Polarization of the Electrical Double Layer. Time Evolution after Application of an Electric Field.

Electrophoresis is one of the electrokinetic phenomena most widely investigated, both from a fundamental point of view and as a research tool in academia and industry. However, the dependence between electrophoretic mobility and zeta potential is, in a general case, far from simple, because of the many physical processes involved. In this work, we first describe qualitatively and (in some cases) quantitatively the time behavior of the dipole moment induced in the electrical double layer by an applied electric field. Further, a simple relationship is deduced between the dipole moment and the electrophoretic mobility. Through the analysis of the time dependence of the former, it is possible to resolve the different contributions to the stationary values of the mobility. Three characteristic relaxation times are distinguished in the time evolution of the dipole moment: tau(H) (the time needed for hydrodynamic flows to be established), tau(MW) (time for ionic electromigration to develop), and tau(VD) (after this time, diffusion flows are established in the system, and the double layer polarization is complete). This means that different mechanisms are operating on the double layer for different times after the application of the field, and that computing the mobility at such different times is equivalent to calculating the steady-state electrophoretic mobility under different approximations. A comparison is shown between estimated and computed mobility values as functions of time and of zeta potential, confirming the validity of the asymptotic calculations. Copyright 2000 Academic Press.

Yield Stress of Concentrated Zirconia Suspensions: Correlation with Particle Interactions.

The presence of a sufficient concentration of solid particles in a solution gives rise to a large increase in its viscosity and, more importantly, to significant deviations with respect to its original Newtonian behavior. Different rheological techniques are available to characterize such deviations, but the simplest one, obtention of steady-state rheograms, is already extremely useful with that purpose. In this work, this technique is applied to suspensions of zirconia particles, both synthesized with spherical geometry and commercial. The sigma(shear stress)-gamma;(shear rate) curves show that the suspensions are nonideal plastic, thus exhibiting a finite yield stress, sigma(0), and a shear-thinning flow. It is through sigma(0) that a connection can be established between steady-state rheological behavior and interaction energy between particles, since sigma(0) can be estimated as the maximum attractive force between particles multiplied by the number of bonds per unit area between a given particle and its neighbors. Having an experimental determination of sigma(0), the verification of its relation with the attractive forces requires estimation of the potential energy of interaction between any pair of particles. Two approaches will be considered: one is the classical DLVO model, in which the potential energy, V, is the sum of the van der Waals (V(LW)) and electrostatic (V(EL)) contributions. The second approach is the so-called extended DLVO theory, in which the acid-base interaction V(AB) (related to the hydrophilic repulsion or hydrophobic attraction between the particles) is considered in addition to V(LW) and V(EL). The three contributions can be calculated as a function of the interparticle distance if the particle-solution interface is characterized from both the electric and the thermodynamic points of view. The former is carried out by means of electrophoretic mobility measurements and the latter by contact angle determinations for three probe liquids on zirconia powder layers. Comparison between measured and calculated sigma(0) values was carried out for suspensions of spherical, monodisperse ZrO(2) particles, with volume fraction of solids, straight phi, ranging between 4.6 and 21.7%, in 10(-3) M NaCl solutions. In the case of commercial particles, the effects of both NaCl concentration (10(-5) to 10(-1) M) and volume fraction (3.5 to 21%) were investigated. It is found that the classical DLVO theory cannot be used to predict the yield stress when [NaCl]=10(-5) M, since the high zeta potentials and thick double layers never yield partial differential V/ partial differential R>0 (the interaction is repulsive for all distances) in such a case. A similar problem was encountered in 10(-1) M solutions, but now because V is always attractive, and no maximum force can be found. On the contrary, the extended DLVO model always yield physically reasonable sigma(0) values (coincident with those deduced from the classical approach when calculation is possible in the latter case). The comparison with experimental data shows that theory clearly underestimates sigma(0) by one order of magnitude or even more. The possible role of particle aggregation in this underestimation is discussed in terms of the scaling behavior of sigma(0) as a function of straight phi. Copyright 2000 Academic Press.

Rheological and Electrokinetic Properties of Sodium Montmorillonite Suspensions.

