barrier is higher than 5 kBT. Particle deposition becomes virtually impossible when the height of the repulsive energy barrier increases beyond 20 kBT.     

Micrometer scale adhesion on nanometer-scale patchy surfaces: adhesion rates, adhesion thresholds, and curvature-based selectivity

Using a model system based on electrostatics, we probe interactions between spherical particles (negative silica) and planar surfaces that present randomly placed discrete attractive regions, 10 nm in size, in a repulsive background (silica flats carrying cationic surface constructs). Experiments measure the adhesion rates of particles onto the patchy collecting surfaces from flowing dispersions, as a function of the surface loading of the attractive patches, for different particle sizes (0.5 and 1 mum diameter spheres) and different ionic strengths. Surfaces densely populated with patches, such that they present net electrostatic attractions to approaching particles, capture particles at the transport-limited (maximum) rate. Surfaces sparsely loaded with attractive patches (which present a repulsive mean field to approaching particles) are usually still adhesive, but the particle adhesion rate depends on particle size, ionic strength, and patch loading. Most significant is an adhesion threshold, a critical density of patches needed to capture particles. This threshold, which occurs at average patch spacings of 30 nm and larger and which can be tuned through ionic strength, comprises the ability of the patchy surfaces to selectively distinguish particles of different sizes or objects of different local curvature or roughness. The observation of such an adhesion threshold implicates spatial fluctuations in patch arrangement. In addition to experiments, this paper develops arguments for lengthscales that govern adhesion rate behavior, comparing particle geometry and fluctuation lengthscales, and then demonstrating qualitative consistency with the localized colloidal potentials involved.     

Theoretical analysis of factors affecting the formation and stability of multilayered colloidal dispersions

A mathematical analysis of the major factors influencing the formation and stability of colloidal dispersions containing spherical particles surrounded by multilayered polymeric interfacial membranes formed by the layer-by-layer electrostatic deposition technique is carried out. The mathematical model assumes that (i) the colloidal dispersion initially consists of a mixture of electrically charged monodisperse spherical particles and oppositely charged polymer molecules, (ii) the adsorption of polymer molecules to the particle surfaces is diffusion-limited, and (iii) the dominant particle-particle collision mechanism is Brownian motion. This approach was used to produce stability maps that highlight conditions under which bridging flocculation, multilayer formation, or depletion flocculation occurs. The stability maps are derived from calculations of the critical polymer concentrations required to (i) saturate the particle surfaces (C(Sat)), (ii) ensure that polymer adsorption is faster than particle collisions (C(Ads)), and (iii) promote depletion flocculation (C(Dep)). In addition, the influence of interfacial properties on the stability of multilayer colloidal dispersions was assessed by calculating the colloidal interactions between the coated particles (i.e., van der Waals, electrostatic, steric, and depletion). These calculations indicated that the major factors are the interfacial charge and composition rather than the interfacial thickness. This article provides useful insights into the factors affecting the formation of stable multilayer colloidal dispersions.     

Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.     

Effect of temperature on the reentrant condensation in polyelectrolyte-liposome complexation

Interactions of oppositely charged macroions in aqueous solution give rise to intriguing aggregation phenomena, resulting in finite-size, long-lived clusters, characterized by a quite narrow size distribution. Particularly, the adsorption of highly charged linear polyelectrolytes on oppositely charged colloidal particles is strongly correlated and some short-range order arises from competing electrostatic interactions between like-charged polymer chains (repulsion) and between polymer chains and particle surface (attraction). In these systems, in an interval of concentrations around the isoelectric point, relatively large clusters of polyelectrolyte-decorated particles form. However, the mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well-defined size of the aggregates are not completely understood. Nor is clear the role that the correlated polyion adsorption plays in the aggregation, although the importance of "patchy interactions" has been stressed as the possible source of attractive interaction term between colloidal particles. Different models have been proposed to explain the formation of the observed cluster phase. However, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregates. To elucidate this point, in this work, we have investigated the effect of the temperature on the cluster formation. We employed liposomes built up by DOTAP lipids interacting with a simple anionic polyion, polyacrylate sodium salt, over an extended concentration range below and above the isoelectric condition. Our results show that the aggregation process can be described by a thermally activated mechanism.     

Adsorption free energy of variable-charge nanoparticles to a charged surface in relation to the change of the average chemical state of the particles

Variable-charge nanoparticles such as proteins and humics can adsorb strongly to charged macroscopic surfaces such as silica and iron oxide minerals. To model the adsorption of variable-charge particles to charged surfaces, one has to be able to calculate the adsorption free energy involved. It has been shown that the change in the free energy of variable-charge particles is related to the change in their average chemical state upon adsorption, which is commonly described using surface complexation models. In this work, expressions for the free-energy change in variable-charge particles due to changes in chemical binding are derived for three ion-binding models (i.e., the Langmuir, Langmuir-Freundlich, and NICA models) and for changes due to nonspecific binding for the Donnan model. The expressions for the adsorption free energy of the variable-charge particles to a charged surface are derived on the basis of the equality of the (electro)chemical potential of the particles in the bulk solution and adsorption phase. The expressions derived are general in the sense that they account for the competition between charge-determining ions that bind chemically to the particles, and they also apply in case of the formation of chemical bonds between particle ligands and surface sites. The derived expressions can be applied in the future to model the adsorption of variable-charge nanoparticles to charged surfaces. The results obtained for the NICA-Donnan model make it possible to apply this advanced surface complexation model to describe the adsorption of humics to minerals.     

