Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects.

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Electrokinetic detection of the salt-free condition in colloids. Application to polystyrene latexes.

Because of their singular phenomenology, the so-called salt-free colloids constitute a special family of dispersed systems. Their main characteristic is that the dispersion medium ideally contains only the solvent and the ions compensating exactly the surface charge of the particles. These ions (often called released counterions) come into the solution when the surface groups responsible for the particles charge get ionized. An increasing effort is nowadays dedicated to rigorously compare theoretical model predictions for ideal salt-free suspensions, where only the released counterions are supposed to be present in solution, with appropriately devised experiments dealing with colloids as close as possible to the ideal salt-free ones. Of course, if the supporting solution is aqueous, the presence of atmospheric contamination and any other charged species different from the released counterions in the solution must be avoided. Because this is not an easy task, the presence of dissolved atmospheric CO2 and of H+ and OH- from water dissociation cannot be fully discarded in aqueous salt-free solutions (often denominated realistic in such case). Ultimately, at some point, the role of the released counterions will be comparable or even larger in highly charged concentrated colloids than that of added salts. These topics are covered in the present contribution. The model results are compared with experimental data on the dynamic mobility and dielectric dispersion of polystyrene spheres of various charges and sizes. As a rule, it is found that the model correctly predicts the significance of alpha and Maxwell-Wagner-O'Konski relaxations. Positions and amplitudes of such relaxations are well predicted, although it is necessary to assume that the released counterions are potassium or sodium instead of protons, otherwise the frequency spectra of experimental mobility and permittivity differ very significantly from those theoretically calculated. The proposed electrokinetic evaluation is an ideal tool for detecting in situ the possible contamination (or incomplete ion exchange of the latexes). A satisfactory agreement is found when potassium counterions are assumed to be in solution, mostly if one considers that the comparison is carried out without using any adjustable parameters.

Multiionic effects on the capacitance of porous electrodes.

The rapid and reversible ionic electrosorption in the electrical double layers (EDLs) of moderately charged micropores in contact with a solution is the main concept underlying capacitive energy and desalination devices. For the usual operating conditions, the ion concentration is large enough for the confinement of ions to play an important role in their distribution in the EDL. On the other hand, although most laboratory experiments have been carried out with simple salt solutions, realistic applications require a proper analysis of the effect of the different ionic species existing in natural waters. Here we focus on the role of multiionic solutions on the double layer structure. For this purpose, a model is presented in which the EDL overlap and the existence of a Stern layer are considered. It is also taken into account that the ions can be tightly packed by using the Carnahan-Starling model. This model is applied to analyze the structure of the EDL with multiionic solutions containing divalent ions. The predictions of this model are found to largely differ from those of the better known Bikerman equation, and are more realistic. It is demonstrated that the presence of tiny amounts of divalent ions in the bulk is enough to dominate the EDL behavior, and hence, its capacitance, energy storage, and desalination properties.

Dynamic electrophoretic mobility and electric permittivity of concentrated suspensions of plate-like gibbsite particles.

In this paper we present experimental results on the electrokinetic behavior of planar gibbsite particles in concentrated suspensions. The dc electrophoretic mobility measurements are in this case of little significance, as they are scarcely informative. In the present investigation, we show that the dielectric dispersion and dynamic electrophoresis can in contrast provide such information. The complicating factors are of course the non-spherical shape and the finite particle concentration, as no complete theory of these phenomena exists for such systems. We propose to use first of all a model of dynamic electrophoresis of spheroids in which the effect of volume fraction is considered by means of an approximate theory previously obtained for spheres, based on the evaluation of electrical and hydrodynamic interactions between particles. In addition, the role of volume fraction on the high frequency inertial relaxation is also ascertained and used to obtain a volume fraction-independent radius of the gibbsite spheroids. A similar approach is used for the evaluation of dielectric dispersion data. Both the dynamic mobility and dielectric constant dependencies on frequency were obtained for gibbsite suspensions of different volume fractions in 0.5mMKCl. The theoretical treatments elaborated were applied to these data, and a coherent picture of the geometrical and electrical characteristics of the particles was obtained.

