Particles electrolyte concentration

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

We will focus on one experimental study here. Monovoukas and Cast studied polystyrene particles witli a = 61 nm in potassium chloride solutions [86]. They obtained a very good agreement between tlieir observations and tire predicted Yukawa phase diagram (see figure C2.6.9). In order to make tire comparison tliey rescaled the particle charges according to Alexander et al [43] (see also [82]). At high electrolyte concentrations, tire particle interactions tend to hard-sphere behaviour (see section C2.6.4) and tire phase transition shifts to volume fractions around 0.5 [88]. 

For some apphcations, eg, foam mbber, high soHds (>60%) latices are requited. In the direct process, the polymerization conditions are adjusted to favor the production of relatively large average particle-size latices by lowering the initial emulsifier and electrolyte concentration and the water level ia the recipe, and by controlling the initiation step to produce fewer particles. Emulsifier and electrolyte are added ia increments as the polymerization progresses to control latex stabiUty. A latex of wt% soHds is obtained and concentrated by evaporation to 60—65 wt % soHds. 

Table II also shows the effect of electrolyte concentration on Rf and kj. Both effects reflect the fact that at the higher ionic strengths particle/substrate repulsion is decreased, thus effectively increasing the available pore volume at a given particle size. These results are illustrated in Figure 3. Included in this figure are data from work by Nagy (14) with a column set similar in configuration to that employed here.

The first observation of PSEs for the MOR on Pt was reported by Attwood and co-workers in 1980. They found a beU-shaped curve for the dependence of SA on particle size, with the maximum at about 2nm [Attwood et al., 1980]. Takasu and co-workers reported a decrease in SA with decreasing particle size for Pt particles deposited on GC by vacuum deposition, as depicted in Fig. 15.11 [Yahikozawa et al., 1991]. This PSE was detected in both HCIO4 and H2SO4 and at various electrolyte concentrations [Yahikozawa et al., 1991]. The PSE was confirmed by Kabbabi... 

Spherical microparticles are more difficult to manufacture and can be prepared by several methods. One method prepares silica hydrogel beads by emulsification of a silica sol in an immiscible organic liquid [20,21,24,25]. To promote gelling a silica hydrosol, prepared as before, is dispersed into small droplets in a iater immiscible liquid and the temperature, pH, and/or electrolyte concentration adjusted to promote solidification. Over time the liquid droplets become increasingly viscous and solidify as a coherent assembly of particles in bead form. The hydrogel beads are then dehydrated to porous, spherical, silica beads. An alternative approach is based on the agglutination of a silica sol by coacervation [25-27], Urea and formaldehyde are polymerized at low pH in the presence of colloidal silica. Coacervatec liquid... 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

It is interesting to compare these results with the electrophoretic measurements made under identical electrolyte concentrations. Figure 8 shows that the variation of electrophoretic mobility with sodium chloride concentration is different for the bare and the PVA-covered particles. For the bare particles, the mobility remains constant up to a certain salt concentration, then increases to a maximum and decreases sharply, finally approaching zero. The maximum in electrophoretic mobility-electrolyte concentration curve with bare particles has been explained earlier (21) by postulating the adsorption of chloride ions on hydrophobic polystyrene particles. In contrast, for the PVA-covered particles, the mobility decreases with increasing electrolyte concentration until it approaches zero at high salt concentration. 

Figure 7. W versus electrolyte concentration (NaCl) for different-size particles (o) 190nm particles ( ) 400nm particles open points for bare particles and closed points for particles covered withVinol 107 at saturation.

Critical Flocculation Electrolyte Concentration The critical flocculation electrolyte (Na2S0.) concentration was determined by following the average particle size of the dilute dispersion (where the particles were coated with PVA corresponding to the plateau adsorption) as a function of Na2S0 concentration, using a Coulters Nanosizer (Coulters Electronics Ltd) as described before (20). 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

Figure 2.16 The pair potential calculated for rutile particles with a radius of 100 nm, background electrolyte concentration of 10 4moldm 3 and a -potential of —50 mV. Curve a was calculated for an isolated pair of particles and curve b corresponds to the potential for a pair ofparticles in a dispersion at a volume fraction of 0.45. Note how the increased electrolyte content due to the counterions introduced with the particles shorten the range of the repulsion enough for a small secondary minimum to be found at h 70 nm...

Here z is the ion valency, nQ is the number density of added electrolyte and q is the surface charge density of the particles. Figure 3.21 clearly illustrates the sensitivity at the lower added electrolyte concentrations where the diffuse layer Debye length is equivalent to that which would be estimated for an added electrolyte concentration two orders of magnitude higher, at a volume fraction of 0.5. Clearly higher concentrations of added electrolyte are not as sensitive but the variation is still significant. 

An equilibrium model may not be representative of the true situation commonly faced in the laboratory. The relaxation behaviour of the samples becomes progressively longer with increasing volume fraction. It is quite reasonable to suppose that, at high particle concentrations and low electrolyte concentrations, the relaxation times become so long that it is impractical to allow all the stresses and strains to relax from the sample prior to measurement. Stress relaxation studies for a range of particles that show nearly complete relaxation is shown in Figure 5.16.21... 

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