Because of their particular electric surface properties and crystal structure, most clay minerals possess a very high ion exchange capacity. Furthermore, the surface charge distribution is anisotropic: while faces of the laminar clay particles have a negative, pH-independent charge, edges may be positive or negative, depending on pH. In this work, we propose to contribute new data on particle-particle interaction and charge distribution, by means of measurements of the low-frequency dielectric dispersion (LFDD) of the clay suspensions. Because of the nonspherical shape of clay particles, there are no theoretical models capable of explaining the experimental relaxation spectra. Hence, we limit ourselves to obtaining indirect information by comparing LFDD spectra in different experimental conditions. The quantities of interest in LFDD are the value of the low-frequency dielectric constant, epsilon'(r)(0), and the characteristic or relaxation frequency, omega(cr). These two parameters were measured varying the weight fraction, straight phi, of clay (0.5, 1, and 1.5% w/v) and the pH of the dispersion medium (5, 7, and 9), while maintaining the ionic strength constant ([NaCl]=10(-4) M). It was found that the characteristic relaxation frequency of the dielectric constant was pH-dependent, with a significant minimum at pH 7 in all cases. The results are interpreted as the superposition of two independent relaxation phenomena, associated with edges and faces. With respect to the weight fraction influence, we have found a linear behavior of epsilon'(r)(0) with straight phi at pH 9, indicating the existence of no significant interaction between particles. However, at pH 7 a slight deviation of linearity is observed, and at pH 5 we observe a clearly nonlinear behavior, indicating a stronger degree of interaction between particles. This is in good agreement with the initial assumption that at acid pH values, the electric surface charge of faces is negative, whereas the edges possess a positive charge, thus favoring attractive face-to-edge interaction. Copyright 2000 Academic Press.

Dynamics of the Electric Double Layer: Analysis in the Frequency and Time Domains.

No rigorous theory of electrokinetic phenomena is conceivable without properly accounting for double layer polarization under the action of external fields. Since processes leading to such polarization need a finite time to develop, an analysis of the behavior of the quantities of interest (potential and ion concentration profiles, particle or fluid velocity, and so on) as a function of time should be extremely illustrative. In this work, we analyze how those quantities evolve in the nanosecond to microsecond time range after the application of an electric field. The network method is proposed (in which, essentially, an electric circuit simulator program is used to solve the differential equations involved, after their proper interpretation in terms of fluxes and forces) to gain information about the evolution with time of the potential, counterion, and co-ion perturbations, the particle velocity, and the fluid velocity profile. The performance of the method is first ckecked in the frequency domain, for which rigorous solutions exist, and then the procedure is used in the time domain. Reasons are discussed for the observed time dependencies of the analyzed quantities. Copyright 2000 Academic Press.

Measurement of the Low-Frequency Dielectric Properties of Colloidal Suspensions: Comparison between Different Methods.

A careful analysis of the main factors that affect the low-frequency dielectric measurements of conducting liquid samples is carried out. The influence of the type of the measurement cell, the calibration method, and the type of the instrument used, on the spectra obtained using the variable electrode spacing technique, is investigated. Permittivity and conductivity measurements in the 10 Hz to 10 MHz range are reported for low (sigma approximately 0.01 S/m) and high (sigma approximately 0.7 S/m) conductivity samples, both electrolyte solutions and polystyrene particle suspensions. Two measurement cells are evaluated: one made of glass currently used at Granada and the other made of acrylic currently used at Tucumán. Two calibration methods, the classical Short/Open correction and the quadrupolar technique (similar to the Short/Open/Load correction), are contrasted, and two impedance analyzers, the HP 4284 A and the HP 4192 A, are compared. Copyright 2000 Academic Press.

Effect of a Dynamic Stern Layer on the Sedimentation Velocity and Potential in a Dilute Suspension of Colloidal Particles.