Iron/Magnetite Nanoparticles as Magnetic Delivery Systems for Antitumor Drugs.

In this study we investigate on the possible use of a new kind of magnetic nanostructures as drug delivery systems for anticancer drugs. The starting particles are formed by an inner core of iron, coated by magnetite as a stabilizing, magnetic layer. These units are further coated by a poly(ethylenglycol) (PEG) layer to make them less prone to the attack by macrophages and to favour longer stays in the blood stream. The resulting particles consist of several magnetic cores encapsulated by a polymer layer around 5 nm thick. The crystal structure of the designed nanostructures, as determined by X-ray powder diffraction, is compatible with a crystalline magnetite component, whereas the magnetization hysteresis data indicate a superparamagnetic behavior. Both the initial susceptibility and the saturation magnetization are lower than for the bare magnetic cores, but still significant. Drug adsorption and release tests were performed on two anticancer drugs, namely 5-fluorouracil and doxorubicin. Both are found to adsorb on the particles, but only the latter appears to be released at a reasonable rate, which is found to be very slow for 5-fluorouracil.

Multi-ionic effects on energy production based on double layer expansion by salinity exchange.

It has been recently shown that the free energy change upon salinity mixing in river mouths can be harvested taking advantage of the fact that the capacitance of charged solid/liquid interfaces (electrical double layers, EDLs) depends strongly on the ionic composition of the liquid medium. This has led to a new generation of techniques called Capmix technologies, one of them (CDLE or capacitive energy extraction based on DL expansion) based precisely on such dependence. Despite the solution composition playing a crucial role on the whole process, most of the research carried out so far has mainly focused on pure sodium chloride solutions. However, the effect of other species usually present in river and seawaters should be considered both theoretically and experimentally in order to succeed in optimizing a future device. In this paper, we analyse solutions of a more realistic composition from two points of view. Firstly, we find both experimentally and theoretically that the presence of ions other than sodium and chloride, even at low concentrations, may lead to a lower energy extraction in the process. Secondly, we experimentally consider the possible effects of other materials usually dispersed in natural water (mineral particles, microbes, shells, pollutants) by checking their accumulation in the carbon films used, after being exposed for a long period to natural sea water during CDLE cycles.

Modification of the surface of activated carbon electrodes for capacitive mixing energy extraction from salinity differences.

The "capacitive mixing" (CAPMIX) is one of the techniques aimed at the extraction of energy from the salinity difference between sea and rivers. It is based on the rise of the voltage between two electrodes, taking place when the salt concentration of the solution in which they are dipped is changed. We study the rise of the potential of activated carbon electrodes in NaCl solutions, as a function of their charging state. We evaluate the effect of the modification of the materials obtained by adsorption of charged molecules. We observe a displacement of the potential at which the potential rise vanishes, as predicted by the electric double layer theories. Moreover, we observe a saturation of the potential rise at high charging states, to a value that is nearly independent of the analyzed material. This saturation represents the most relevant element that determines the performances of the CAPMIX cell under study; we attribute it to a kinetic effect.

Polyelectrolyte-coated carbons used in the generation of blue energy from salinity differences.

In this work we present a method for the production of clean, renewable electrical energy from the exchange of solutions with different salinities. Activated carbon films are coated with negatively or positively charged polyelectrolytes using well-established adsorption methods. When two oppositely charged coated films are placed in contact with an ionic solution, the potential difference between them will be equal to the difference between their Donnan potentials, and hence, energy can be extracted by building an electrochemical cell with such electrodes. A model is elaborated on the operation of the cell, based on the electrokinetic theory of soft particles. All the features of the model are experimentally reproduced, although a small quantitative difference concerning the maximum open-circuit voltage is found, suggesting that the coating is the key point to improve the efficiency. In the experimental conditions used, we obtain a power of 12.1 mW m(-2). Overall, the method proves to be a fruitful and simple approach to salinity-gradient energy production.

