Emilio Ruiz-Reina

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

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

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

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.

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.

The primary electroviscous effect of polystyrene latexes

Abstract An investigation on the primary electroviscous effect of polystyrene latexes has been made. Capillary viscometers of Ubbelohde type have been used. The comparison of the results obtained with the theories allow us to conclude that the effect is underestimated for low electrolyte concentrations. We suggest that this underestimation is due to an additional surface conductance into the electric double layer. This interpretation is consistent with previous studies on electrophoretic mobility of the same system.

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.

An experimental study on the influence of a dynamic Stern-layer on the primary electroviscous effect

Abstract The most recent theory by Watterson and White for the primary electroviscous effect of a suspension of charged spherical particles has been extended by considering the influence of a dynamic Stern-layer. In this work we have tested the theoretical results by measuring the viscosity of polystyrene suspensions in different electrolyte concentrations. Zeta potential values have been obtained by electrophoresis and conductivity experiments using the theoretical approachs by Mangelsdorf and White that include the Stern-layer conductance. In order to obtain the same potential values calculated from these two independent methods, we have fitted the Stern-layer parameters of our systems. These parameters and zeta values have been used to calculate the theoretical viscosity. The theoretical results have been compared with the experimental viscosity data obtained with a semiauthomatic Ubbelohde capillary viscometer. We can conclude that the dynamic Stern-layer model used in this work has only a slight influence on the correction of the primary electroviscous effect theory due to Watterson and White. We suggest to study the correction supplied by another dynamic Stern-layer model due to Dukhin and Semenikhin, considering its success when is applied to electrophoresis.

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.

The additional surface conductance: its role in the primary electroviscous effect

The influence of the additional surface conductance on the primary electroviscous effect has been checked by means of an experimental study. Polystyrene latexes and alumina suspensions have been used as the colloidal systems. Combined electrokinetic techniques have been used to determine -potential and Stern parameters of the systems. The results suggest that this conductance mechanism, that takes place into the Stern layer, has a great influence on the primary electroviscous effect.

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.

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.