María L. Jiménez

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...

Hydrolysis versus ion correlation models in electrokinetic charge inversion: establishing application ranges.

In this article, we investigate experimentally a wide range of situations where charge inversion (i.e., overcompensation of the surface charge of a colloidal particle by the countercharge) can occur. To that end, the electrophoretic mobility of sodium montmorillonite, silica, and polystyrene latex as functions of pH and concentration of different salts is presented, and conditions are established where charge inversion occurs. The reason for this study is to provide experimental evidence for distinguishing between two existing models for the explanation of charge inversion. One of these is the specific adsorption of ions located in the Stern layer in combination with a Gouy-Chapman diffuse part of the double layer. The other ion-correlation theories explain the phenomenon in terms of purely physical arguments based on Coulombic pair interactions between ions and surface charges and on excluded volume effects. In distinguishing between these two interpretations, the influence of the pH plays a central role because of its effect on the hydrolysis of multivalent cations. In our experiments, it is found that although 1-2 and 2-2 electrolytes provoke a decrease in the absolute values of the electrophoretic mobilities when their concentration in solution is increased, they never lead to charge inversion, whatever the surface charge or the pH. However, in the case of salts of trivalent cations, electrokinetic charge reversal is often observed above a certain critical electrolyte concentration. In addition, the extent of overcharging increases when the concentration is raised above the critical value. This trend occurs for any system in which the surface charge is pH-independent, as in polystyrene latex and montmorillonite. Most of the results presented here are compatible with the specific adsorption of hydrolyzed metal ions as the main driving force for charge inversion. At low pH, when the hydrolysis of trivalent cations is likely to be absent, overcharging can be attributed to ion correlation effects.

Temperature Effects on Energy Production by Salinity Exchange

In recent years, the capacitance of the interface between charged electrodes and ionic solutions (the electric double layer) has been investigated as a source of clean energy. Charge is placed on the electrodes either by means of ion-exchange membranes or of an external power source. In the latter method, net energy is produced by simple solution exchange in open circuit, due to the associated decrease in the capacitance of the electric double layer. In this work, we consider the change in capacitance associated with temperature variations: the former decreases when temperature is raised, and, hence, a cycle is possible in which some charge is put on the electrode at a certain potential and returned at a higher one. We demonstrate experimentally that it is thus viable to obtain energy from electric double layers if these are successively contacted with water at different temperatures. In addition, we show theoretically and experimentally that temperature and salinity variations can be conveniently combined to maximize the electrode potential increase. The resulting available energy is also estimated.

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.

Effect of Solution Composition on the Energy Production by Capacitive Mixing in Membrane-Electrode Assembly

In this work, we consider the extent to which the presence of multivalent ions in solution modifies the equilibrium and dynamics of the energy production in a capacitive cell built with ion-exchange membranes in contact with high surface area electrodes. The cell potential in open circuit (OCV) is controlled by the difference between both membrane potentials, simulated as constant volume charge regions. A theoretical model is elaborated for steady state OCV, first in the case of monovalent solutions, as a reference. This is compared to the results in multi-ionic systems, containing divalent cations in concentrations similar to those in real seawater. It is found that the OCV is reduced by about 25% (as compared to the results in pure NaCl solutions) due to the presence of the divalent ions, even in low concentrations. Interestingly, this can be related to the “uphill” transport of such ions against their concentration gradients. On the contrary, their effect on the dynamics of the cell potential is negligible in the case of highly charged membranes. The comparison between model predictions and experimental results shows a very satisfactory agreement, and gives clues for the practical application of these recently introduced energy production methods.

Electrophoresis and dielectric dispersion of spherical polyelectrolyte brushes.

Spherical polyelectrolyte brushes (SPBs) consist of a rigid core on which polyelectrolyte chains are grafted in such a way that in certain conditions (low ionic strength and high charge of the chains) the polymer chains extend radially toward the liquid medium. Because of the hairy-like structure of the polymer brushes, the typical soft-particle approach used for explaining the behavior of polyelectrolyte-coated particles must be modified, using the assumptions that the density of charged segments in the polymer chains decreases with the squared distance to the rigid core surface and that the same happens to the friction between the brushes and the surrounding fluid. Interest in clarifying the electrokinetics of these systems is not just academic. It has recently been found experimentally (Jiménez et al., Soft Matter 2011, 7, 3758-3762) that the response of concentrated suspensions of spherical polyelectrolyte brushes in the presence of alternating electric fields shows a number of unexpected features. Both dielectric and dynamic electrophoretic mobility spectra (respectively, dependences of the electric permittivity and the AC electrophoretic mobility on the frequency of the applied field) showed very special aspects, with giant values of the mobility and an unusually strong dielectric relaxation in the kHz region. In the present paper we give a full account of the electrodynamics of such systems, based on a cell model for describing the hydrodynamic and electrical interactions between the particles. It is found that the low-frequency dynamic mobility of SPBs is much higher than that of rigid particles of comparable size and charge, making any interpretation based on zeta potential estimations of very limited applicability. The very characteristic feature of SPBs in concentrated suspensions, namely, the enhanced alpha relaxation, can be explained by considering an adequate description of the field-induced perturbations in the counterion and co-ion concentrations, well developed both outside and inside the soft layer in the case of brush-coated particles. It can be also pointed out that the dynamic electrophoretic mobility of SPBs increases with the volume fraction of particles, as a consequence of the large thickness of the brush. Predictions are also shown for the effects of friction coefficient and charge of the polyelectrolyte layer. The results compare well with experimental spectra of the dynamic mobility and electric permittivity of moderately concentrated suspensions of SPBs consisting of a 50 nm polystyrene core with grafted poly(styrene sulfonate) chains some 140 nm in length.

