Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid.

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García et al. [Phys. Rev. Fluids 4, 103702 (2019)10.1103/PhysRevFluids.4.103702] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the dc electrophoretic mobility and dc electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite-ion-size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration leads to a decrease of the magnitude of the previous electrokinetic results. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free 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.

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.

Effect of recombinant growth hormone on leptin, adiponectin, resistin, interleukin-6, tumor necrosis factor-α and ghrelin levels in growth hormone-deficient children.

BACKGROUND: Treatment with GH promotes linear growth and decreases body fat in patients with isolated GH deficiency (GHD). However, few studies have analyzed how GH replacement modifies ghrelin levels and the adipokine profile and the relationship of these modifications with the metabolic changes. AIMS: To analyze the eventual differences between serum levels of leptin, leptin soluble receptor (sOBR), resistin, adiponectin, interleukin-6 (IL-6), tumor necrosis factor-α (TNF-α), total (TG) and acylated ghrelin (AG) and lipid and glycemic profiles in children with GHD, as well as to determine the effect of GH replacement on these parameters during the first year of therapy. SUBJECTS AND METHODS: Thirty pre-pubertal (Tanner stage I) GHD children and 30 matched controls were enrolled. Children with GHD were studied before and after 6 and 12 months of GH treatment. Weight, height, BMI, fasting glucose, insulin, lipid profile and serum levels of adipokines and ghrelin were studied at every visit. Adi - pokines, insulin and ghrelin levels were determined by using commercial radio- and enzymoimmunoassays. RESULTS: At baseline children with GHD had significantly higher sOBR (p<0.01) and adiponectin (p<0.01) levels than controls. Treatment with GH resulted in a decline in leptin (p<0.05) and TG (p<0.001) levels, an increase of homeostasis model assessment index and restored IGF-I levels (p<0.001). CONCLUSIONS: These data indicate that GH replacement has a negative effect on leptin levels and may also produce a slight unfavorable effect on carbohydrate metabolism. In addition, the changes observed in the adipokine profile appear to be independent of body mass index.

Negative electrorheological behavior in suspensions of inorganic particles.

An investigation is described on the electric-field-induced structures in colloidal dispersions. Both rheological determinations and direct microscopic observations are used with that aim. The starting point of this study is the so-called electrorheological (ER) effect, consisting of the mechanical reinforcing of a fluid or suspension due to formation of chains of molecules or particles after being polarized by the action of the field. One macroscopic manifestation of this phenomenon is the transformation of the fluid from a typically Newtonian behavior to a viscoelastic material, with finite yield stress and high elastic modulus. The systems investigated were suspensions of elongated goethite (ß-FeOOH) particles in silicone oils with varying amounts of silica nanoparticles. The results showed the rather unusual behavior known as "negative ER effect", which can be best described by saying that the application of an electric field reduces the yield stress and the elastic modulus, that is, produces destruction of structures rather than their build up. The negative behavior is also found for suspensions of other inorganic powders, including hematite and quartz. On the contrary, the usual positive ER response is found for suspensions of cellulose and montmorillonite clay. The same happens if goethite suspensions are prepared in high volume fractions, high-viscosity fluids, or both. All of the results found are compatible with the so-called interfacial model of electrorheology: the reduction of the yield stress of goethite suspensions when the applied field is high enough is the consequence of particle migration toward the electrodes because of charge injection and subsequent electrophoresis. The migration leaves the gap between the electrodes devoid of particles and explains the decrease in yield stress. The addition of silica nanoparticles contributes to reduce the strength of this effect by hindering the charging and making it necessary to increase the field strength to observe the negative effect. The model appears to also be applicable to cellulose, although the positive response found for such particles is explained by their large size: larger diameters bring about larger attraction forces between particles, leading to a tendency to produce strong aggregates. This is likely to occur in suspensions of colloids which, because of their relatively high electrical conductivity, tend to acquire charge even in such nonpolar liquids as silicone oils.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields.

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

Surface conductivity of colloidal particles: experimental assessment of its contributions.

In this work we investigate how combined data on dielectric dispersion and electrophoretic mobility of colloidal suspensions at different temperatures can be used to evaluate the two main quantities characterizing the solid/liquid interface, namely, the zeta potential and the stagnant layer conductivity (SLC). This is possible because the electric permittivity depends on the total surface conductivity, while the electrophoretic mobility is governed by both the zeta potential and that conductivity. Based on a simple analytical theory, we can also estimate the diffusion coefficient of counterions in the stagnant layer, D(SL), for each temperature. The results lead to a good agreement between theory and experiment, although with somewhat high values of D(SL). With the aim of improving this description, we use a full theory of the electric permittivity of suspensions that accounts for the existence both of SLC and of a finite volume fraction of solids. An excellent description of the whole dielectric spectrum and of the electrophoretic mobility is possible in this case, although with still overestimated diffusion coefficients. This fact is discussed, and the importance of considering particle concentration effects even for suspensions that are often considered dilute is also stressed.