In this paper the theory of the sedimentation velocity and potential (gradient) in a dilute suspension of charged spherical colloidal particles developed by Ohshima et al. (H. Ohshima, T. W. Healy, L. R. White, and R. W. O'Brien, J. Chem. Soc., Faraday Trans. 2, 80, 1299 (1984)) has been modified to include the presence of a dynamic Stern layer on the particle surfaces. The starting point has been the theory that Mangelsdorf and White (C. S. Mangelsdorf, and L. R. White, J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) developed to calculate the electrophoretic mobility of a colloidal particle allowing for the lateral motion of ions in the inner region of the double layer (dynamic Stern layer). The effects of varying the different Stern layer parameters on the sedimentation velocity and potential are discussed and compared to the case when a Stern layer is absent. The influence of electrolyte concentration and zeta potential of the particles is also analyzed. The results show that regardless of the chosen set of Stern layer and solution parameters, the presence of a dynamic Stern layer causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case (no Stern layer present). These changes are almost negligible when sedimentation velocity is concerned, but they are very important when it comes to the sedimentation potential. A justification for this fact can be given in terms of an Onsager reciprocal relation, connecting the magnitudes of the sedimentation potential and the electrophoretic mobility. As previously reported, the presence of a dynamic Stern layer exerts a great influence on the electrophoretic mobility of a colloidal particle, and by means of the Onsager relation, the same is confirmed to occur when the sedimentation potential is concerned. Copyright 2000 Academic Press.

Effects of Temperature and Polydispersity on the Dielectric Relaxation of Dilute Ethylcellulose Suspensions.

The role of temperature on the low-frequency dielectric dispersion is analyzed for moderately polydisperse suspensions of spherical ethylcellulose latex particles. The study is carried out in the 10-50 degrees C temperature range for two different electrolyte concentrations, namely, 5 x 10(-5) and 10(-4) M NaCl. It is found that the relaxation frequency increases with temperature, whereas the amplitude of the dielectric dispersion decreases when temperature is raised. This agrees qualitatively with predictions based on the classical electrokinetic theory (DeLacey, E. H. B., and White, L. R., J. Chem. Soc., Faraday Trans. 2 77, 2007 (1983)). However, the quantitative agreement is very far from being satisfactory. To try to overcome these differences, we have applied a more complete model in which tangential motions of ions in the inner part of the electric double layer is allowed for (DSL model, Mangelsdorf, C. S., and White, L. R., J. Chem. Soc., Faraday Trans. 86, 2859 (1990)). Although in most situations DSL models considerably improve the agreement between theory and experiment, in our case the dynamic Stern layer correction does not seem to be enough to bring much closer experimental data and predictions. It is for this reason that we also consider the fact that our suspensions are not strictly monodisperse. Keeping polydispersity in mind (this can be done by simply taking the volume average particle radius as a representative size parameter) and introducing it in the DSL model, it is shown that a much better description of the main features of the dielectric dispersion, that is, the amplitude of the dielectric increment, and the characteristic relaxation frequency of the suspensions can be reached. Copyright 1999 Academic Press.

Dielectric Dispersion of Colloidal Suspensions in the Presence of Stern Layer Conductance: Particle Size Effects.

In this work, we discuss the role that particle size plays in the manifestations of surface conduction on the dielectric response of colloidal dispersions. To that aim, experimental data on the dielectric constant of polystyrene suspensions of two different particle diameters (23 and 530 nm) are first compared to the predictions of a classical or standard model (E. H. B. DeLacey and L. R. White, J. Chem. Soc. Faraday Trans. 2 77, 2007 (1983)), and it is found that, while the latter explains reasonably the dielectric behavior of the smallest particles, it considerably underestimates the phenomenon in the case of large particles. To explain these results in terms of contributions of ion motions in the inner region of the double layer of the particles, the approach followed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans. 86, 2859 (1990)) is used to incorporate surface conductance in the theory of dielectric response of suspensions. In ac fields it is found that the model considerably improves the comparison between theory and experiment, whereas its use seems unnecessary for the smallest particles, where, whatever the combination used for the parameters of the theory, its predictions do not differ from the standard theory. Only in the case of the larger particles studied does the introduction of surface conductance play any role. A comparison between both types of theoretical results in a wide range of particle sizes demonstrates that Stern layer conductance always increases the magnitude of the low-frequency dielectric constant of suspensions, but its effect is less important the smaller the particle size and the larger the zeta potential for fixed ionic conditions in the dispersion medium. Copyright 1999 Academic Press.

Effect of Size Polydispersity on the Dielectric Relaxation of Colloidal Suspensions: A Numerical Study in the Frequency and Time Domains.

