AC Electrokinetics of Salt-Free Multilayered Polymer-Grafted Particles.

Interest in the electrical properties of the interface between soft (or polymer-grafted) nanoparticles and solutions is considerable. Of particular significance is the case of polyelectrolyte-coated particles, mainly taking into account that the layer-by-layer procedure allows the control of the thickness and permeability of the layer, and the overall charge of the coated particle. Like in simpler systems, electrokinetic determinations in AC fields (including dielectric dispersion in the 1 kHz-1 MHz frequency range and dynamic electrophoresis by electroacoustic methods in the 1-18 MHz range) provide a large amount of information about the physics of the interface. Different models have dealt with the electrokinetics of particles coated by a single polymer layer, but studies regarding multi-layered particles are far scarcer. This is even more significant in the case of so-called salt-free systems; ideally, the only charges existing in this case consist of the charge in the layer(s) and the core particle itself, and their corresponding countercharges, with no other ions added. The aims of this paper are as follows: (i) the elaboration of a model for the evaluation of the electrokinetics of multi-grafted polymer particles in the presence of alternating electric fields, in dispersion media where no salts are added; (ii) to carry out an experimental evaluation of the frequency dependence of the dynamic (or AC) electrophoretic mobility and the dielectric permittivity of suspensions of polystyrene latex spherical particles coated with successive layers of cationic, anionic, and neutral polymers; and (iii) finally, to perform a comparison between predictions and experimental results, so that it can be demonstrated that the electrokinetic analysis is a useful tool for the in situ characterization of multilayered particles.

Non-monotonic concentration dependence of the electro-phoretic mobility of charged spheres in realistic salt free suspensions.

Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the optically accessible range of concentrations in experiments on colloidal electro-kinetics. Here, we measured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic concentration dependence of the mobility for a single particle species. Our observations reconcile previous experimental observations made on other species over restricted concentration ranges. We compare our results to the state-of-the-art theoretical calculations using a constant particle charge and the carefully determined experimental boundary conditions as input. In particular, we consider the so-called realistic salt free conditions, i.e., we respect the release of counterions by the particles, the solvent hydrolysis, and the formation of carbonic acid from dissolved neutral CO2. We also compare our results to previous results obtained under similarly well-defined conditions. This allows identification of three distinct regions of differing density dependence. There is an ascent during the build-up of double layer overlap, which is not expected by theory, an extended plateau region in quantitative agreement with theoretical expectation based on a constant effective charge and a sudden decrease, which occurs way before the expected gradual decrease. Our observations suggest a relation of the non-monotonic behavior to a decrease in particle charge, and we tentatively discuss possibly underlying mechanisms.

Dynamic viscosity of colloidal silica suspensions at low and high volume fractions.

A comprehensive study was carried out on the dynamic viscosity of X30 silica dispersions at both high and low volume fractions of colloidal silica particles at various electrolyte ionic strength and pH values. Booth and Ruiz-Reina and Carrique theoretical models (R-R&C) were compared in predicting the primary electroviscous effect (PEE) for viscosity at low volume fractions. To this respect the colloidal dispersion was well characterised with regards to electrolyte properties such as the Debye length, κ-1, calculated from the ionic strength, and zeta potential, ζ, calculated from the electrophoretic mobility using the full numerical model by O'Brien and White (O'B&W). R-R&C hard sphere model (which is a modified version of Simha hard sphere model that includes a boundary condition by Happel on the outer radius of the cell) and the semi-empirical Krieger-Dougherty (K-D) models were fitted to the experimental data at high volume fractions. At both low and high volume fractions the viscosity increased with pH and decreased with ionic strength. At low volume fractions both theoretical models significantly underestimated the experimental dynamic viscosities obtained in this work. This could be attributed to the fuzzy structures for silica particles in aqueous conditions reported previously in the literature, where a significantly larger electroviscous parameter, p, was obtained experimentally for silica particles. The experimental electroviscous parameter, pexp, in this work was found to be roughly an order of magnitude up to 26 times larger than that predicted by Booth and around 5 ±â€¯1 times larger than the predicted p by R-R&C model allowing the introduction of a correction factor in the PEE coefficient obtained from R-R&C model enabling good prediction for X30 silica dispersions by the latter model. The significant improvement of the electroviscous effect predictions by R-R&C model compared to Booth model may be attributed to the limitations invalidating the Booth model at the electrolyte conditions in this study. At high volume fractions, the R-R&C hard sphere cell model, gave a much better fit to the experimental data compared to the K-D model, which also had the advantage of being only dependent on a coefficient that linearly relates an effective volume fraction postulated for the fuzzy silica particles to the experimental. The K-D model however, depends on the intrinsic viscosity, [η], which requires the calculation of the experimental slope of the dynamic viscosity against volume fraction in the dilute limit, and also on a maximum packing fraction as a fitting parameter. Due to the effect of the fuzzy structures on the viscosity, the latter effective volume fraction ϕeff was calculated using two approaches: (i) as a fitting parameter by fitting the R-R&C hard sphere model to the experimental viscosity data over the entire volume fraction range, and (ii) by fitting only the linear part of the experimental viscosity at low volume fractions, It is concluded that the R-R&C hard sphere model with the effective volume fraction accounting for the fuzzy structures fits reasonably well the full range of experimental results at low and high volume fractions. When the model was used with the Adamczyk effective volume fraction (i.e., considering only the dilute region in the fitting procedure), the predictions became worse at high volume fractions where significant deviations from the experimental results were found upon the increase of pH.

