F.J. Arroyo

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...

The effect of the concentration of dispersed particles on the mechanisms of low-frequency dielectric dispersion (LFDD) in colloidal suspensions

Abstract There are two mechanisms which are currently used to explain the low-frequency (kHz range) dispersion of the dielectric permittivity of suspensions in electrolyte solutions (LFDD). The first, the surface diffusion mechanism (SDM), associates the LFDD with the diffusion of bound ions along the particle surface caused by the applied electric field. The second, the volume diffusion mechanism (VDM), follows from the generalization for alternating fields of the classical theory of the relaxation effect in electrophoresis and associates the LFDD with the diffusion of free ions in the diffuse double layer. It has been found that VDM is much more strongly dependent on particle concentration than SDM, opening new possibilities for the investigation of each of these two mechanisms separately. The reason is that when the concentration of particles in suspension increases, the characteristic length for the propagation of volume diffusion processes decreases together with the decrease of the free electrolyte volume, whereas the characteristic length for the surface diffusion remains constant. Correspondingly, when particle concentration is raised, the relaxation time of the VDM effect must decrease, whereas it must remain constant for the SDM mechanism. Thus, by varying the concentration of particles in suspension, one can separate the dispersion curves of SDM and VDM. A simple model is elaborated which can be useful to predict the volume fraction dependence of the parameters of LFDD; in particular, its amplitude and critical frequency. The results are compared with experimental data obtained with polymer latex dispersions of volume fractions ranging from 3 to 16%. It is found that the dielectric behaviour (the volume fraction dependence of both the amplitude and critical frequency of LFDD) of the dispersions is reasonably well explained with our model, thus demonstrating that VDM prevails in the systems studied. Experimental data previously found by other authors are also discussed in the light of the model presented.

Electrokinetic characterization of magnetite nanoparticles functionalized with amino acids

The synthesis of nanoparticles consisting of a magnetite core coated with one or more layers of amino acid (L-arginine, L-lysine, glycine, and L-glutamine) is described in this paper. For all the amino acids it is found that adsorption increases with concentration in solution in the range 0.5-10 mg/mL. The adsorption, however, differs substantially from one amino acid to another, depending on the length of the hydrocarbon chain and the polarity and charge of the side group. Thus, for given concentration and pH, adsorption is found to increase in the order L-arginine < L-lysine < L-glutamine < glycine. This order corresponds roughly to amino acids with decreasing chain length; in addition, the presence of the less polarizable guanidine group in the arginine molecule may explain why this amino acid is slightly less adsorbed than lysine. The pH dependence of the adsorption of each amino acid is reasonably explained considering the surface charge of magnetite and the charge of the amino acid molecules for different pHs, indicating a significant role of electrostatics in adsorption. This is further checked by means of determinations of the electrophoretic mobility of amino acid-coated magnetite as a function of pH: the results indicate a shift of the isoelectric point of the raw magnetite toward more basic pHs, an indication of adsorption of positive species, as confirmed by the tendency of the mobility of amino acid-coated magnetite toward more positive values below neutral pH. The electrophoretic mobility of coated particles was also measured as a function of the concentration of amino acid, and it was found that for low concentrations the four amino acids provoke charge inversion and overcharging of the magnetite surface at pH 6. Finally, the dependence of the electrophoretic mobility on the ionic strength indicated that from an electrophoretic point of view, the functionalized magnetite-amino acid particles do not behave as soft particles, and that the amino acid coating should be very compact.

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.

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.

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.

ELECTROKINETIC PROPERTIES OF COLLOIDS OF VARIABLE CHARGE. II. ELECTRIC BIREFRINGENCE VERSUS DIELECTRIC PROPERTIES

We present a detailed comparison between the low frequency behavior of the electric birefringence (as measured by the Kerr constant, B) and of the real part of the dielectric increment Δe′, in aqueous colloidal dispersions of nearly monodisperse, elongated, polytetrafluoroethylene (PTFE) particles with adjustable surface charge. The electric charge and, consequently, the ζ-potential of the particles, is modified by adding a nonionic surfactant to the dispersion, as discussed in the first paper of this series [J. Chem. Phys. 103, 8228 (1995)]. We find that both B and Δe′ decrease upon decreasing the absolute value of the ζ-potential. Upon increasing the ionic strength, B and Δe′ display opposite behavior: B decreases while Δe′ increases. We propose an expression which connects B to the standard electrokinetic model and compare the experimental data to a calculation based on spheroids with thin double layers. If we calculate B and Δe′ using the particle ζ-potential obtained from electrophoretic mobility mea...

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.

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.

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.