In this article, a systematic numerical study is described of the effect of the polydispersity of suspensions of spherical particles on their dielectric behavior, in both the frequency and time domains, starting from the model proposed by DeLacey and White (J. Chem. Soc., Faraday Trans. 2 77, 2007 (1981)) for monodisperse suspensions. The distribution function of relaxation times, characterizing the dielectric response of the systems, is also calculated. It is found that in both the frequency and time domains the predicted behavior does not differ in any essential way from the one obtained for a monodisperse suspension with particle radius close to the volume-averaged mean radius of the polydisperse system. Hence, no arguments related to polydispersity seem to be useful for explaining the discrepancies frequently found between measured and calculated dielectric increments in suspensions, namely, those concerning the magnitude of the dielectric constant of the suspension (its low-frequency value), the value of the characteristic or relaxation frequency, or the overall shape of the relaxation pattern. Copyright 1998 Academic Press.

Surface Chemical Analysis and Electrokinetic Properties of Spherical Hematite Particles Coated with Yttrium Compounds

We describe in this work the chemical and electrokinetic surface characterization of core-shell particles consisting of a practically spherical hematite nucleus coated by a layer of yttrium basic carbonate or yttrium oxide (obtained after calcination of the carbonate-coated particles, following the method of E. Matijevic and B. Aiken (J. Colloid Interface Sci. 126, 645 (1988))). The morphological and surface characteristics of the particles were controlled by modifying the initial yttrium nitrate concentration and the growing time. A total of 14 samples of hematite-yttrium basic carbonate composites were obtained, and three of them (obtained by keeping at 90degreesC solutions containing 6.5 x 10(-4) M alpha-Fe2O3, 1.8 M urea, and 1.1, 3, and 4.9 mM Y(NO3)3, respectively) were then converted into hematite-Y2O3 particles. Transmission electron microscopy was used to ascertain the shape and size of the particles. The spherical geometry of the core hematite is found, as a rule, on the core-shell particles; in general, carbonate samples obtained with intermediate initial concentration of Y(NO3)3 have the maximum coating thickness, whereas increasing that concentration does not lead to thicker coatings. Hence, formation of individual yttrium basic carbonate, together with coated hematite, cannot be completely ruled out under such conditions. Two techniques were employed for the elucidation of the surface composition of the particles, namely EDX and XPS (or ESCA). In particular, XPS data show that the coating of hematite by yttrium carbonate is almost complete in the case of particles obtained with 3 mM Y(NO3)3 concentration and 9-h heating time. The oxide samples obtained after calcination show high contents of yttrium and low iron surface concentration for initial [Y(NO3)3] = 1.1 mM (sample OB9) and 3 mM. According to XPS analysis, both types of particles have a quite similar surface composition and structure. For all types of particles but the carbonate-coated ones obtained at the shortest reaction times, the pHiep was found to be above that of pure hematite, approaching that of yttrium basic carbonate or oxide. In particular, among the oxide-coated particles, it is sample OB9 the one that most closely approaches its pHiep to that of Y2O3, in good agreement with the surface chemical analysis performed with XPS. Copyright 1997 Academic Press. Copyright 1997Academic Press

Surface Chemical Analysis and Electrokinetic Properties of Synthetic Spherical Mixed Zinc-Cadmium Sulfides