General electrokinetic model for concentrated suspensions in aqueous electrolyte solutions: Electrophoretic mobility and electrical conductivity in static electric fields.

In recent years different electrokinetic cell models for concentrated colloidal suspensions in aqueous electrolyte solutions have been developed. They share some of its premises with the standard electrokinetic model for dilute colloidal suspensions, in particular, neglecting both the specific role of the so-called added counterions (i.e., those released by the particles to the solution as they get charged), and the realistic chemistry of the aqueous solution on such electrokinetic phenomena as electrophoresis and electrical conductivity. These assumptions, while having been accepted for dilute conditions (volume fractions of solids well below 1%, say), are now questioned when dealing with concentrated suspensions. In this work, we present a general electrokinetic cell model for such kind of systems, including the mentioned effects, and we also carry out a comparative study with the standard treatment (the standard solution only contains the ions that one purposely adds, without ionic contributions from particle charging or water chemistry). We also consider an intermediate model that neglects the realistic aqueous chemistry of the solution but accounts for the correct contribution of the added counterions. The results show the limits of applicability of the classical assumptions and allow one to better understand the relative role of the added counterions and ions stemming from the electrolyte in a realistic aqueous solution, on electrokinetic properties. For example, at low salt concentrations the realistic effects of the aqueous solution are the dominant ones, while as salt concentration is increased, it is this that progressively takes the control of the electrokinetic response for low to moderate volume fractions. As expected, if the solids concentration is high enough the added counterions will play the dominant role (more important the higher the particle surface charge), no matter the salt concentration if it is not too high. We hope this work can help in setting up the real limits of applicability of the standard cell model for concentrated suspensions by a quantitative analysis of the different effects that have been classically disregarded, showing that in many cases they can be determinant to get rigorous predictions.

DC electrophoresis and viscosity of realistic salt-free concentrated suspensions: non-equilibrium dissociation-association processes.

Most of the suspensions usually found in industrial applications are concentrated, aqueous and in contact with the atmospheric CO2. The case of suspensions with a high concentration of added salt is relatively well understood and has been considered in many studies. In this work we are concerned with the case of concentrated suspensions that have no ions different than: (1) those stemming from the charged colloidal particles (the added counterions, that counterbalance their surface charge); (2) the H(+) and OH(-) ions from water dissociation, and (3) the ions generated by the atmospheric CO2 contamination. We call this kind of systems "realistic salt-free suspensions". We show some theoretical results about the electrophoretic mobility of a colloidal particle and the electroviscous effect of realistic salt-free concentrated suspensions. The theoretical framework is based on a cell model that accounts for particle-particle interactions in concentrated suspensions, which has been successfully applied to many different phenomena in concentrated suspensions. On the other hand, the water dissociation and CO2 contamination can be described following two different levels of approximation: (a) by local equilibrium mass-action equations, because it is supposed that the reactions are so fast that chemical equilibrium is attained everywhere in the suspension, or (b) by non-equilibrium dissociation-association kinetic equations, because it is considered that some reactions are not rapid enough to ensure local chemical equilibrium. Both approaches give rise to different results in the range from dilute to semidilute suspensions, causing possible discrepancies when comparing standard theories and experiments concerning transport properties of realistic salt-free suspensions.

Effects of non-equilibrium association-dissociation processes in the dynamic electrophoretic mobility and dielectric response of realistic salt-free concentrated suspensions.

