Electrokinetic behavior and colloidal stability of polystyrene latex coated with ionic surfactants

This work is focused on analyzing the electrokinetic behavior and colloidal stability of latex dispersions having different amounts of adsorbed ionic surfactants. The effects of the surface charge sign and value, and the type of ionic surfactant were examined. The analysis of the electrophoretic mobility (mu(e)) versus the electrolyte concentration up to really high amounts of salt, much higher than in usual studies, supports the colloidal stability results. In addition, useful information to understand the adsorption isotherms was obtained by studying mu(e) versus the amount of the adsorbed surfactant. Aggregation studies were carried out using a low-angle light scattering technique. The critical coagulation concentrations (ccc) of the particles were obtained for different surfactant coverage. For latex particles covered by ionic surfactants, the electrostatic repulsion was, in general, the main contribution to the colloidal stability of the system; however, steric effects played an important role in some cases. For latices with not very high colloidal stability, the adsorption of ionic surfactants always improved the colloidal stability of the dispersion above certain coverage, independently of the sign of both, latex and surfactant charge. This was in agreement with higher mobility values. Several theoretical models have been applied to the electrophoretic mobility data in order to obtain different interfacial properties of the complexes (i.e., zeta potential and density charge of the surface charged layer).     

Smoluchowski equation and the colloidal charge reversal

Smoluchowski equation and the Monte Carlo simulations are used to study the conditions leading to the reversal of the electrophoretic mobility. Zeta (zeta) potential is identified with the diffuse potential at the shear plane which, we argue, must be placed at least one ionic diameter away from the colloidal surface. For sufficiently strongly charged colloids, zeta potential changes sign as a function of the multivalent electrolyte concentration, resulting in a reversal of the electrophoretic mobility. This behavior occurs even for very small ions of 4 A diameter as long as the surface charge density of the colloidal particles is sufficiently large and the concentration of 1:1 electrolyte is sufficiently low.     

Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Electrophoretic mobility, zeta potential, and fixed charge density of bovine knee chondrocytes, methyl methacrylate-sulfopropyl methacrylate, polybutylcyanoacrylate, and solid lipid nanoparticles

The electrophoretic mobility and zeta potential of bovine knee chondrocytes (BKCs), methyl methacrylate-sulfopropyl methacrylate (MMA-SPM) nanoparticles (NPs), polybutylcyanoacrylate (PBCA) NPs, and solid lipid nanoparticles (SLNs) were investigated under the influences of Na+, K+, and Ca2+ with various ionic strengths. The fixed charge density in the surface layers of the four biocolloidal particles was estimated from the experimental mobility of capillary electrophoresis with a theory of soft charged colloids. The results revealed that, for a specific cationic species, the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density decreased with an increase in ionic strength. For a constant ionic strength, the effect of ionic species on the reduction in the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density followed the order Na+>K+>Ca2+ for the negatively charged BKCs, MMA-SPM NPs, and SLNs. The reverse order is true for the positively charged PBCA NPs.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Electrophoresis of Spherical Particles with a Random Distribution of Zeta Potential or Surface Charge

Electrophoresis is often used to measure the "average" zeta (zeta) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of zeta potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or zeta potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92sigma(zeta)/N, and the average magnitude of the quadrupole moment is 1.302sigma(zeta)/N, where sigma(zeta) is the standard deviation of zeta potential over the surface of individual spheres. This is true for any random distribution of zeta potential, and the results emphasize that "random" implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (sigma(zeta)) of zeta potential. Monte Carlo simulations were done to confirm and extend the analytical results. Copyright 2000 Academic Press.     

Surface charge microscopy: novel technique for mapping charge-mosaic surfaces in electrolyte solutions

