F. Carrique

Dielectric response of concentrated colloidal suspensions

The determination of the low-frequency (typically 0–1 MHz) dielectric dispersion of colloidal suspensions may become an electrokinetic tool of wider use if the accuracy of experimental data can be improved and if trustable theories, available for a wide range of situations, are made available. In the present work, we focus on the latter aspect: Since the dielectric constant of the suspensions is in fact a collective property, its determination could be most useful in concentrated suspensions. This is our aim in this paper. Using the classical electrokinetic equations and a cell model accounting for particle–particle interactions, we present calculations of the dielectric spectra of concentrated (volume fractions up to 50%) suspensions of spheres. Most of our results cannot be thought of as any sort of extrapolation of those corresponding to dilute suspensions (the reverse is true), and in fact the notion of a dilute colloidal system is itself not free of uncertainties, as no “critical volume fraction” can...

AC Electrokinetics of Concentrated Suspensions of Soft Particles

In this work, we show how the cell model traditionally used for the evaluation of the electrokinetic properties of concentrated suspensions can be modified to include the case of soft particles, that is, particles consisting of a rigid core and a polyelectrolyte membrane. The Navier-Stokes and Poissons equations have been modified to account for the presence of extra friction and a volume-distributed charge in the membrane. In addition to the boundary conditions on the particle and the cell boundary, it is necessary to define conditions on the polymer-electrolyte solution interface. The frequency dependence of the dynamic mobility and electric permittivity of suspensions of soft particles with arbitrary solids concentration is computed. It is shown that the dynamic mobility of these systems is larger than that corresponding to hard particles with the same charge. For the permittivity, the same trends are observed: the R-relaxation amplitude increases upon coating. It is found that friction plays an important role in determining the mobility, while the permittivity is more affected by the concentration of solids. The model also predicts that the charges on the core and in the membrane are very important parameters, although their effects differ on the mobility and the permittivity. While the former depends mainly on the membrane charge, the latter is responsive to both charges at comparable extents.

Sedimentation velocity and potential in a concentrated colloidal suspension: Effect of a dynamic Stern layer

Abstract The standard theory of the sedimentation velocity and potential of a concentrated suspension of charged spherical colloidal particles, developed by H. Ohshima on the basis of the Kuwabara cell model (J. Colloid Interf. Sci. 208 (1998) 295), has been numerically solved for the case of non-overlapping double layers and different conditions concerning volume fraction, and ζ-potential of the particles. The Onsager relation between the sedimentation potential and the electrophoretic mobility of spherical colloidal particles in concentrated suspensions, derived by Ohshima for low ζ-potentials, is also analyzed as well as its appropriate range of validity. On the other hand, the above-mentioned Ohshimas theory has also been modified to include the presence of a dynamic Stern layer (DSL) on the particles’ surface. The starting point has been the theory that Mangelsdorf and White (J. Chem. Soc. Faraday Trans. 86 (1990) 2859) 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 (DSL). The role of different Stern layer parameters on the sedimentation velocity and potential are discussed and compared with the case of no Stern layer present. For every volume fraction, the results show that the sedimentation velocity is lower when a Stern layer is present than that of Ohshimas prediction. Likewise, it is worth pointing out that the sedimentation field always decreases when a Stern layer is present, undergoing large changes in magnitude upon varying the different Stern layer parameters. In conclusion, the presence of a DSL causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case, for every volume fraction. Reasons for these behaviors are given in terms of the decrease in the magnitude of the induced electric dipole moment on the particles, and therefore on the relaxation effect, when a DSL is present. Finally, we have modified Ohshimas model of electrophoresis in concentrated suspensions, to fulfill the requirements of Shilov–Zharkhiks cell model. In doing so, the well-known Onsager reciprocal relation between sedimentation and electrophoresis previously obtained for the dilute case is again recovered but now for concentrated suspensions, being valid for every ζ-potential and volume fraction.

Dielectric relaxation in polystyrene suspensions. Effect of ionic strength

Abstract The study of the conductivity and dielectric response of colloidal suspensions in a.c. fields of frequency ω can help in improving our understanding of the electrical characteristics of the solid—liquid interface in colloidal systems. In fact, the strong dielectric dispersion shown by such systems at low frequencies is intimately related to the polarization of the double layer surrounding the particles. In this work, we present recent data on the real and imaginary parts of the conductivity and dielectric constant of spherical polystyrene suspensions as a function of the frequency of the applied field, and of KCl concentration in the dispersion medium. The conductivity and dielectric increments are compared to the predictions of accepted theoretical models. The qualitative agreement between both types of data is excellent, although the experimental results are significantly higher than the theoretical ones. Reasons for such discrepancies are discussed in the light of recently reported determinations.

