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.     

Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

The electrophoretic mobility of spherical soft particles in concentrated colloidal suspensions is numerically calculated. The particle is modeled as a hard core coated with an ion-penetrable membrane bearing a uniform distribution of fixed charges, while the high particle concentration is taken into account by means of a cell model. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as particle concentration, membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of ionic species, electrolyte concentration, etc. The theoretical model used is similar to the one presented by Ohshima [H. Ohshima, J. Colloid Interface Sci. 225 (2000) 233], except for the use of the Shilov-Zharkikh, rather than the Levine-Neale, boundary condition for the electric potential, and the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle [J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265 (2003) 327]. The obtained results only coincide with existing analytical expressions for low particle concentrations, low particle charge, and when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high. This suggests that most interpretations of the electrophoretic mobility of soft particles in concentrated suspensions require numerical calculations.     

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.     

A light scattering study of concentrated dispersions in nonaqueous media

Interparticle interactions between colloidal poly(methylmethacrylate) particles stabilised by poly(12-hydroxystearic acid) in non-aqueous media have been investigated using time-average light scattering. The problem of multiple scattering was avoided by using a binary mixture of solvents such that the colloidal particles were optically matched. This enabled the static structure factor to be measured and from the small scattering vector expansion the osmotic pressure to be determined. The softness of the pairwise interaction potential has been exposed using the Chandler-Weeks-Anderson perturbation theory. However, it is concluded that dispersions of the type studied can be reasonably well approximated by a hard sphere fluid model.     

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.     

Cell model calculation for electrokinetic phenomena in concentrated suspensions: an Onsager relation between sedimentation potential and electrophoretic mobility

Cell model calculations for the electrophoretic mobility, electrical conductivity and sedimentation potential in concentrated suspensions of colloidal particles with low zeta potentials are reviewed with particular emphasis on an Onsager relation between sedimentation potential and electrophoretic mobility. A general Onsager relation is derived on the basis of the thermodynamics of irreversible processes. This relation, which involves the ratio of the electrical conductivity K* of the suspension to the conductivity Kinfinity in the absence of the particles, reproduces the Onsager relation derived from cell model calculations at low zeta potentials, where K*/Kinfinity becomes (1 - phi)/(1 + phi/2), phi being the particle volume fraction.     

Accurate electrophoretic analyses of concentrated suspensions (electrophoresis of concentrates)

In conventional moving-boundary electrophoresis, boundary anomalies and erroneous analyses were shown to result in work with concentrated suspensions. An apparatus and a technique are described which, using auxiliary probes and an electrolyte tailored to the test suspension, allowed accurate data to be obtained even with highly concentrated suspensions. Thus, the usefulness of moving-boundary electrophoresis has been expanded, as now concentrated as well as dilute suspensions can be investigated.     

On the electrophoretic mobility and zeta potential of montmorillonite in non-aqueous media

Experimental results on the electrophoretic velocity and mobility of Ca-montmorillonite in 2-propanol are reported. The variation of the electrophoretic velocity with the externally applied electric field and the particle size range, at constant volume fraction and temperature, is considered. Given the difficulties for determining the types and concentrations of ions present in these liquid media, two methods are discussed for the estimation of the double layer thickness and hence the product, necessary for the determination of the zeta potential () of the interface. Although both methods of calculation yield different values of, the results for the zeta potential are very similar in the regions of and characteristic of our systems. The application to the experimental data of three theoretical relations between electrophoretic mobility and zeta potential is also discussed.     

Measurement of the field dependent electrophoretic mobility of surface modified silica/AOT suspensions

We have investigated the electrophoretic mobility of silica spheres in a silica/AOT/paraffin ternary system as a function of the applied electric field and observed a large discrepancy with data published on a similar system ( Jin, F. H. ; Davis, H. T. ; Evans, D. F. Int. Conf. Digital Printing Technol. 1998, 206-209 ). We attribute the discrepancy to an artifact in the measurement technique used to obtain that published data. We believe the artifact is caused by high velocity particles being "swept" from the measurement volume, thereby biasing the result toward lower mobilities. Thus, the published measurements appear to indicate a high field plateau in mobility data around 500 kV/m. Our results indicate that the silica/AOT/paraffin solution is reaching dielectric breakdown prior to a conclusive high field plateau being unambiguously measured. At low field the mobility is in general agreement with the prior work ( Jin, F. H. ; Davis, H. T. ; Evans, D. F. Int. Conf. Digital Printing Technol. 1998, 206- 209 ). Any proposed models of apparent charging of particles which utilize the presence of a high field plateau are inappropriate unless the high field plateau is clearly established. Our work indicates that caution is required regarding the measurement of electrophoretic mobility at high electric fields.     

Cerimetry in nonaqueous media

Summary The reaction between ascorbic acid and ammonium hexa nitrato cerate was studied potentiometrically in the mixed solvent glacial acetic acid acetonitrile medium. It was found that one mole of ascorbic acid consumes four equivalents of cerate in non-aqueous medium. This reaction can be made use of to estimate potentiometrically ascorbic acid with ammonium nitrato cerate in non-aqueous media, using either glass or antimony as reference electrode and platinum as indicator electrode.