Electrokinetic investigations in nanoparticle suspensions in aqueous media are most often performed assuming that the liquid medium is a strong electrolyte solution with specified concentration. The role of the ions produced by the process of charging the surfaces of the particles is often neglected or, at most, the concentrations of such ions are estimated in some way and added to the concentrations of the ions in the externally prepared solution. The situation here considered is quite different: no electrolyte is dissolved in the medium, and ideally only the counterions stemming from the particle charging are assumed to be in solution. This is the case of so-called salt-free systems. With the aim of making a model for such kind of dispersions as close to real situations as possible, it was previously found to consider the unavoidable presence of H(+) and OH(-) coming from water dissociation, as well as the (almost unavoidable) ions stemming from the dissolution of atmospheric CO2. In this work, we extend such approach by considering that the chemical reactions involved in dissociation and recombination of the (weak) electrolytes in solution must not necessarily be in equilibrium conditions (equal rates of forward and backward reactions). To that aim, we calculate the frequency spectra of the electric permittivity and dynamic electrophoretic mobility of salt-free suspensions considering realistic non-equilibrium conditions, using literature values for the rate constants of the reactions. Four species are linked by such reactions, namely H(+) (from water, from the--assumed acidic--groups on the particle surfaces, and from CO2 dissolution), OH(-) (from water), HCO3(-) and H2CO3 (again from CO2). A cell model is used for the calculations, which are extended to arbitrary values of the surface charge, the particle size, and particle volume fraction, in a wide range of the field frequency ω. Both approaches predict a high frequency relaxation of the counterion condensated layer and a Maxwell-Wagner-O'Konski electric double layer relaxation at intermediate frequencies. Also, in both cases an inertial decay of the electrophoretic mobility at high ω takes place. The most significant difference between the present model and previous results based on the equilibrium hypothesis is by no means negligible: only in non-equilibrium conditions do we find a low-frequency relaxation (mostly noticed in permittivity data, while its significance is lower in dynamic mobility spectra). This new relaxation presents all the characteristic features of the concentration polarization (or alpha) dispersion. These are: i) the average electric polarization of the system increases when the relaxation frequency is surpassed, contrary to the behavior after Maxwell-Wagner type relaxations; ii) the amplitude of the relaxation increases with surface charge, reaching a sort of saturation if the charge is too high; iii) the relaxation frequency increases with volume fraction while the relaxation amplitude decreases; iv) the characteristic frequency is reduced by the increase in particle radius. All these facts confirm that the non-equilibrium approach seems to better describe the physics of the system by giving rise to a concentration polarization kind of relaxation, only possible when ions can accumulate on both sides of the particles as dictated by the field, and not as determined by equilibrium conditions in the dissociation-recombination reactions involved.

Dielectric spectroscopy of concentrated colloidal suspensions.

A comparison between experimental measurements and theoretical calculations of the permittivity and conductivity of concentrated colloidal suspensions is presented. Dielectric spectroscopy measurements for 100nm and 200nm diameter polystyrene spheres at volume fractions between ϕ=0.01-0.18 and electrolyte concentrations 0.01-1mM KCl (P.J. Beltramo, E.M. Furst, Langmuir 28 (2012) 10703-10712) are compared to cell-model calculations that account for the hydrodynamic and electrokinetic interactions between particles (F. Carrique, F.J. Arroyo, M.L. Jimenez, A.V. Delgado, J. Chem. Phys. 118 (2003) 1945-1956). Under most conditions, there is good agreement between experiment and theory. At low ionic strengths, the dielectric increment exhibits a low-frequency plateau in the experimental spectroscopy and cell model calculations. However, at the highest ionic strengths, the cell model predicts a low frequency plateau that is not observed experimentally. The conductivity increments qualitatively agree over all volume fractions, ionic strengths and frequencies.

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields.

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O'Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects.

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.

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.

Ion size effects on the electric double layer of a spherical particle in a realistic salt-free concentrated suspension.

A new modified Poisson-Boltzmann equation accounting for the finite size of the ions valid for realistic salt-free concentrated suspensions has been derived, extending the formalism developed for pure salt-free suspensions [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] to real experimental conditions. These realistic suspensions include water dissociation ions and those generated by atmospheric carbon dioxide contamination, in addition to the added counterions released by the particles to the solution. The electric potential at the particle surface will be calculated for different ion sizes and compared with classical Poisson-Boltzmann predictions for point-like ions, as a function of particle charge and volume fraction. The realistic predictions turn out to be essential to achieve a closer picture of real salt-free suspensions, and even more important when ionic size effects are incorporated to the electric double layer description. We think that both corrections have to be taken into account when developing new realistic electrokinetic models, and surely will help in the comparison with experiments for low-salt or realistic salt-free systems.

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.

Dynamic electrophoretic mobility of spherical colloidal particles in realistic aqueous salt-free concentrated suspensions.