Stability in Colloidal Mixtures Containing Particles with a Large Disparity in Size

An experimental approach, based on turbidity measurements, is proposed for studies of the stability in colloidal mixtures containing particles with large disparity in size. The main advantage of this approach is that it permits investigations even under conditions of comparable particle number concentrations of the two colloidal populations. Binary mixtures containing a poly(vinyl acetate) (PVAc) latex and a Ludox AS-40 silica sol were investigated. The silica particles were much smaller than the latex ones. The experimental stability factors were compared with the theoretical values computed on the basis of the Kihira-Ryde-Matijevic model (J. Chem. Soc., Faraday Trans. 88(16), 2379 (1992)) for interaction between spherical particles with unevenly distributed surface charges. All the experimental results support the idea that, even when both sols are negatively charged, the small silica particles are adsorbed onto the latex surface. Under these conditions, the heteroaggregates, which are composed of PVAc cores surrounded with silica particles, can be modeled as PVAc particles having "modified" surface characteristics (i.e., average Stern potential and varying extents of the surface charge segregation). Copyright 2001 Academic Press.     

Electrostatic interactions between amphoteric latex particles and proteins

The electrostatic interactions between amphoteric polymethyl methacrylate latex particles and proteins with different pI values were investigated. These latex particles possess a net positive charge at low pH, but they become negatively charged at high pH. The nature and degree of interactions between these polymer particles and proteins are primarily controlled by the electrostatic characteristics of the particles and proteins under the experimental conditions. The self-promoting adsorption process from the charge neutralization of latex particles by the proteins, which have the opposite net charge to that of the particles, leads to a rapid reduction in the zeta potential of the particles (in other words colloidal stability), and so strong flocculation occurs. On the other hand, the electrostatic repulsion forces between similarly charged latex particles and the proteins retard the adsorption of protein molecules onto the surfaces of the particles. Therefore, latex particles exhibit excellent colloidal stability over a wide range of protein concentrations. A transition from net negative charge to net positive charge, and vice versa (charge reversal), was observed when the particle surface charge density was not high enough to be predominant in the protein adsorption process.     

Size-dependent self-organization of colloidal particles on chemically patterned surfaces

A study of the self-organization of colloidal particles during the evaporation of particle solutions on chemically patterned surfaces is presented. On a surface with hydrophilic and hydrophobic regions, colloidal particles form compact structures on the hydrophilic sites. When a colloidal solution containing a mixture of particles with a variation in size is used, the number density of each type of particle deposited on the hydrophilic islands after evaporation decreases with increasing particle size. This makes it possible to produce a concentration gradient of the particles on islands of different sizes. It is shown that this technique could allow for particle separation.     

Dynamic Light Scattering Based Microelectrophoresis: Main Prospects and Limitations

Microelectrophoresis based on the dynamic light scattering (DLS) effect has been a major tool for assessing and controlling the conditions for stability of colloidal systems. However, both the DLS methods for characterization of the hydrodynamic size of dispersed submicron particles and the theory behind the electrokinetic phenomena are associated with fundamental and practical approximations that limit their sensitivity and information output. Some of these fundamental limitations, including the spherical approximation of DLS measurements and an inability of microelectrophoretic analyses of colloidal systems to detect discrete charges and differ between differently charged particle surfaces due to rotational diffusion and particle orientation averaging, are revisited in this work. Along with that, the main prospects of these two analytical methods are mentioned. A detailed review of the role of zeta potential in processes of biochemical nature is given too. It is argued that although zeta potential has been used as one of the main parameters in controlling the stability of colloidal dispersions, its application potentials are much broader. Manipulating surface charges of interacting species in designing complex soft matter morphologies using the concept of zeta potential, intensively investigated recently, is given as one of the examples. Branching out from the field of colloid chemistry, DLS and zeta potential analyses are now increasingly finding application in drug delivery, biotechnologies, physical chemistry of nanoscale phenomena and other research fields that stand on the frontier of the contemporary science. Coupling the DLS-based microelectrophoretic systems with complementary characterization methods is mentioned as one of the prosperous paths for increasing the information output of these two analytical techniques.     

Application of the extended RSA models in studies of particle deposition at partially covered surfaces

This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.     

Hofmeister effects on the colloidal stability of an IgG-coated polystyrene latex

The effect of various ions related to the Hofmeister series (HS) on different properties of a cationic latex covered with a protein (IgG) is analyzed in this study. NaNO3, NH4NO3, and Ca(NO3)2 were used to compare the specificity of the cations, and NaCl, NaSCN, NaNO3, and Na2SO4, to compare the specificity of the anions. Two pH values, 4 and 10, were chosen to analyze the behavior of these ions acting as counter- and co-ions. At pH 4, the total surface charge is positive, whereas at pH 10 it is negative. Three different phenomena have been studied in the presence of these Hofmeister ions: (1) colloidal aggregation, (2) electrophoretic mobility, and (3) colloidal restabilization. The specific effect of the ions was clearly observed in all experiments, obtaining ion sequences ordered according to their specificity. The most important parameter for ion ordering was the sign of the charge of the colloidal particle. Positively charged particles displayed an ion order opposite that observed for negatively charged surfaces. Another influential factor was the hydrophobic/hydrophilic character of the particle surface. IgG-latex particle surfaces at pH 10 were more hydrophilic than those at pH 4. The SCN- ion had a peculiar specific effect on the phenomena studied (1)-(3) at pH 10. With respect to the restabilization studies at high ionic strengths, new interesting results were obtained. Whereas it is commonly known that cations may provoke colloidal restabilization in negative particles when they act as counterions, our experiments demonstrated that such restabilization is also possible with positively charged particles. Likewise, restabilization of negative surfaces induced by the specific effect of chaotropic anions (acting as co-ions) was also observed.     

Distribution of colloidal particles in a spherical cavity

The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle-cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein-Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle-cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.     

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.