The effective surface potential, called the zeta potential, is commonly determined from electrophoretic mobility measurements for particles moving in a solution in response to an electric field applied between two electrodes. The situation can be reversed, with the solution being forced to flow through a plug of packed particles, and the streaming potential of the particles can be calculated. A significant limitation of these electrokinetic measurements is that only an average value of the zeta potential/streaming potential is measured--regardless of whether the surface charge distribution is homogeneous or otherwise. However, in real-world situations, nearly all solids (and liquids) of technological significance exhibit surface heterogeneities. To detect heterogeneities in surface charge, analytical tools which provide accurate and spatially resolved information about the material surface potential--particularly at microscopic and submicroscopic resolutions--are needed. In this study, atomic force microscopy (AFM) was used to measure the surface interaction forces between a silicon nitride AFM cantilever and a multiphase volcanic rock. The experiments were conducted in electrolyte solutions with different ionic strengths and pH values. The colloidal force measurements were carried out stepwise across the boundary between adjacent phases. At each location, the force-distance curves were recorded. Surface charge densities were then calculated by fitting the experimental data with a DLVO theoretical model. Significant differences between the surface charge densities of the two phases and gradual transitions in the surface charge density at the interface were observed. It is demonstrated that this novel technique can be applied to examine one- and two-dimensional distributions of the surface potential.     

Analysis of the response of suspended colloidal soft particles to a constant electric field

A network model, originally designed for an electrokinetic study of soft particle suspensions, has been used for an in-depth analysis of the physical behavior of these systems under the action of an externally applied DC electric field. The versatility of the network simulation method used makes it possible to obtain information readily not only about the electrophoretic mobility, but also about any physical variable of interest at all points around the suspended particle: electric potential, ion concentrations, fluid velocity. The field-induced polarization of the double layer is described in terms of the dependence of these and other derived variables (volume charge density, electric field components, ion flux components) on the distance to the membrane-solution interface. In contrast to colloidal suspensions of hard particles, which basically depend on just two parameters (the reciprocal Debye length multiplied by the particle radius, kappaa, and the zeta potential, zeta), soft particle suspensions require a wider parameter set. First, there are two characteristic diffusion lengths in the system (one inside the membrane and the other in the solution) and two geometrical lengths (the core radius a and the membrane thickness (b-a)). Furthermore, there is the fixed charge density inside the membrane (and possibly a surface charge density over the core) that cannot be represented by a zeta potential. Finally, the parameter that characterizes the interaction between the fluid and the permeable membrane, gamma, strongly influences the behavior of the system. Dependences on all these parameters (except the geometrical ones) are included in this study.     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

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.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

Recent advances in the electric double layer in colloid science

The interaction between charged colloidal particles is mediated by their electric double layers. Given that pairs of like-charged particles experience a repulsion, why do some dilute colloidal dispersions become unstable and condense at low ionic strengths? This puzzling paradox appears to have been largely resolved over the past year by a careful analysis of all the contributions to the thermodynamic potential of the dispersion. Condensation can be predicted using the traditional pair repulsion of the Poisson–Boltzmann theory without invoking any long-range attractions in the pair potential. However, it has emerged that one has to go beyond the Poisson–Boltzmann theory to account for the instability that occurs in confined colloidal dispersions. Other recent advances in the ubiquitous Poisson–Boltzmann theory have included effective surface charge approaches in calculating the electrokinetic zeta potential, and the modelling of charge regulation in colloidal systems.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.     

CE characterization of semiconductor nanocrystals encapsulated with amorphous silicium dioxide

The electrophoretic mobility of silica-encapsulated semiconductor nanocrystals (quantum dots) dependent on the pH and the ionic strength of the separation electrolyte has been determined by CE. Having shown the viability of the approach, the electrophoretic mobility mu of the nanoparticles investigated is calculated for varied zeta potential zeta, particle radius r, and ionic strength I employing an approximate analytical expression presented by Ohshima (J. Colloid Interface Sci. 2001, 239, 587-590). The comparison of calculated with measured data shows that the experimental observations exactly follow what would be expected from theory. Within the parameter range investigated at fixed zeta and I there is an increase in mu with r which is a nonlinear function. This dependence of mu on size parameters can be used for the size-dependent separation of particles. Modeling of mu as function of I and zeta makes it possible to calculate the size distribution of nanoparticles from electrophoretic data (using the peak shape of the particle zone in the electropherogram) without the need for calibration provided that zeta is known with adequate accuracy. Comparison of size distributions calculated via the presented method with size histograms determined from transmission electron microscopy (TEM) micrographs reveals that there is an excellent matching of the size distribution curves obtained with the two independent methods. A comparison of calculated with measured distributions of the electrophoretic mobility showed that the observed broad bands in CE studies of colloidal nanoparticles are mainly due to electrophoretic heterogeneity resulting from the particle size distribution.     

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.     