In this contribution, the dynamic (or alternating current (AC)) electrophoretic mobility of spherical colloidal particles in a realistic salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Such a suspension is a concentrated one (in charged solid particles) in an aqueous solution without any electrolyte added during the preparation. The ionic species in solution can solely be: (i) the "added counterions" stemming from the particles (for example, by ionization of particle surface ionizable groups), (ii) the H(+) and OH(-) ions from water dissociation, and (iii) the ions produced by the atmospheric CO(2) contamination. The corrections related to water dissociation and CO(2) contamination in suspensions open to the atmosphere have turned out to be tremendous in many of the experimental situations of interest in direct current (DC) electric fields. Thus, it is mandatory to explore their influence in the more complex situation of AC electrophoresis. The results confirm the importance of ions produced by water dissociation and those originated by the acidification of the aqueous solution in suspensions contaminated with atmospheric CO(2), for low to moderate particle volume fractions, where the role of the added counterions is screened by the other ionic species. It is worth mentioning that, for high particle charges, two Maxwell-Wagner processes develop in the mobility frequency spectrum, respectively linked to the diffuse layer relaxation and to the relaxation of a condensed layer of counterions located very close to the particle surface. This is the so-called ionic condensation effect for highly charged particles, already described in the literature, and which for the first time will be studied in detail in realistic salt-free systems. The dynamic electrophoretic mobility will be numerically computed throughout a wide frequency range and compared with the cases of pure and realistic salt-free conditions. In addition, the competition between different relaxation processes associated to the complex electric dipole moment induced on the particles by the field, the particle inertia, as well as their influence on the dynamic response, will be explored for pure and realistic cases.

Electroviscous effect of concentrated suspensions in salt-free media: water dissociation and CO2 influence.

The electroviscous effect of realistic salt-free colloidal suspensions is analyzed theoretically. We study the influence on the electroviscous coefficient of the surface charge density and the particle volume fraction. By realistic salt-free colloidal suspensions we mean aqueous suspensions which have been deionized as far as possible without any electrolyte added during the preparation, in which the only ions present can be (i) the so-called added counterions, coming from the ionization of surface groups and thus counterbalancing the surface charge, (ii) the H(+) and OH(-) ions from water dissociation, and (iii) the ions produced by the atmospheric CO(2) contamination. Our model is elaborated in the framework of a classical mean-field theory, using the spherical cell model approach and the appropriate local equilibrium reactions. It is valid for arbitrary surface charge density and particle concentrations. We have also made a new interpretation of the electroviscous coefficient: the electroviscous coefficient p of the suspension is the ratio between the electrohydrodynamic and the pure hydrodynamic contributions to the specific viscosity of the suspension. The numerical results show that it is necessary to consider the water dissociation influence for volume fractions lower than approximately 10(-3), whereas the atmospheric contamination, if the suspensions are open to the atmosphere, is important in the region of volume fractions φ<0.03.

Role of surface conductivity in the dynamic mobility of concentrated suspensions.

In this article, a cell model is used for the evaluation of the alternating current (ac) mobility (dynamic mobility) of spherical particles in suspensions of arbitrary volume fractions of solids. The main subject is the consideration of the role of the electrical conductivity (SLC or K(sigmai)) of the stagnant layer (SL) on the mobility. It is assumed that the total surface conductivity (K(sigma)), resulting from both K(sigmai) and the diffuse layer conductivity (K(sigmad)), is constant in the cases considered and that it is the K(sigmai)-K(sigmad) balance that determines the SL effects. We first explore the effect of K(sigmai) on the frequency dependence of the dynamic mobility. It is found that the mobility decreases on average, for any frequency, when K(sigmai) increases. This is a consequence of stagnancy: ions in the SL, although contributing to the surface conductivity, do not drag liquid with them when they migrate and do not contribute to electro-osmotic flow or, equivalently, to electrophoresis. Three relaxations are observed in the mobility-frequency spectrum: inertial (the particle and liquid motions are hindered), Maxwell-Wagner-O'Konski (ions in the double layer cannot follow the field oscillations and can move only over a distance much smaller that the diffuse layer thickness), and the so-called alpha or concentration polarization process (the ions can rearrange around the particle, but they cannot form the electrolyte concentration field that appears at low frequency). Whereas the first two relaxations are little affected by K(sigmai), the alpha process undergoes significant changes. Thus, the mobility increases with frequency around the alpha relaxation region if K(sigmai) is negligible, but it decreases with frequency in the same interval if K(sigmai) is finite. With the aim of explaining this behavior, we calculate the capillary osmosis velocity field that is the fluid flow provoked by the concentration gradient around the particle. The calculations presented demonstrate that the velocity is reduced (for each frequency and position) when the SLC is raised. It is proposed that such a decrease adds to that due to the changes in the induced dipole moment of the particle, also favoring a decrease in the mobility. These tendencies are also present when the volume fraction of solids, phi, is modified, although higher phi values somewhat hide the effect of K(sigmai), as in fact observed with all features of electrokinetics associated with the phenomenon of concentration polarization.