Predictions of the maximum energy extracted from salinity exchange inside porous electrodes.

Capacitive energy extraction based on double layer expansion (CDLE) is the name of a new method devised for extracting energy from the exchange of fresh and salty water in porous electrodes. It is based on the change of the capacitance of electrical double layers (EDLs) at the electrode/solution interface when the concentration of the bulk electrolyte solution is modified. The use of porous electrodes provides huge amounts of surface area, but given the typically small pore size, the curvature of the interface and EDL overlap should affect the final result. This is the first aspect dealt with in this contribution: we envisage the electrode as a swarm of spherical particles, and from the knowledge of their EDL structure, we evaluate the stored charge, the differential capacitance and the extracted energy per CDLE cycle. In all cases, different pore radii and particle sizes and possible EDL overlap are taken into account. The second aspect is the consideration of finite ion size instead of the usual point-like ion model: given the size of the pores and the relatively high potentials that can be applied to the electrode, excluded volume effects can have a significant role. We find an extremely strong effect: the double layer capacitance is maximum for a certain value of the surface potential. This is a consequence of the limited ionic concentration at the particle-solution interface imposed by the finite size of ions, and leads to the presence of two potential ranges: for low electric potentials the capacitance increases with the ionic strength, while for large potentials we find the opposite trend. The consequences of these facts on the possibility of net energy extraction from porous electrodes, upon changing the solution in contact with them, are evaluated.

Adsorption of anionic and cationic surfactants on anionic colloids: supercharging and destabilization.

We present herein a study on the adsorption of anionic (SDS), cationic (CTAB), and nonionic (C(12)E(5)) surfactants onto anionic silica nanoparticles. The effects of this adsorption are studied by means of the static structure factor, S(q), and the collective diffusion coefficient, D(c), obtained from small-angle X-ray scattering and dynamic light scattering measurements, respectively. The effective charge on the particles was determined also from classical electrophoresis and electroacoustic sonic-amplitude measurements. The surface tension of the sample was also investigated. Of particular note is the adsorption of SDS onto the silica nanoparticles, which leads to supercharging of the interface. This has interesting repercussions for structures obtained by the layer-by-layer (LbL) technique, because emulsions stabilized with supercharged and hydrophobized silica are perfect candidates for use in a multilayer system.

Consideration of polydispersity in the evaluation of the dynamic mobility of concentrated suspensions.

Many practical uses of electroacoustic methods for the characterization of disperse systems involve concentrated and/or polydisperse suspensions. While the effects of particle concentration have been well described experimentally and theoretically, similar studies considering a wide size distribution of the dispersed particles are lacking. This is not a minor point, as these methods are based on the action of alternating fields (either electric or acoustic) on the systems and the characteristic frequencies and amplitudes are largely determined by the particle geometry. In this work, we first evaluate the effect, on the dynamic (or ac) mobility, of changing the size distribution in the suspension. It is found that the inertia (also called hydrodynamic) relaxation of the mobility is shifted toward lower frequencies, and that the overall mobility spectrum is smoothed when the size polydispersity of the suspension increases. The results theoretically obtained are subsequently used for fitting experimental mobility data corresponding to two alumina samples, in a wide range of particle concentrations and ionic strengths. It is demonstrated that a complete model accounting for polydispersity leads to a better description of the results; very significantly, this can be done by using the zeta potential as the only fitting parameter, and forcing this parameter to be determined only by the ionic strength, and not by the volume fraction.

Use of a cell model for the evaluation of the dynamic mobility of spherical silica suspensions.

