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.     

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.     

The metastable states of foam films containing electrically charged micelles or particles: experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case - surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson-Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Effect of Charge,Size and Temperature on Stability of Charged Colloidal Nano Particles

Molecular simulation of charged colloidal suspension is performed in NVT canonical ensemble using Monte Carlo method and primitive model. The well-known Derjaguin-Landau-Verwey-Overbeek theory is applied to account for effective interactions between particles. Effect of temperature, valance of micro-ions and the size of colloidal particles on the phase stability of the solution is investigated. The results indicate that the suspension is more stable at higher temperatures. On the other hand, for a more stable suspension to exist, lower micro-ion valance is favorable. For micro-ions of higher charge the number of aggregates and the number of particle in each of aggregate on average is higher. However for the best of our results larger colloidal particle are less stable. Comparing the results with theoretical formula considering the influence of surface curvature shows qualitative consistency.     

Dynamic electrophoretic mobility of spherical colloidal particles in a salt-free medium

A theory is proposed for the dynamic electrophoretic mobility mu(omega) of spherical colloidal particles in a salt-free medium containing only counterions in an oscillating electric field of frequency omega. The dynamic mobility depends on the frequency omega of the applied electric field and on the particle volume fraction as well as on the particle surface charge. It is found that as in the case of the static electrophoretic mobility mu(0) in salt-free media, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case (in the latter case the counterion condensation takes place near the particle surface). For the low-surface-charge case, the dynamic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations kappaa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter and a is the particle radius. For the high-surface-charge case, however, the dynamic mobility becomes constant independent of the particle surface charge, because of the counterion condensation effects. A simple expression for the ratio mu(omega)/mu(0) applicable for all cases is given.     

Numerical calculation of the electrophoretic mobility of a spherical particle in a salt-free medium

By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499--503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electro-neutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Hückel's formula for high particle charges or zeta potentials because of the counterion condensation effect.     

Enhanced pearl-chain formation by electrokinetic interaction with the bottom surface of vessel

Counterions in an electric double layer (EDL) around a colloidal particle accumulate on one side of the EDL and are deficient on the other side under an electric field, resulting in an imbalance of ionic concentration in the EDL, that is to say, the ionic polarization of EDL. It is well known that the ionic polarization of EDL induces electric dipole moments whereby the alignments of colloidal particles (e.g., pearl chains) are formed under alternating electric fields. In this study, we focus on the effect of the frequency of applied electric fields (100 Hz-1 kHz) on the alignment of silica particles settling at the bottom of a silica glass vessel. In digital imaging analyses for pearl chains of silica particles, it is confirmed that surface distances between two neighboring particles decrease but the number of particles in a pearl chain increases as the frequency of the applied electric field is lowered from 1 kHz to 100 Hz. More interestingly, electrical conductance measurements suggest that the induced ionic polarization of EDL around silica particles at the bottom of the silica vessel is enhanced as the frequency is lowered from 1 kHz to 100 Hz, whereas the ionic polarization around isolated silica particles in uniform dispersions is alleviated by the relaxation of ionic concentration in the EDL as a result of the diffusion of counterions. This curious phenomenon can be explained by considering that the ionic polarization of EDL of silica particles at the bottom of a vessel is affected by the electro-osmosis of the silica surface at the bottom of the vessel.     

Effect of ionic size on the deposition of charge-regulated particles to a charged surface

The deposition of charge-regulated particles to a rigid, planar charged surface is modeled theoretically, taking the effects of the excluded area arising from deposited particles and finite ionic sizes into account. Here, a particle comprises a rigid core and an ion-penetrable charged membrane layer, which represents a general type of particle. If the membrane layer has a negligible thickness, the particle simulates a regular inorganic particle, and if the membrane layer has a finite thickness, it simulates biocolloids such as cells. The results of numerical simulation reveal that the rate of particle deposition is faster under the following conditions: (1) lower potential of the planar surface, (2) thicker membrane, (3) higher counterion valance, (4) lower fixed charge density, (5) smaller counterions, (6) larger co-ions, (7) larger functional group, and (8) lower pH. Neglecting the sizes of ionic species may lead to an appreciable deviation in both the electrical repulsive force between particle and surface and the rate of deposition. Typical deviation for the former is approximately 20%, and that for the latter is approximately -75%.     

