Suspensions of charged spheres

This value of kn is actually low by an order of magnitude for dilute suspensions of charged spheres of radius Rg. This is due to the neglect of interchain correlations for c < c in the structure factor used in the derivation of Eqs. (295)-(298). If the repulsive interaction between polyelectrolyte chains dominates, as expected in salt-free solutions, the virial expansion for viscosity may be valid over considerable range of concentrations where the average distance between chains scales as. This virial series may be approxi-... 

For illustration, consider for a moment the particular case of a suspension of charged spheres of radius a and volume fraction N(47r/3)a3 (see Fig. L2.14). 

FIG. 7 Radial distribution function of a typical suspension of charged spheres with screened Coulomb interaction. The exact results (open circles) from Monte Carlo computer simulations are compared with the theoretical predictions of the Ornstein-Zernike equation and different closure relations (lines). 

The effective enlargement of the diameter of charged spheres leads to enhancement of the low-shear-rate viscosity. According to Russel (1978 Russel et al. 1989), the zero-shear viscosity out to second order in 0 of a disordered suspension of charged spheres is... 

Problem 7.2 Consider a suspension of charged spheres. Suppose the suspension is a soft solid (i.e., with a yield stress) when no electrolyte has been added. After adding 0.01 M NaCl, the suspension becomes a runny liquid. After adding an additional 0.1 M NaCl, it is a solid again Can you give an explanation ... 

The maximum in the reduced viscosity has also been observed for aqueous suspensions of charged spheres [108, 109] which cannot undergo a conformational transition, as already discussed in Sect. 2.3.1. These experiments strongly... 

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... 

Figure 6.1 Viscosity versus shear stress for aqueous suspensions of charged poly(styrene-ethylacrylate) copolymer spheres of diameter d = 250 nm at various volume fractions 0 and T = 25°C. The NaOH concentration was varied with

Figure 6.29 Zero-shear relative viscosity versus particle volume fraction for aqueous suspensions of charged polystyrene spheres (a = 34 nm) in 5 x lO " M NaCl ( ) (Buscall et al. 1982a). The line is calculated by using Eq. (6-66) for the viscosity, with 0eff given by Eq. (6-64), and d ff by Eq. (6-67a) or (6-67b). The potential 1T(/ ) is given by Eq. (6-58) or (6-59) with k given by Eq. (6-61) the constant K is 0.10, and is in the range 50-90 mV. (From Buscall 1991, reproduced with permission of the Royal Society of Chemistry.)...

Keh HJ, Li YL (2007) Diffusiophoresis in a suspension of charge-regulating colloidal spheres. Langmuir 23 1061-1072... 

For our experiments we used a charge stabilized suspension of polystyrene spheres dispersed in ultrapure water (Batch No. PS-F-3390, Berlin Microparticles GmbH Germany). The diameter was determined by electron microscopy to be 590 nm. The size polydispersity was determined to be 5.8%. The particles are stabilized with CCX)H- and HSOq-groups and the effective charge was measured by conductivity to be Z = 3(XX) 100. For diluting of the stock solution to a definite volume fraction deionized water of a MilliQ water system was used. To adjust the salt concentration of the suspension NaCl was added to screen the interaction of the particles (typically 1 mM). 

Latex dispersions have attracted a great deal of interest as model colloid systems in addition to their industrial relevance in paints and adhesives. A latex dispersion is a colloidal sol formed by polymeric particles. They are easy to prepare by emulsion polymerization, and the result is a nearly monodisperse suspension of colloidal spheres. These particles usually comprise poly(methyl methacrylate) or poly(styrene) (Table 2.1). They can be modified in a controlled manner to produce charge-stabilized colloids or by grafting polymer chains on to the particles to create a sterically stabilized dispersion. Charge-stabiHzed latex particles obviously interact through Coulombic forces. However, sterically stabilized systems can effectively behave as hard spheres (Section 1.2). Despite its simpHcity, the hard sphere model is found to work surprisingly well for sterically stabilized latexes. 

Third, dilute phases can be regarded as one-dimensional colloidal suspensions of sheets in analogy to the familiar three-dimensional suspensions of charged polystyrene spheres (e.g. polyballs). We shall see that the Poisson-Boltzmann equation in one-dimension accurately describes the intermembrane interactions for phases where the dilution is a consequence of long range electrostatic repulsion (rather than undulation forces). This happens when charged sheets are separated by water containing only the counter-ions. 

Fig. 6.16 Static structure factor S(q), short-time collective diffusion coefficient D(.4), and hydro-dynamic function H(q) for a suspension of charged latex spheres in a 0.5 mM NaQ solvent...

Russel, W.B. 1978. Rheology of suspensions of charged rigid spheres. J. Fluid Meek 85 209-232. 

The validity of Einstein s equation has been confirmed experimentally for dilute suspensions (0 < c 0.02) of glass spheres, certain spores and fungi, polystyrene particles, etc., in the presence of sufficient electrolyte to eliminate charge effects. 

Consider a dilute suspension of spherical colloidal particles of radius a with a surface charge density cr or the total surface charge Q = 4na a in a salt-free medium containing only counterions. We assume that each sphere is surrounded by a concentric spherical cell of radius R [5,7] (Fig. 6.1), within which counterions are distributed so that electrical neutrality as a whole is satisfied. The particle volume fraction [Pg.133]

The stability of colloidal systems consisting of charged particles can be essentially explained by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1-7]. According to this theory, the stability of a suspension of colloidal particles is determined by the balance between the electrostatic interaction and the van der Waals interaction between particles. A number of studies on colloid stability are based on the DLVO theory. In this chapter, as an example, we consider the interaction between lipid bilayers, which serves as a model for cell-cell interactions [8, 9]. Then, we consider some aspects of the interaction between two soft spheres, by taking into account both the electrostatic and van der Waals interactions acting between them. 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

The effective viscosity of a suspension of particles of types other than rigid particles has also been theoretically investigated. Taylor [22] proposed a theory of the electroviscous effect in a suspension of uncharged liquid drops. This theory has been extended to the case of charged liquid drops by Ohshima [17]. Natraj and Chen [23] developed a theory for charged porous spheres, and Allison et al. [24] and Allison and Xin [25] discussed the case of polyelectrolyte-coated particles. 

In this chapter, we first present a theory of the primary electroviscous effect in a dilute suspension of soft particles, that is, particles covered with an ion-penetrable surface layer of charged or uncharged polymers. We derive expressions for the effective viscosity and the primary electroviscous coefficient of a dilute suspension of soft particles [26]. We then derive an expression for the effective viscosity of uncharged porous spheres (i.e., spherical soft particles with no particle core) [27]. 

Figure 3. Scattering from silica spheres bound with PEO macromolecules In water (/, compared with free silica spheres (O) and with a concentrated suspension where the spheres repel each other (+). The solvent Is water at pH = 8 In this solvent the spheres bear about 0.3 S10 group per nm of surface, and the macromolecules bind to the remaining SlOH groups (1 ). Very long macromolecules (M 2E6) are used to promote bridging and flocculation with shorter ones no floes are obtained unless the surface charges are neutralized or screened (16).

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