The stability of a salt-free colloidal dispersion

The electrical potential for the case of two identical, planar parallel particles immersed in a salt-free medium, where the ionic species in the counterions come solely from those that dissociated from the surfaces, is evaluated. Analytical expressions for the electrical potential, the concentration of counterions, and the electrical energy are derived. We show that in a salt-free dispersion, if the separation distance between two particles is sufficiently far, the electrical repulsive force dominates, that is, the total energy is positive and does not have a secondary minimum, which is not the case for a dispersion where both coions and counterions are present. Also, the conditions used to calculate the critical coagulation concentration in the classic Derjaguin-Landau-Verwey-Overbeek theory become inappropriate and the Derjaguin approximation is inapplicable. We show that if the surface charge density exceeds approximately 0.04 Cm(2), the stability of a salt-free dispersion remains essentially the same. If the surface charge density is sufficiently high, the maximum separation distance between two particles below which coagulation occurs is in the ranges of [0,1 nm] and [1,7 nm] for the cases where the Hamaker constant is 10(-20) and 10(-19) J, respectively.     

Electrophoresis of a spherical dispersion of polyelectrolytes in a salt-free solution

The electrophoretic behavior of a spherical dispersion of polyelectrolytes of arbitrary concentration is analyzed theoretically under a salt-free condition, that is, the liquid phase contains only counterions which come from the dissociation of the functional groups of polyelectrolytes. We show that, in general, the surface potential of a polyelectrolyte increases nonlinearly with its surface charge. A linear relation exists between them, however, when the latter is sufficiently small; and the more dilute the concentration of polyelectrolytes, the broader the range in which they are linearly correlated. If the amount of surface charge is sufficiently large, counterion condensation occurs, and the rate of increase of surface potential as the amount of surface charge increases declined. Also, it leads to an inverse in the perturbed potential near the surface of a polyelectrolyte, and its mobility decreases accordingly. For a fixed amount of surface charge, the lower the concentration of polyelectrolytes and/or the lower the valence of counterions, the higher the surface potential. The qualitative behavior of the mobility of a polyelectrolyte as the amount of its surface charge varies is similar to that of its surface charge.     

Approximate analytical expressions for the electrical potential between two planar, cylindrical, and spherical surfaces

Approximate analytical expressions for the electrical potential of planar, cylindrical, and spherical surfaces are derived for the case in which the dispersion medium contains counterions only. On the basis of the results for single surfaces, those for two identical surfaces can be derived. The curvature effect of a surface on the electrical potential distribution can be neglected when the order of its radius exceeds approximately 100 times the thickness of the corresponding double layer. If this effect needs to be considered, it can be taken into account by multiplying a correction function by the electrical potential of a planar surface. The electrical potential at the center between two derived surfaces is readily applicable to the evaluation of the electrostatic force per unit area between two surfaces, or the osmotic pressure. For the same set of parameters, the magnitudes of the osmotic pressure for various types of surfaces rank as follows: planar surface > cylindrical surfaces > spherical surfaces.     

Approximate analytical expressions for the electrical potential in a cavity containing salt-free medium

The electrical potential in a closed surface such as a cavity containing counterions only is derived for the cases of constant surface potential and constant surface charge density. The results obtained have applications in, for example, microemulsion-related systems in which ionic surfactants are introduced to maintain the stability of a dispersion and electroosmotic flow-related analysis. An analytical expression for the electrical potential is derived for a planar slit, and the methodology used is modified to derive approximate analytical expressions for spherical and cylindrical cavities. The higher the surface potential, the better the performance of these expressions. For the case where the surface potential is above ca. 50 mV, the performance of the approximate analytical expressions can further be improved by multiplying a correction function.     

Experimental study of electrostatically stabilized colloidal particles: colloidal stability and charge reversal

We consider the interaction of colloidal spheres in the presence of mono-, di-, and trivalent ions. The colloids are stabilized by electrostatic repulsion due to surface charges. The repulsive part of the interaction potential Ψ(d) is deduced from precise measurements of the rate of slow coagulation. These "microsurface potential measurements" allow us to determine a weak repulsion in which Ψ(d) is of the order of a few k(B)T. These data are compared to ζ potential measured under similar conditions. At higher concentrations both di- and trivalent counterions accumulate at the very proximity of the particle surface leading to charge reversal. The salt concentration c(cr) at which charge reversal occurs is found to be always above the critical coagulation concentration c(ccc). The analysis of Ψ(d) and of the ζ potential demonstrates, however, that adsorption of multivalent counterions starts far below c(cr). Hence, colloid stability in the presence of di- and trivalent ions cannot be described in terms of a DLVO ansatz assuming a surface charge that is constant with regard to the ionic strength.     