Electrokinetics in extremely bimodal suspensions.

Prompted by the results obtained by Mantegazza et al. [Nature Physics 1 (2005) 103], where the electric birefringence of suspensions of elongated particles was strikingly affected by the presence of a sea of very small (size ratio lower than 10:1) colloidal spheres, we have undertaken an investigation of other electrokinetic phenomena in suspensions containing various relative concentrations of large (Teflon or polystyrene latex) and small (nanometer-sized silica spheres) colloids. We have determined the quantities that might be greatly affected by the size distribution of the particles, mainly in the presence of ac electric fields, since the response of the suspensions will show very characteristic relaxations, dominated in principle by the size of the particles. In this work, we report on measurements of the dielectric dispersion of mixed particles as a function of the concentration, ionic strength, and field frequency. The results indicate that the response is not just a simple combination of those obtained with suspensions of the individual particles, and in fact the presence of even small amounts of the small particles affects considerably the frequency response of the suspensions.

Influence of cell-model boundary conditions on the conductivity and electrophoretic mobility of concentrated suspensions.

In the last few years, different theoretical models and analytical approximations have been developed addressing the problem of the electrical conductivity of a concentrated colloidal suspension. Most of them are based on the cell model concept, and coincide in using Kuwabara's hydrodynamic boundary conditions, but there are different possible approaches to the electrostatic boundary conditions. We will call them Levine-Neale's (LN, they are Neumann type, that is they specify the gradient of the electrical potential at the boundary), and Shilov-Zharkikh's (SZ, Dirichlet type). The important point in our paper is that we show by direct numerical calculation that both approaches lead to identical evaluations of the conductivity of the suspensions if each of them is associated to its corresponding evaluation of the macroscopic electric field. The same agreement between the two calculations is reached for the case of electrophoretic mobility. Interestingly, there is no way to reach such identity if two possible choices are considered for the boundary conditions imposed to the field-induced perturbations in ionic concentrations on the cell boundary (r = b), deltan(i) (r = b). It is demonstrated that the conditions deltan(i)(b) = 0 lead to consistently larger conductivities and mobilities. A qualitative explanation is offered to this fact, based on the plausibility of counter-ion diffusion fluxes favoring both the electrical conduction and the motion of the particles.

Determination of stagnant layer conductivity in polystyrene suspensions: temperature effects.

In the classical theory of electrokinetic phenomena, it is admitted that the whole electrokinetic behavior of any colloidal system is fully determined by the zeta potential, zeta, of the interface. However, both experimental data and theoretical models have shown that this is an incomplete picture, as ions in the stagnant layer (the region between the solid surface and the slip plane--the plane where the equilibrium potential equals zeta) may respond to the field. In this paper, we aim at the evaluation of this contribution by the estimation of both K(SL)(sigma) (the surface conductivity of the stagnant layer) and K(d)(sigma) (the conductivity associated with the diffuse layer). This will be done by measuring the high-frequency dielectric dispersion (HFDD) in polystyrene suspensions; here "high-frequency" means the frequency interval where Maxwell-Wagner-O'Konski relaxation takes place (typically at MHz frequencies). Prior to any conclusions, a treatment of electrode polarization effects in the measurements was needed: we used two methods, and both led to similar results. Simulating the existence of surface conductivity by bulk conductivity, we reached the conclusion that no consistent explanation can be given for our HFDD and additional electrophoresis data based on the existence of diffuse-layer conductivity alone. We thus show how K(SL)(sigma) can be estimated and demonstrate that it can be explained by an ionic mobility very close to that characteristic of ions in the bulk solution. Such mobility, and hence also the values of K(SL)(sigma), increases with temperature as expected on simple physical grounds.

Analysis of the dielectric permittivity of suspensions by means of the logarithmic derivative of its real part.

Measurement of the dielectric permittivity of colloidal suspensions in the kilohertz frequency range (the so-called low-frequency dielectric dispersion) is a promising tool for the electrokinetic characterization of colloids. However, this technique is less used than would be desirable because of the difficulties associated with the measurements, the most important of which is the electrode polarization (EP). Recently (M. Wübbenhorst and J. Van Turnhout, Dielectrics Newsl. November (2000)) a method was proposed that appears capable of separating the unwanted electrode effects from the double-layer relaxation that we are interested in. The method, based on the logarithmic derivative of raw epsilon'(omega) data (epsilon'(omega) is the real part of the permittivity of the suspension for a frequency omega of the applied AC field), is first checked against the well-known theory of the AC permittivity of colloidal suspensions developed by DeLacey and White (E. H. B. DeLacey and L. R. White, J. Chem. Soc. Faraday Trans. 277, 2007 (1981)). We show that the derivative epsilon''(D)(omega)=-(pi/2)(partial differential epsilon'/partial differential ln omega) gives an excellent representation of the true imaginary part of the permittivity, epsilon''(omega). The technique is then applied to experimental data of the dielectric constant of polystyrene and ethylcellulose suspensions. We found that epsilon''(D) displays two separated behaviors when plotted against log omega in the frequency range 100 Hz-1 MHz: a monotonous decrease (associated with EP) followed by an absorption peak (associated with the double-layer relaxation, or alpha-relaxation). Interestingly, they are separated enough to make it possible to easily find the characteristic frequency of the alpha-relaxation. Fitting a relaxation function to epsilon''(D)(omega) after eliminating the part due to EP, we could calculate the real part epsilon'(omega) and compare it to the DeLacey and White (DW) theoretical predictions. A significantly better agreement between DW calculations and experimental epsilon'(omega) data is obtained when the logarithmic derivative method is used, as compared to the classical electrode-separation techniques.