Electrical conductivity of aqueous salt-free concentrated suspensions. Effects of water dissociation and CO2 contamination.

In this paper we explore the effects of water dissociation and CO2 contamination on the electrical conductivity of salt-free concentrated suspensions in static electric fields. The conductivity model here presented is based on a new description of the equilibrium double layer for particles in "realistic" salt-free suspensions recently developed by the authors to account for the latter effects (Ruiz-Reina, E.; Carrique, F. J. Phys. Chem. B 2008, 112, 11960). It was shown that in most of the cases the neglecting of those effects would lead to a very poor description of common salt-free suspensions, especially, but not only, if the suspensions have been in contact with air. As shown in this paper, the presence of only water dissociation ions suffices to provoke very important changes in the standard salt-free predictions. A realistic aqueous salt-free suspension consists of an aqueous suspension without any electrolyte added during the preparation but including the following ionic species: (i) the "added counterions" stemming from the particle charging process that counterbalance their surface charge (with just this ionic species, the suspension can be considered as an ideal or pure salt-free one), (ii) the H+ and OH- ions from water dissociation, and (iii) the ions produced by the atmospheric CO2 contamination. The model is based on the classical Poisson-Boltzmann theory, the appropriate local chemical reactions, the standard electrokinetic equations, and the cell model approximation to account for electro-hydrodynamic particle-particle interactions. Thus, we have studied the electrical conductivity of such realistic salt-free suspensions for different particle volume fraction phi and surface charge density sigma, and compared it with results of pure salt-free conductivity predictions. The numerical results have shown that water dissociation ions and/or CO2 contamination has an extreme influence on the suspension conductivity values at low-moderate particle volume fractions. In these situations the role of the added counterions is screened by the other ionic species. Even if the suspensions have not been exposed to the atmosphere, the quantitative changes in conductivity at low volume fractions associated with the presence of water dissociation ions over the added counterions are enormous. It is concluded that it is necessary to take into account the water dissociation influence for phi lower than approximately 10(-2)-10(-3), whereas the atmospheric CO2 contamination is not negligible if phi<10(-1)-10(-2), depending on the particle charge. The present work sets the basis for further theoretical models concerning, particularly, the dynamic electrophoresis and dielectric response of such systems.

Effects of water dissociation and CO2 contamination on the electrophoretic mobility of a spherical particle in aqueous salt-free concentrated suspensions.

In a very recent paper ( Ruiz-Reina , E. ; Carrique , F. J. Phys. Chem. B 2008 , 112 , 11960. ) we studied the effect of water dissociation and CO(2) contamination on the equilibrium electrical double layer of spherical particles in salt-free concentrated suspensions in aqueous solutions. It was shown that in most cases (dilute to moderately concentrated suspensions), the neglecting of those effects would lead to a very poor description of common salt-free suspensions, especially if the suspensions have been in contact with air. In the present contribution we explore the influence of the latter effects on the dc electrophoresis in realistic salt-free suspensions. This kind of system consists of aqueous suspensions without any electrolyte added during the preparation. The ionic species in solution can solely be (i) the "added counterions" stemming from the particles that counterbalance their surface charge, (ii) the H(+) and OH(-) ions from water dissociation, and (iii) the ions produced by the atmospheric CO(2) contamination. Our model follows the classical Poisson-Boltzmann approach, a spherical cell model and the appropriate local chemical reactions. We have applied it to the study of the electrophoretic mobility of a spherical particle for different particle volume fractions varphi and surface charge densities. The numerical results have shown the quite large influence that water dissociation ions and/or CO(2) contamination have on the electrophoretic mobility at low-moderate particle volume fractions. In those situations the role of the added counterions is screened by the other ionic species. These effects yield the mobility to reach plateau values instead of further increasing as volume fraction decreases. It is concluded that it is necessary to take into account the water dissociation influence for varphi lower than approximately 10(-2), whereas the atmospheric contamination, if the suspensions have been exposed to the atmosphere, is not negligible if varphi < 10(-1). The present work sets the basis for further theoretical models concerning particularly the ac electrokinetics and dielectric response of such systems.

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 Poisson's 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.

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.

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.