The effect of the salt concentration and counterion valence on the aggregation of latex particles at the air/water interface

An experimental study on colloidal aggregation in two dimensions is presented. This study shows that a high amount of electrolyte concentration is necessary to screen the particle interactions and to induce the aggregation process. Our results indicate that the stability of the colloidal particles, with a diameter of 735 nm, increases when they are trapped at the air-water interface. The reason for this stability is the existence of long-range repulsive interactions between the external parts of the particles that are propagated at the air phase. The subphase electrolyte concentration that separates the slow aggregation rate region from the fast aggregation rate region, the critical coagulation concentration (C.C.C.), has been determined for counterions with a different valence. Two regimes can be distinguished: at low salt concentration the aggregation process becomes slower and the aggregation is reaction limited. At high ionic strength the repulsive interactions between the immersed part of the particles are very weak and the aggregation rate tends to grow. However, because of the aerial repulsive interactions, pure diffusion-limited cluster aggregation is never found.     

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

Stability of silicon and titanium carbide suspensions in electrolyte, poly(ethylene oxide), and PEO-surfactant solutions

It has been shown that the coagulation values of counterions for SiC and TiC suspensions with particle radius from 0.5 to 5 microm obey a z(2.5-3.5) law and there is an insufficient change in the critical concentration of 1-1 electrolytes (CCE) when the surface potential of particles increases more than two times. Also, the CCE values hardly depend on the position of counterions in the lyotropic sequence. This is explained by aggregation of SiC and TiC particles at a secondary minimum, which is proved by calculations of the potential curves of interparticle interactions using the DLVO theory. The adsorption of poly(ethylene oxide) on the surfaces studied does not cause--in contradiction to dispersions with smaller particles--an unlimited growth in the stability of suspensions. This is due to the aggregation of large particles with adsorbed PEO, as in polymer-free dispersions, under barrierless conditions in which the coordinates of the secondary minimum are determined by superposition of molecular attractive forces and steric repulsive forces of adsorbed polymeric chains, without a contribution from the electric repulsion term. PEO-anionic surfactant complexes possess higher stabilizing capacity compared to the individual components of the mixture. Our results show that the adsorbed polymer layers may hinder the aggregation both in the primary and in the secondary minimum for not very large particles only, the critical size of which depends on the dispersed phase nature and the molecular mass of the polymer.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

Dynamics and stability of dispersions of polyelectrolyte-filled multilayer microcapsules

The authors report dynamic and coagulation properties of a dispersion of polyelectrolyte multilayer microcapsules filled with solutions of a strong polyelectrolyte. Microcapsules are shown to take a charge of the sign of encapsulated polyions and are characterized by a nonuniform distribution of inner polyions, which indicates a semipermeability of the shell and a leakage of counterions. The capsule self-diffusion coefficient in the vicinity of the similarly charged wall is measured using a particle tracking procedure from confocal images of the dispersion. The diffusion of capsules in the force field suggests that the effective interaction potential contains an electrostatic barrier, so that we deal with the same types of interaction forces as for solid particles. The theoretical estimates of the authors show that when microcapsules are in close proximity, their interaction should even be quantitatively the same as that of colloids with the same surface potential. However, due to the mobility of inner polyions they might repel stronger at large distances. The authors thus conclude that the encapsulation of charged polymers is an important factor in determining the adhesion and interaction properties of multilayer microcapsules.     

Effect of Complexation on the Zeta Potential of Titanium Dioxide Dispersions

Abstract

The present paper deals with the surface charge properties and the dispersion stability of an aqueous titania suspension. Generally the titania powder surface is negatively charged. The dispersion stability of TiO₂ suspension is governed by the value of zeta potential. The zeta potential was measured as a function of barium acetate and zinc acetate concentrations, at pH 6.0, and the addition of electrolytes caused sharp decrease of surface charge. Ethylenediaminetetraacetic acid (EDTA) was used to chelate the bivalent metal ions, so that the charge of counterions was reduced. The complexation of bivalent counterions favors the increase of the negative zeta potential and the dispersion stability of aqueous TiO₂ suspension.     

The similarity of electric double-layer interaction from the general Poisson-Boltzmann theory

We studied electric double-layer (EDL) interactions in electrolytes with different valence combinations. Our results show that the interactions are similar for electrolytes with the same co-ion valences and concentrations and such similarity increases with the co-ion valence and surface potential. A scaled surface potential was defined and found to be useful in characterizing the difference in EDL interaction. These results show that co-ions play a more important role than counterions in determining EDL potential and interaction in an electrolyte solution, especially for systems with high co-ion valence and/or high surface potentials.     