In this work, we analyze the surface and bulk chemical composition, as well as the crystal structure, of colloidal spherical particles of Zn-Cd mixed sulfides of different Zn/Cd ratios. The particles were obtained by precipitation from solution according to the method described by Wilhelmy and Matijevic [Colloids Surfaces 16, 1 (1985)]. Transmision electron microscopy of the particles show that their average diameter ranges from 50-60 nm (when the synthesis is carried out at 50degreesC) up to 150-200 nm (for a temperature of 70degreesC). Atomic absorption analysis of the twelve samples obtained indicated that the bulk Zn/Cd ratio increases with aging temperature; the same behavior is found when the concentration of Cd(NO3)2 used in the synthesis is decreased. Similarly, the bulk proportion of Zn in the particles is higher the longer the growth time. EDX microanalysis was also performed on all the samples; although this technique is not a bulk (but rather surface) analytical tool, the fact that it gives information down to a depth of approximately 500 A from the surface makes the type of information obtained with EDX comparable to atomic absorption. Although the overall Zn/Cd trends are reproduced by EDX data, these are not as sensitive as atomic absorption. The surface composition of three selected samples (M3, 50 min growth time, 50degreesC, 0.52 mM Cd2+ in the growing solution; M8, 100 min, 60degreesC, 0.52 mM; M12, 100 min, 70degreesC, 0.52 mM) was determined by XPS spectra od Cd 3d5/2, Zn 2p3/2, and O 1s electrons, for the three samples. The sequence of variation of the Zn/Cd ratio of M3, M8, and M12 particles agrees qualitatively with that found by atomic absorption or EDX; the fact that no detectable Cd is found in sample M12 suggests that the particles have a nonhomogeneous composition that changes from the core to the surface layer. The analysis of O 1s electrons allows to reach the conclusion that the surface oxidation changes in the order M3 > M8 > M12, i.e., the particles are more oxidized the larger the amount of cadmium on their surface. This is confirmed by electric conductivity determinations in aqueous suspensions of the samples, both in the presence of natural light and in the dark, as a function of time. These data, together with crystal structure determinations by XRD, suggest that, when the growth temperature is 50-60degreesC, the particles contain a ZnS (sphalerite) nucleus covered by a layer of mixed, hexagonal Zn-CdS and a surface layer of cubic ZnS. When the aging temperature is 70degreesC, the ZnS core is surrounded by a shell containing cubic ZnS and amorphous CdS. The surface electrical properties of the particles in aqueous suspensions were analyzed by electrophoresis: the effect of pH on the electrophoretic mobility, and in particular the pH value at which the mobility is zero (isoelectric point or pHiep) confirms the conclusions obtained from our previous surface chemical analysis concerning the surface oxidation of the particles. The effect of lattice ions (Zn2+, Cd2+, S2-) in solution on the mobility (and hence on the surface charge) of the particles is very significant: the latter ions are able to find easily their way to the surface of the sulfides and change to a large extent the overall pH-dependence of the mobility and specifically the values of the pHiep. Copyright 1997 Academic Press. Copyright 1997Academic Press

Adsorption of a Corticoid on Colloidal Hematite Particles of Different Geometries

An electrokinetic study of the adsorption of a glucocorticoid drug, betamethasone disodium phosphate (BMP), on hematite (alpha-Fe2O3) particles is presented in this work. We analyze the electrophoretic mobility of both spherical and elongated hematite as a function of the concentration of BMP in the dispersion medium; it is found that, even for the lowest BMP concentration, the drug molecules adsorb onto the particles, changing their surface charge from positive to negative. When the drug concentration is increased between 10(-5) and 5 x 10(-3) M, the mobility of spherical hematite shows a monotonous increase from approximately -1.5 to approximately -3.5 &mgr;ms-1/Vcm-1; in the case of elongated particles, the mobility increases with BMP concentration up to 10(-4) M, larger concentrations of the corticoid having little effect on the electrokinetic properties of the particles. The effect of pH on the electrophoretic mobility of hematite is also investigated for two constant drug concentrations (0.05 and 0.5 mM); the isoelectric point of the particles is shifted to a pH below 3, another indication of adsorption of the negatively charged phosphate groups of BMP. These qualitative reasonings are confirmed by direct spectrophotometric determinations of the amount of BMP adsorbed on both hematite samples: spherical and ellipsoidal. The effect of pH on the adsorption density, Gamma, suggests that electrostatic interactions are not the only forces responsible for adsorption. In fact, although Gamma decreases with pH for both types of particles, it remains measurable up to pH 10, when strong electric repulsion is to be expected between hematite and phosphate groups. The effect of initial BMP concentration on Gamma is also studied. It is shown that a plateau region is reached in both samples, this indicating that their surfaces get saturated with BMP: the saturation begins when the coverage is of the order of approximately 1/8 (spherical particles) and approximately 1/40 (elongated particles) of a drug monolayer. Such difference might be due to the ellipsoidal hematite particles having a lower positive surface charge, since they are synthesized in a different dispersion medium.