Effect of ionic mobility on the enhanced dielectric and electro-optic susceptibility of suspensions: Theory and experiments

It is a well-known fact that the presence of charged dispersed solid particles in an electrolyte solution considerably modifies the dielectric permittivity and conductivity of the system as compared to that of the pure dispersing medium. The enhanced conductivity of the electrical double layer, and its polarization under the action of the external field are responsible for that fact. A related phenomenon, which is also a manifestation of large induced dipole moments, is the enhanced electric birefringence ~Kerr effect!, which measures the electric torque on charged nonspherical colloids. Measurements of the Kerr constant are significant because a direct relationship exists between electrically induced birefringence and the particle’s electric polarizability. In this work we analyze, from the experimental and theoretical points of view, the effects of coion and counterion mobility on the enhancement of both dielectric and Kerr constants: we show that, quite unexpectedly, the diffusion coefficient of coions has a large effect on both dielectric response and electric birefringence of the suspensions. To our knowledge, this effect had never been described before. Experimental data have been obtained on suspensions of various polymer particles, in different concentrations of NaCl and Na-salicylate: since the particles are anionic, this choice enables to assess the effects of the mobility of coions. We find that both the dielectric response and the Kerr effect are smaller ~beyond experimental errors! in the presence of salicylate solutions. Experimental results and physical reasons for this behavior are discussed, and it is concluded that the classical theory of the low-frequency dielectric dispersion of colloidal systems provides a quantitative explanation for the coion effect on the dielectric constant. In the case of the Kerr effect, only qualitative arguments can be given in the low-frequency regime. In contrast, the high-frequency behavior is better justified in terms of a Maxwell‐Wagner model.

Compensating for electrode polarization in dielectric spectroscopy studies of colloidal suspensions : Theoretical assessment of existing methods

Dielectric spectroscopy can be used to determine the dipole moment of colloidal particles from which important interfacial electrokinetic properties, for instance their zeta potential, can be deduced. Unfortunately, dielectric spectroscopy measurements are hampered by electrode polarization (EP). In this article, we review several procedures to compensate for this effect. First EP in electrolyte solutions is described: the complex conductivity is derived as function of frequency, for two cell geometries (planar and cylindrical) with blocking electrodes. The corresponding equivalent circuit for the electrolyte solution is given for each geometry. This equivalent circuit model is extended to suspensions. The complex conductivity of a suspension, in the presence of EP, is then calculated from the impedance. Different methods for compensating for EP are critically assessed, with the help of the theoretical findings. Their limit of validity is given in terms of characteristic frequencies. We can identify with one of these frequencies the frequency range within which data uncorrected for EP may be used to assess the dipole moment of colloidal particles. In order to extract this dipole moment from the measured data, two methods are reviewed: one is based on the use of existing models for the complex conductivity of suspensions, the other is the logarithmic derivative method. An extension to multiple relaxations of the logarithmic derivative method is proposed.

Effect of the volume fraction of solids on the concentration polarization around spheroidal hematite particles

We present the first experimental results on the effect of the particles content (up to ϕ = 20% volume fraction of solids) in the low frequency dielectric dispersion (LFDD) of suspensions of hematite (α-Fe2O3) prolate spheroidal colloids. Two α-relaxations, each one associated to a characteristic dimension of the particles, are clearly observed, but they present different dependencies with volume fraction. Accounting for particle–particle interactions, in terms of models for spheres, allows a comprehensive interpretation of the mechanisms involved, suggesting the presence of a nematic phase in our suspensions.

Dielectric behaviour of suspensions of non-spherical colloidal particles

In this paper, we explore the possibility of using low-frequency dielectric dispersion (LFDD) measurements in suspensions of non-spherical particles. We present results on the LFDD of clay suspensions, with laminar, non-homogeneously charged particles, and of monodisperse spheroids of haematite (iron III oxide). The heterogeneous surface of the clay (montmorillonite) is manifested in dielectric measurements, since two relaxation times (one associated with faces and the other with edges) can be separated. Furthermore, it is found that the latter is absent at pH 7, thereby directly confirming that the edges of the clay platelets are uncharged at such pH. Experiments conducted with monodisperse haematite spheroids allow a preliminary check of existing theories for the LFDD in such geometries. Comparison of the zeta potentials deduced from dielectric and electrophoresis measurements confirm the validity of the models, and suggest that haematite could be a model spheroidal colloid, to which standard electrokinetic theories are applicable.