Dielectric relaxation in concentrated nonaqueous colloidal suspensions.

In this work we report on the permittivity of suspensions of elongated goethite particles in silicone oils of different viscosities. In spite of the low conductivity of the systems, the electrode polarization is significant. To correct this phenomenon, the procedure chosen is the one called logarithmic derivative of the real part of the permittivity, and it proves to efficiently reduce the effect of electrodes to the extent that the spectra of pure liquids are flat in the accessible frequency range (20 Hz-1 MHz). In our suspensions, we observe the presence of a dielectric relaxation for frequencies in the range 4-40 kHz. In principle, such relaxations might be ascribed to the Maxwell-Wagner (MW) polarization. However, it is found that both the characteristic frequency and the relaxation amplitude of the suspensions increase with volume fraction, something unexpected for an MW relaxation. Such discrepancy can be explained by considering the Frenkel-Trukhan model, which reproduces the Maxwell-Wagner results in conditions of thin electrical double layers (which it is not our case). An excellent agreement is found between our data and the model predictions, using only the particle surface charge as a parameter.

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.

Electrokinetic characterization of magnetite nanoparticles functionalized with amino acids.

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

Effect of stagnant-layer conductivity on the electric permittivity of concentrated colloidal suspensions.

A long-lasting experience in the electrokinetics of suspensions has shown that the so-called standard model may be partly in error in explaining experimental data. In this model, the stagnant layer is considered nonconducting (Ksigmai=0), and only the diffuse layer contributes to the total surface conductivity (Ksigma=Ksigmad). In the present work, the authors analyze the consequences of assuming a nonzero stagnant layer conductivity on the permittivity of concentrated suspensions. Using a cell model to account for the particle-particle interactions, and a well established ion adsorption isotherm on the inner region of the double layer, the authors find the frequency-dependent electric permittivity of suspensions of spherical particles with volume fractions of solids up to above 40%. It is demonstrated that the addition of Ksigmai significantly increases the contributions of the double layer to the polarization of the suspension: the alpha or concentration polarization at low (kilohertz) frequencies, and the Maxwell-Wagner-O'Konski (associated with conductivity mismatch between particle and medium) one at intermediate (megahertz) frequencies. While checking for the possibility that the results obtained in conditions of Ksigmai not equal 0 could be reproduced assuming Ksigmai=0 and raising Ksigmad to reach identical total Ksigma, it is found that this is approximately possible in the calculation of the permittivity. Interestingly, this does not occur in the case of electrophoretic mobility, where the situations Ksigma=Ksigmad and Ksigma=Ksigmad+Ksigmai (for equal Ksigma) can be distinguished for all frequencies. This points to the importance of using more than one electrokinetic technique to properly evaluate not only the zeta potential but other transport properties of concentrated suspensions, particularly Ksigmai.

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields.

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.

Scaling Behavior of the Rheological Properties of Montmorillonite Suspensions: Correlation between Interparticle Interaction and Degree of Flocculation.

In this work we investigate some aspects of the rheological behavior of sodium montmorillonite (NaMt) suspensions in the pH range 3 to 9, of NaCl concentrations between 10(-3) and 10(-1) M, and of solid concentrations between 5 and 11% w/v. Three kinds of experiments were performed: steady-state viscometry, oscillatory test, and creep recovery. The physical quantities of interest were the yield stress sigma(y) of the suspensions, the elastic rigidity modulus G', and the instantaneous elastic compliance. Furthermore, G' was obtained from oscillatory tests in three different experiments: determination of the viscoelastic linear region, oscillograms, and the gelation process. All quantities were found to scale with the concentration of solids, C, according to a power law of the form Y=k(y)C(n). The exponents n were found to change from approximately 3 to approximately 6 when the pH was increased from 3 to 9 (at constant ionic strength 10(-2) M), although values as high as 10 were estimated when the NaCl concentration was reduced to 1 mM. Such values of n correlate well with the characteristics of the edge-to-face (E-F), edge-to-edge (E-E), and face-to-face (F-F) interparticle interactions. The minimum values of n correspond to maximum E-F attractions, whereas the largest n are associated with strong F-F repulsions. Copyright 2001 Academic Press.