Electrokinetics in nanochannels: part II. Mobility dependence on ion density and ionic current measurements

In the first of this two-paper series, a new model was developed for calculating the electric potential field in a long, thin nanochannel with overlapped electric double layers. The model takes into account the dependence of ion mobility on local ion densities and pH. This model is used here to study and demonstrate the effect of ion density and pH on ionic current measurements. A comparison is shown of predictions based on each of three boundary conditions, as studied in Part I. The model developed in Part I is validated by comparing simulations with measurements of ionic current as a function of sodium borate concentration. Results show that predictions based on extended Debye-Hückel theory for ion mobility significantly improve the accuracy of simulations, but that these do not predict exact scaling behavior. A simple bulk conductivity measurement used as input parameter for the simulations, in place of the predicted bulk conductivity (K(0)), guarantees agreement with data in the thin EDL region. Results also indicate that the charge regulation boundary condition, complemented with an adequate bulk electrolyte model, provides better agreement with experimental trends than the specified zeta potential or specified surface net charge boundary conditions. Further, it is shown that currents due to advection (by electroosmotic flow) are in all cases studied less than 25% of the total current in the system.     

Electrophoretic mobility of a spherical colloidal particle in a salt-free medium

A general expression as well as approximate expressions are derived for the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counter ions. It is shown that there is a certain critical value of the particle surface charge. When the particle surface charge is lower than the critical value, the electrophoretic mobility is proportional to the particle surface charge or the particle zeta potential, following Hückel's formula. When the particle surface charge is higher than the critical value, the electrophoretic mobility becomes independent of the particle surface charge. This is due to the effect of counter ion condensation in the vicinity of the particle surface.     

Colloidal stability of chitosan-modified poly(methyl methacrylate) latex particles

Experiments of coagulation kinetics were used to study the influence of the electrolyte concentration on the colloidal stability of cationic poly(methyl methacrylate) latex particles with various degrees of chitosan modification. For the chitosan-free latex products prepared by various levels of 2,2′ azobis(2-amidinopropane) dihydrochloride (V-50) at constant pH, the critical coagulation concentration (ccc) increases with increasing V-50 concentration, due to the enhanced particle surface charge density. On the other hand, the chitosan-modified latex products at constant pH do not exhibit very different values of ccc. This result is attributed to the counterbalance between two opposite effects related to the grafted chitosan, that is, the increased particle surface charge density and the enhanced shift of the particle's shear plane toward the aqueous phase with the chitosan content. The ccc of the latex products with various degrees of chitosan modification decreases significantly when the pH increases from 3 to 7. This is because the degree of ionization of the surface amino groups (the particle surface charge density) decreases with increasing pH. As a result, the stability of the colloidal system decreases significantly with increasing pH. The apparent Hamaker constant and diffuse potential were obtained from the coagulation kinetics data. These two parameters along with the zeta potential and particle size data for the latex samples taken immediately after the end of the coagulation experiments were also used to study the effect of ionic strength on the colloidal stability of the latex particles. Received: 10 October 1998 Accepted in revised form: 16 December 1998     

The adsorption of cationic and amphoteric copolymers on glass surfaces: zeta potential measurements,adsorption isotherm determination,and FT Raman characterization

The adsorption of cationic and amphoteric copolymers onto controlled pore glass (CPG) powders has been studied by measurement of the powder particle zeta (zeta) potential, by determination of the adsorption isotherm, and by FT Raman measurements of the polymer-coated powder. The cationic polymers consisted chiefly of homopolymers of dimethyldiallylammonium chloride (DMDAAC) or copolymers of DMDAAC and acrylamide. The amphoteric polymers studied included copolymers of DMDAAC and acrylic acid. The comonomer ratio was varied to explore the dependence of cationic charge density on the extent and effect of adsorption. Both types of polymers adsorb onto the anionic glass surface via an ion-exchange mechanism. Consequently, a correspondingly higher mass of a low-charge-density copolymer adsorbs than of a cationic homopolymer. The presence of the anionic portion in the amphoteric polymers does not significantly alter this picture. The zeta potential, however, reflects the overall nature of the polymer. Cationic polymers effectively neutralize the glass surface, while amphoteric polymers leave the zeta potential net negative. Adsorption isotherms, determined via the depletion technique using colloidal titration, were used to "calibrate" a FT Raman method. The latter was used to determined the amount of adsorbed polymer under solution conditions in which colloidal titration could not be performed.