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Zusammenfassung Die Reaktion zwischen Ascorbinsäure und Ammoniumhexanitratocerat wird in einem Medium von Eisessig + Acetonitril untersucht. Im nichtwäßrigen Medium verbraucht 1 Mol Ascorbinsäure 4 Äquivalente Cerat. Die Reaktion kann zur potentiometrischen Bestimmung von Ascorbinsäure benutzt werden; dabei wird als Indicatorelektrode Platin und als Vergleichselektrode die Glas- oder Antimonelektrode verwendet.

     

Rheological peculiarities of concentrated suspensions

The rheological properties of concentrated suspensions of metal oxides dispersed in transformer oil, which are used as electrorheological fluids, are systematically studied. Colloidal particles have intermediate sizes between nano- and microsized scales. Low-amplitude dynamic measurements show that the storage moduli of the examined suspensions are independent of frequency and these materials should be considered as solidlike elastic media. The storage modulus is proportional to the five-powdered particle volume concentration. At the same time, a transition through an apparent yield stress with a reduction in the viscosity by approximately six orders of magnitude is distinctly seen upon shear deformation. The character of the rheological behavior depends on the regime of suspension deformation. At very low shear rates, a steady flow is possible; however, upon an increase in the rate, an unsteady regime is realized with development of self-oscillations. When constant shear stresses are preset, in some range of stresses, thickening of the medium takes place, which can also be accompanied by self-oscillations. In order to gain insight into the nature of this effect, measurements are performed for samples with different volume/surface ratios, which show that, in some deformation regimes, suspension is separated into layers and slipping occurs along a low-viscosity layer with a thickness of several dozen microns. Direct observations show a distinct structural inhomogeneity of the flow. The separation and motion of layers with different compositions explain the transition to the flow with the lowest apparent Newtonian viscosity. Thus, the deformation of concentrated suspensions is associated with self-oscillations of stresses and slipping along a low-viscosity interlayer.     

Dynamic electrophoretic mobility of a concentrated dispersion of particles with a charge-regulated surface at arbitrary potential

The dynamic electrophoretic mobility of a concentrated dispersion of biocolloids such as cells and microorganisms is modeled theoretically. Here, a biological particle is simulated by a particle, the surface of which contains dissociable functional groups. The results derived provide basic theory for the quantification of the surface properties of a biocolloid through an electroacoustic device, which has the merit of making direct measurement on a concentrated dispersion without dilution. Two key parameters are defined to characterize the phenomenon under consideration: the first, A, is associated with the pH of the dispersion, and the second, B, is associated with the equilibrium constant of the dissociation reaction of the functional group. We show that if A is large and/or B is small, the surface potential is high, and the effect of double-layer polarization becomes significant. In this case the dynamic electrophoretic mobility may have a local maximum and a phase lead as the frequency of the applied electric field varies. Due to the hydrodynamic interaction between neighboring particles, the dynamic electrophoretic mobility decreases with the concentration of dispersion.     

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.     

Colloidal stabilization of nanoparticles in concentrated suspensions

The stabilization of nanoparticles in concentrated aqueous suspensions is required in many manufacturing technologies and industrial products. Nanoparticles are commonly stabilized through the adsorption of a dispersant layer around the particle surface. The formation of a dispersant layer (adlayer) of appropriate thickness is crucial for the stabilization of suspensions containing high nanoparticle concentrations. Thick adlayers result in an excessive excluded volume around the particles, whereas thin adlayers lead to particle agglomeration. Both effects reduce the maximum concentration of nanoparticles in the suspension. However, conventional dispersants do not allow for a systematic control of the adlayer thickness on the particle surface. In this study, we synthesized dispersants with a molecular architecture that enables better control over the particle adlayer thickness. By tailoring the chemistry and length of these novel dispersants, we were able to prepare fluid suspensions (viscosity < 1 Pa.s at 100 s-1) with more than 40 vol % of 65-nm alumina particles in water, as opposed to the 30 vol % achieved with a state-of-the-art dispersing agent. This remarkably high concentration facilitates the fabrication of a wide range of products and intermediates in materials technology, cosmetics, pharmacy, and in all other areas where concentrated nanoparticle suspensions are required. On the basis of the proposed molecular architecture, one can also envisage other similar molecules that could be successfully applied for the functionalization of surfaces for biosensing, chromatography, medical imaging, drug delivery, and aqueous lubrication, among others.     

The viscoelastic properties of concentrated suspensions

The viscoelastic properties of concentrated, well dispersed, sterically stabilised polymethyl methacrylate particles were studied using a specially developed low frequency, controlled shear stress rheometer. The experimental results show a well defined viscoelastic transition over a narrow frequency range. Evidence is produced to show that the particles act as hard, non-interacting spheres. It is argued that the transition represents a change from a randomly packed assemblage with particle motion dominated by Browniandiffusion processes to a lower packing density shear flow regime.