Aggregation numbers for

Figure 6.15 The floe volume in shear against the number of particles per floe for a kaolin suspension. Different aggregation numbers for edge-edge and edge-face interactions were achieved by adjusting pH and electrolyte conditions. Face-face interactions were induced by the addition of a monolayer of HDTAB...

Quenching of pyrene by excimer formation (Py + Py —> (PyPy) —> 2Py) (see Section 4.4.1) is widely used for the determination of micellar aggregation numbers for new surfactant systems. An example is given in Figure B4.2.1. 

The aggregation number for sodium dodecyl sulfate increases with increasing amounts of the indifferent electrolyte NaCl. 

One can extend the above analysis to come up with the values of the packing parameter for which different shapes of aggregates are favored (Israelachvili 1991). These are summarized in Table 8.2. The results shown also serve as rules of thumb for what one can expect as one changes the chemical conditions of the solvent or the structure of the surfactant or for controlling the shape or aggregation number. For example,... 

Figure 12.3 Schematic distribution of surfactant aggregates as a function of the aggregation number for three different concentrations. When the total surfactant concentration is equal to the CMC we assumed a mean aggregation number of Nagg = 50.

TABLE 5. Heats of reaction and solvation, and aggregation numbers for the reaction of lithium pinacolate with pivalaldehyde at 6°C in cyclohexane519,520... 

Figure 7. Variations of aggregation numbers for ionic and non-ionic micelles in aqueous binary mixtures at 298.15 K...

Fig. 8.—Plot of optimal aggregation number M against (y/oo/c) for transition shapes of the ellipsoid of revolution model. M = Atriyiv is the largest possible aggregation number for spheres consistent with packing. Lower curve corresponds to spheres with no packing constraints.

Thus, for alkyl siufactants, the maximum aggregation number for spherical micelles should increase from 26 to 58, as increases from 8 to 12 (Missel et al. 1983). 

On the other hand, the fact that the aggregation numbers for the sulfate... 

Figure 2.14 illustrates the effect of the aggregation number for the case where the surface layer is free of monomers (F < 10 mol/m ). In this case, when the aggregation number exceeds a certain value (n > 20), the curves also become independent of n. Here, if the critical adsorption F is not too small, the curves exhibit a characteristic Iracture which indicates the formation of clusters in the adsorption layer (cf Fig. 2.15). However, for n>50 (that is, for very large clusters) the shape of the curves becomes independent of n.

Here M denotes the micelle, Sj denote surfactant molecules or ions of kind i, and w, are the aggregation numbers for each kind of particles. Let us rewrite the fundamental equation (5.10) for the whole system under the condition that cj = 0 ... 

The presence of the polar groups introduces another factor capable to enhance the aggregation numbers for the zwitterionic samples in n-decane. Much lower Nw values were observed for the amine-capped copolymers, meaning that the amine groups are not polar enough to enhance the association process. Typical LALLS plots are given in figure 12. 

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