Flow ultramicroscopic study of interparticle interaction in suspensions and kinetics of reversible aggregation

The kinetics of coagulation leading, in the long run, to the establishment of the aggregation equilibrium is studied by the flow ultramicroscopy method with allowance for the probability of aggregate formation and disintegration. The case of a slight aggregation is considered when the doublet-to-singlet concentration ratio in a disperse system is low. An equation characterizing the time dependence of the average sizes of aggregates is derived. The equation is analyzed and methods are proposed for determining the repulsive barrier and the depth of the energy minimum characterizing the potential of interparticle pair interaction from experimental data on coagulation kinetics. The case of long-range coagulation is investigated. The effects of particle size, Hamaker’s constant, and electrolyte concentration in a dispersion medium on the probability of disaggregation are estimated in terms of the theory of surface forces. Limits of the flow microscopy method in the determination of the secondary energy minimum value are considered.     

Aggregation and adsorption of sodium dioctylsulfosuccinate in aqueous ammonium chloride solution: role of mixed counterions

The critical micelle concentration (cmc) of sodium dioctylsulfosuccinate (AOT) was determined at 25 °C from surface tension and fluorescence methods in aqueous NH(4)Cl solution for assessing the influence of mixed counterions on the special counterion binding behavior (SCB) of AOT. The SCB of AOT refers to a sudden twofold increase in the value of the counterion binding constant (β) in aqueous medium when the concentration (c(*)) of the added 1:1 sodium salt is about 0.015 mol kg(-1), and it has been tested so far for sodium ion only. In the presence of sodium and ammonium mixed counterions also the SCB of AOT exist, but with lower c(*) (0.009 mol kg(-1) NH(4)Cl). Synergism in the cmc occurs due to mixed counterions. In the case of inorganic counterions, unlike the case with organic counterions, the cmc is dependent on the total counterion concentration in solution and negligibly on the specific type of counterion. Na(+) and NH(4)(+) bind almost equally to the micelle in the region of low β (below c(*)), but in the region of high β (above c(*)) NH(4)(+) binds predominantly. It has been shown that the theoretical expression for the surface excess of ionic surfactant+electrolyte system containing a single counterion can also be used to evaluate the surface excess in the presence of mixed counterions if the two counterions are considered to undergo Henry-type adsorption at the air-solution interface.     

The electrical double layer of micelles in ionic surfactant solutions in the presence of a background electrolyte: 1. Diluted micellar solutions of sodium dodecyl sulfate

The structure of the electrical double layer (EDL) of micelles in dilute micellar solutions in the presence of a background electrolyte is studied within the framework of the Gouy-Chapman-Stern theory. On the basis of the Stern isotherm for counterion adsorption, conditions of electroneutrality, and the Gauss condition at the interface between the diffuse and dense parts of EDL, three equations are derived for the electrostatic potentials of the surface of micelle cores and the diffuse part of EDL as well as for the potential of the specific adsorption of counterions. Model parameters are verified by the example of sodium dodecyl sulfate (SDS). Potentials of the diffuse part of EDL, the degree of binding of counterions with micelles, and the specific adsorption potential are calculated from the experimental data on the potential of the surface of SDS micelle cores and their sizes, critical micellization concentration, aggregation numbers, and the constants of premicellar association. The specific adsorption potential of SDS is found to be ?(4.6 ± 0.1)?, where ? is the product of Boltzmann’s constant and absolute temperature. The specific adsorption potential is independent of the background electrolyte concentration, remains constant within the determination error of the parameters, and substantially contributes to the formation of EDL of micelles.     

Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.     

A generalized model for the stability of polymer colloids

A generalized model has been proposed to describe the stability of polymer colloids stabilized with ionic surfactants by accounting simultaneously for the interactions among three important physicochemical processes: colloidal interactions, surfactant adsorption equilibrium, and association equilibria of surface charge groups with counterions at the particle-liquid interface. A few Fuchs stability ratio values, determined experimentally for various salt types and concentrations through measurements of the doublet formation kinetics, are used to estimate the model parameters, such as the surfactant adsorption and counterion association parameters. With the estimated model parameters, the generalized model allows one to monitor the dynamics of surfactant partitioning between the particle surface and the disperse medium, to analyze the variation of surface charge density and potential as a function of the electrolyte type and concentration, and to predict the critical coagulant concentration for fast coagulation. Three fluorinated polymer colloids, stabilized by perfluoropolyether-based carboxylate surfactant, have been used to demonstrate the feasibility of the proposed colloidal stability model.     

Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

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.     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.