Dispersions of Charged Particles

The multicomponent extension of the SCGLE theory [21] may be summarized, in its simplified form [59], by Equations 1.30 through 1.32, 1.37, and 1.38. It was applied rather recently [72] to the description of dynamic arrest in two simple model colloidal mixtures, namely, the hard-sphere and the repulsive Yukawa binary mixtures. The main contribution of reference [72], however, is the extension to mixtures of Equation 1.39. Thus, the resulting equation for y , the localization length squared of particles of species a, was shown to be 

for a given system one first determines 5 p(A ), as well as the matrices c, h, and X needed in these equations, and then numerically solve the v equations for the v parameters to classify the resulting state. For a binary mixture, for example, the solution Yi = Y2 = corresponds to a fully ergodic state, whereas a finite solution for both of these parameters corresponds to a fully arrested state. Under some conditions we also expect mixed states in which the particles of one species are arrested (e.g., finite Y2). while the other particles remain mobile (Yi = ) In this manner one may scan the state space to determine the regions where these different dynamic states occur, and the boundaries between them. Of course, mixtures with more than two components will present richer dynamic arrest phase diagrams. 

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We have so far focused our attention on dilute systems so that we could avoid dealing with interference of scattering from different particles. The interference effects considered until now are restricted to interference due to scattering centers from within the same particle. When we have a fairly concentrated dispersion or even a dilute dispersion of charged particles that influence the position of each other through their interactions, the scattering data may have to be corrected for interparticle interference effects. Extending the previous discussion to mte/particle interference is not difficult, but the subsequent analysis of the information obtained is not trivial. We shall not go into the details of these here, but just make some brief remarks to establish the connection between interparticle effects and what we have described so far for dilute systems. 

Although the analysis becomes complex for more concentrated dispersions (or even for dilute dispersions of charged particles, which can interact over very large distances), some general observations on two limiting cases are useful ... 

By this term two phenomena are understood, both referring to the Interaction between sound waves and dispersions of charged particles. These methods somewhat transcend the borders set for this section in that the inertia of the particles does play a role in this respect electroacoustics anticipates a.c. electrokinetics and dielectric dispersion (sec. 4.8). 

The extended expression enables studies of phase instability in dispersions of charged particles like ionic colloids. In the context of this review, it helps to explain electrostriction or electrowetting in a confinement maintaining equilibrium with a field-free aqueous bath. Brunet et al. discussed the use of electric field to tune mixing/demixing equilibria in a multicomponent system [64, 65]. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

While precipitation in homogenous solutions is an exceedingly simple method, usually rather low concentrations of electrolytes must be used if well-dispersed uniform particles are to be achieved. This requirement is based on the need to keep the ionic strength of the system below a critical value in order to prevent the coagulation of the precipitates, which consist, almost without exception, of charged particles. In some instances, concentrations of the reactants can be increased, if stabilizers are added into the systems, although the latter may affect the particle uniformity and/ or shape. 

Fig. 15.8. Distribution of charged particles in dense single-layer coating composed of mono-disperse nanoparticles (numerical simulation for dielectric constants e = 1 and e = 10, T = 100°C). Z is the charge multiplicity of nanoparticles.

An aerosol is a dispersion of discrete particles in a stream of gas. Starch and cellulose aerosols are potential fire hazards in granaries where friction between the moving, micronized particles causes electrification, whereupon separate accumulations of positive and negative charges may discharge as an electric spark and ignite the combustible solute (contact electrification synonymous with triboelectrification Ross and Morrison, 1988). 

Electrophoresis — Movement of charged particles (e.g., ions, colloidal particles, dispersions of suspended solid particles, emulsions of suspended immiscible liquid droplets) in an electric field. The speed depends on the size of the particle, as well as the -> viscosity, -> dielectric permittivity, and the -> ionic strength of the solution, and it is directly proportional to the applied electric field. In analytical as well as in synthetic chemistry electrophoresis has been employed to separate species based on different speeds attained in an experimental setup. In a typical setup the sample is put onto a mobile phase (dilute electrolyte solution) filled, e.g., into a capillary or soaked into a paper strip. At the ends of the strip connectors to an electrical power supply (providing voltages up to several hundred volts) are placed. Depending on their polarity and mobility the charged particles move to one of the electrodes, according to the attained speed they are sorted and separated. (See also - Tiselius, - electrophoretic effect, - zetapotential). 

Sedimentation potential— (also called electrophoretic or Dorn potential) Potential difference established during sedimentation (caused, e.g., by gravitation or centrifugation) of small charged particles (suspended in solution dispersion of solid particles or emulsion of immiscible liquid droplets). 

For a unipolar aerosol it is necessary to consider electrostatic dispersion, i.e., the tendency of charged particles of the same sign to... 

This eqiiation accoxmts for the effect of the solvent, presence of charged particles (second term) and pectin (third term) on viscosity (r = 0.996). Sxmimarizing, the viscosity of some complex liquids is adequately represented by empirical equations that have as a structural parameter the volume fraction of the dispersed phase. Particle deformation, specific interactions between particles and the presence of a non-Newtonian continuous phase, all which contribute to the structure of a complex liquid, are more difficult to model. 

In an aqueous latex that has been cleaned to remove various materials such as suifece active agents one is dealing in many cases with a dispersion of charged spherical particles. Frequently, the distribution of particle sizes is veiy narrow and the term monodisperse is used to describe latices of this type. In an attempt to obtain a concise overview of the properties of aqueous latices in electrolyte solutions some of the essential features are summarized schematically in Fig. 4. 

Colloidal dispersions owe their stability to a surface charge and the resultant electrical repulsion of charged particles. This charge is acquired by adsorption of cations or anions on the surface. For example, an ionic precipitate placed in pure water will reach solubility equilibrium as determined by its solubility product, but the solid may not have the same attraction for both its ions. Solid silver iodide has greater attraction for iodide than for silver ions, so that the zero point of charge (the isoelectric point) corresponds to a silver ion concentration much greater than iodide, rather than to equal concentrations of the two ions. The isoelectric points of the three silver halides are ° silver chloride, pAg = 4, pCl = 5.7 silver bromide, pAg = 5.4, pBr = 6.9 silver iodide, pAg = 5.5, pi = 10.6. For barium sulfate the isoelectric point seems to be dependent on the source of the product and its de ee of perfection. ... 

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