In this paper we evaluate the validity of a cell model for the calculation of the dynamic mobility of concentrated suspensions of spheres. The key point is the consideration of the boundary conditions (electrical and hydrodynamic) at the boundary of the fluid cell surrounding a single probe particle. The model proposed is based on a universal criterion for the averages of fluid velocity, electric potential, pressure field or electrochemical properties in the cell. The calculations are checked against a wide set of experimental data on the dynamic mobility of silica suspensions with two different radii, several ionic strengths, and two particle concentrations. The comparison reveals an excellent agreement between theory and experiment, and the model appears to be extremely suitable for correctly predicting the behavior of the dynamic mobility, including the changes in the zeta potential, zeta, with ionic strength, the frequency and amplitude of the Maxwell-Wagner-O'Konski relaxation, and the inertial relaxation occurring at the top of the frequency range accessible to our experimental device.

Nonstationary electro-osmotic flow in closed cylindrical capillaries. Theory and experiment.

Both from the experimental and theoretical viewpoints it is of fundamental importance to know precisely which are the fluid flow characteristics in a (cylindrical, say) closed cell under the action of an externally applied electric field, parallel to the cell axis. This is so because in many cases the experimental determination of the electrophoretic mobility of dispersed particles is carried out in closed cells, whereby the motion of the particles in the laboratory reference system is the result of the superposition of their electrophoretic migration plus the liquid motion with respect to the cell. This makes it of utmost importance to analyze the above-mentioned fluid and particle movements. If, in particular, this evaluation is carried out in the presence of alternating fields of different frequencies, information about the dynamics and time scales of the processes involved can be obtained for different frequencies of the applied field. In the present contribution, we discuss experimental results based on the determination of the velocity of polystyrene latex particles in a closed, cylindrical electrophoresis cell, and compare them to our previous theoretical analysis of the problem. It is concluded that the theory explains with great accuracy the observed particle velocities. In addition to the use of the particles as probes for the fluid velocity distribution, this work intends to give additional clues on the frequencies and positions for which electrophoretic mobility measurements in closed cells can be more reliable.

Dynamic electrophoretic mobility of concentrated dispersions of spherical colloidal particles. On the consistent use of the cell model.

This paper outlines a complete and self-consistent cell model theory of the electrokinetics of dense spherical colloidal suspensions for general electrolyte composition, frequency of applied field, zeta potential, and particle size. The standard electrokinetic equations, first introduced for any given particle configuration, are made tractable to computation by averaging over particle configurations. The focus of this paper is on the systematic development of suitable boundary conditions at the outer cell boundary obtained from global constraints on the suspension. The approach is discussed in relation to previously published boundary conditions that have often been introduced in an ad hoc manner. Results of a robust numerical calculation of high-frequency colloidal transport properties, such as dynamic mobility, using the present model are presented and compared with some existing dense suspension models.

A simple model of the high-frequency dynamic mobility in concentrated suspensions.

Because electroacoustic techniques are gaining interest in many fields of colloid science, a number of theories dealing with the phenomenon of electrophoresis in high-frequency (on the order of the MHz) electric fields have been developed. In the present work we propose a straightforward derivation of a simple formula for the dynamic mobility of colloidal particles in mildly concentrated systems. Starting with a simple expression for the electrophoretic mobility in dilute suspensions, given as a function of the zeta potential and of the dipole coefficient, we introduce successive corrections related to: (i) the back flow of fluid induced by the electrophoretic motion of the particles; (ii) the electrostatic interactions among particles; (iii) the difference between the macroscopic and the external electric fields; (iv) the difference between the zero-momentum and the laboratory reference frames. Considering furthermore that the frequency dependence of the dipole coefficient is due to the Maxwell-Wagner-O'Konski double-layer relaxation, we obtain a mobility expression that compares well with other (semi)analytical models and (in proper conditions) with numerical cell-model calculations. However, its main merit is that it allows to understand, to a large extent, the physical origin of the frequency and volume fraction dependences of the dynamic mobility.