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.     

Electrokinetic parameters of colloidal model systems: analysis and comparison between dilute and concentrated dispersions

In the last decades, the interest of many scientists has been focused on the atypical electrokinetic behavior of charged colloidal systems since several studies have shown, in most cases; it is not so ideal as expected. Particularly, two interesting phenomena have not been clearly explained yet. First, the zeta potential magnitude does not decrease monotonically with increasing ionic strength, as expected according to the Gouy-Chapmann model predicts. Second, the zeta potential obtained from different techniques shows discrepancies. More specifically, the zeta potential obtained from streaming potential is lower (in absolute value) than that measured through electrophoretic mobility. However, a recent work has pointed out that these discrepancies seem to disappear if certain conditions (related with the surface charge density) are satisfied. This work also revealed that unexpected results are found when the electric conductivity was used. Spherical polystyrene particles of appropriate particle size and charge density are employed as polymeric colloidal model in the present work. Common and adequate models are used to make clear and easy our theoretical analysis and its interpretation. To test the surface conductance and ionic mobility effects at the solid-liquid interface, both water medium and alcohol-water mixtures are used.     

Electro-optics of colloid-polyelectrolyte complexes: counterion release from adsorbed macromolecules

Complexation between sodium carboxymethylcellulose (NaCMC) and ellipsoidal particles of oppositely charged beta-FeOOH is studied using electric light scattering and electrophoresis. We focus on the complex behavior for overcharging of the particle surface. In this case, the fraction of condensed counterions on NaCMC is found to remain unchanged during polymer adsorption onto a weakly charged particle surface. Using the theory of Sens and Joanny, we evaluate the fraction of condensed counterions and compare it with results for nonadsorbed NaCMC. The polarization of condensed counterions along the chain of the adsorbed macromolecule is proved to create the electro-optical effect in suspensions stabilized by NaCMC adsorption.     

Experimental study of the effect of external electric fields on interfacial dynamics of colloidal particles

The interaction of colloidal particles with a planar surface (i.e., wall) in the presence of an electric field applied parallel to the planar surface is of interest in various microfluidic devices. Evanescent wave-based particle-tracking velocimetry was used to investigate the dynamics of a dilute suspension of polystyrene and silica particles (radii a = 110-463 nm) in a monovalent electrolyte solution with a Debye length of 6.8 nm driven through a microchannel by external electric fields E = 15-31 V/cm over the first 300 nm next to the channel wall. The particle velocity parallel to the wall due to electrophoresis and electroosmosis was in good agreement with the Helmholtz-Smoluchowski relation, and the hydrodynamic interactions between the wall and the particles were negligible, for all particle types. Measurements of the distribution of particles along the wall-normal coordinate, however, suggest that an additional force as great as 30 fN that repels the negatively charged particles away from the wall is induced by nonzero E. The results suggest that the magnitude of this force scales as E(2) and a(2) but is independent of the particle ζ-potential, in agreement with previous theoretical studies. However, estimates of the force assuming that the particles have a Boltzmann distribution were up to 40 times greater than the theoretical predictions, which only considered "remote" particle-wall interactions. These results are, to our knowledge, the first to observe a repulsive wall-normal force due to an applied electric field for near-wall colloidal particles.     

Ionic correlations in highly charge-asymmetric colloidal liquids

We use electrophoretic mobility (mu) measurements of charged colloidal particles under the presence of multivalent counterions as a probe of the electrostatic correlations between them; they become important for sufficiently high surface charge densities of the colloid (sigma) and result in a decreasing mu upon increasing sigma. The physics of this decrease is the same as that giving rise to charge inversion. We account qualitatively for the observations by considering recent theoretical arguments that assume the counterions next to the colloid surface as a strongly correlated liquid of properties similar to that of a Wigner crystal.