Salt-free Concentrated Suspensions Research Articles

An electric double layer of colloidal particles in salt-free concentrated suspensions including non-uniform size effects and orientational ordering of water dipoles.

The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can predict the phenomena like a heavy decrease in relative permittivity of the suspension and counterion stratification near highly charged colloidal particles. In this work we numerically obtain the electric potential, the counterion concentration and the relative permittivity around a charged particle in a concentrated salt-free suspension corrected by non-uniform size effects and orientational ordering of water dipoles. The results show the worth of such corrections for medium to high particle charges at every particle volume fraction. We conclude that non-uniform size effects and orientational ordering of water dipoles are necessary for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions.

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.

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.

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.

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.

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.

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.

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.

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.