Low frequency dielectric dispersion in ethylcellulose latex. Effect of pH and ionic strength

The study of the conductivity and dielectric response of colloidal suspensions in a.c. electric fields is an excellent probe of the particle double layer characterstics. In fact, the strong dielectric dispersion shown by such systems for frequencies of the field <1 MHz, is intimately related to the polarization mechanisms of both the diffuse and internal parts of the electric double layer. In this work we present experimental determinations of the dielectric constant of latexes of spherical ethylcellulose particles (commercially available as Aquacoat ®). The effect of both the ionic strength (10−4–10−3 M KCl) and pH (at constant KCl concentration) is considered. It was found that the dielectric constant of the suspensions decreases with frequency, tending to the pure solution value for frequencies ca 250 kHz. The increase in ionic strength gives rise to higher dielectric constants at any frequency; similar conclusions are valid for increased pH values of 5–8. The absolute value of the contribution of the dispersed phase to the dielectric permittivity was found to be very high. It exceeds several times the values predicted by theories developed for non-conducting particles even if very high surface charge density is assumed. It is proposed in this paper that this fact can be ascribed to the influence of adsorption oscillations of additional hydrogen counterions reversibly adsorbed in the Stern layer.

Electrophoresis of concentrated colloidal dispersions in low-polar solvents

We present a method to accurately measure the electrophoretic mobility of spherical colloids at high volume fractions in real space using confocal laser scanning microscopy (CLSM) and particle tracking. We show that for polymethylmethacrylate (PMMA) particles in a low-polar, density- and refractive-index-matched mixture of cyclohexylbromide and cis-decahydronaphthalene, the electrophoretic mobility decreases nonlinearly with increasing volume fraction. From the electrophoretic mobilities, we calculate the ζ-potential and the particle charge with and without correcting for volume fraction effects. For both cases, we find a decreasing particle charge as a function of volume fraction. This is in accordance with the fact that the charges originate from chemical equilibria that represent so-called weak association and/or dissociation reactions. Finally, as our methodology also provides data on particle self-diffusion in the presence of an electric field, we also analyze the diffusion at different volume fractions and identify a nonlinear decreasing trend for increasing volume fraction.

Electric double layer of spherical particles in salt-free concentrated suspensions: water dissociation and CO2 influence.

We present a model for the theoretical description of the electric double layer of realistic salt-free colloidal suspensions. This kind of systems consist of aqueous suspensions deionized maximally without any electrolyte added during the preparation, in which the only ions present can be (i) the added counterions that counterbalance the surface charge, (ii) the H(+) and OH(-) ions from water dissociation, and (iii) the ions produced by the atmospheric CO2 contamination. Our theory is elaborated in the framework of the classical Poisson-Boltzmann theory, the spherical cell model approach, and the appropriate local equilibrium reactions, and it also includes an efficient mathematical treatment for dealing with the resulting integro-differential equations. We have applied it to the study of the surface electric potential in a wide range of volume fraction and surface charge density values in a variety of cases. The numerical results show that it is necessary to consider the water dissociation influence for volume fractions lower than approximately 10(-2), whereas the atmospheric contamination, if the suspensions are open to the atmosphere, is important in the region of phi<10(-1). The present work sets the basis for theoretical models concerning the equilibrium phase diagram, electrokinetics, and rheology of such systems.

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.

The primary electroviscous effect in silica suspensions. Ionic strength and pH effects

Abstract An experimental investigation of the electrokinetic phenomenon known as the primary electroviscous effect is described. A characteristic coefficient for the effect has been measured in spherical silica suspensions by means of an automatic method for the determination of the viscosity of liquids using capillary viscometers. The effects of the pH and the KCl concentration are investigated, and the electrophoretic mobilities and zeta potentials of the particles are determined under the different experimental conditions. A comparison between theoretical and experimental values of the electroviscous coefficient demonstrates that the most elaborate models reproduce the trends in variation of the data, although they significantly underestimate the latter. At pH 8 and 9, theory and experiment disagree; this is explained by a hypothesis of silica dissolution.

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

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