Degree of aggregation

Surface active electrolytes produce charged micelles whose effective charge can be measured by electrophoretic mobility [117,156]. The net charge is lower than the degree of aggregation, however, since some of the counterions remain associated with the micelle, presumably as part of a Stem layer (see Section V-3) [157]. Combination of self-diffusion with electrophoretic mobility measurements indicates that a typical micelle of a univalent surfactant contains about 1(X) monomer units and carries a net charge of 50-70. Additional colloidal characterization techniques are applicable to micelles such as ultrafiltration [158]. 

Raw ] Ia.teria.ls. Most of the raw materials are oxides (PbO, Ti02, Zr02) or carbonates (BaCO, SrCO, CaCO ). The levels of certain impurities and particle size are specified by the chemical suppHer. However, particle size and degree of aggregation are more difficult to specify. Because reactivity depends on particle size and the perfection of the crystals comprising the particles, the more detailed the specification, the more expensive the material. Thus raw materials are usually selected to meet appHcation-dependent requirements. 

If polytungstates are considered as formed by the addition of acid to WO , then a series of isopolytungstates appears, in which the degree of aggregation in solution increases with decreasing pH. The relationships of the species, in order of increasing H20" W0 4 ratio, are shown in Table 3. 

Specification for Particulates Feed, recycle, and product from size reduction operations are defined in terms of the sizes involved. It is also important to have an understanding of the degree of aggregation or agglomeration that exists in the measured distribution. 

One of the general features of the reactivity of enolate anions is the sensitivity of both the reaction rate and the ratio of C- versus O-alkylation to the degree of aggregation of the enolate. For example, addition of HMPA fiequently increases the rate of enolate alkylation... 

The polymerization of acidified solutions of molybdenum(VI) or tungsten(VI) yields the most complicated of all the polyanion systems and, in spite of the fact that the tungsten system has been the most intensively studied, it is still probably the least well understood. This arises from the problem inevitably associated with studies of such equilibria, and which were noted (p. 983) in the discussion of the Group 5 isopolyanions. It must also be admitted that, whilst the observed structures of individual polyanions are reasonable, it is often difficult to explain why, under given circumstances, a particular degree of aggregation or a particular structure is preferred over other possibilities. 

Before beginning a size determination, it is customary to look at the material, preferably under a microscope. This examination reveals the approx size range and distribution of the particles, and especially the shapes of the particles and the degree of aggregation. If microscopic examination reveals that the ratios between max and min diameters of individual particles do not exceed 4, and indirect technique for particle size distribution based on sedimentation or elutria-tion may be used. Sedimentation techniques for particle size determination were first used by Hall (Ref 2) in 1904, He showed that the rate of fall of individual particles in a fluid was directly related to the particle size by the hydrodynamic... 

The degree of aggregation of polystyryl alkali salts in hydrocarbons, as well as the reactivity of their respective unassociated pairs, decrease along the series Li +, Na+, K +, Cs+ (Ref.Il, pp. 20 21). For example, the propagation constant of the lithium pair in benzene at 25 °C is estimated to be greater than 100 M "1 sec- while those of K +, Rb+, and Cs+ were determined as 47, 24, and 18 M-1 sec-1, respectively. Such a gradation contrasts with that of the reactivities of tight pairs in ethereal solvents,... 

It is important to keep the position of the equilibria in mind as we consider reactions of carbanions. The base and solvent used determine the extent of deprotonation. Another important physical characteristic that has to be kept in mind is the degree of aggregation of the carbanion. Both the solvent and the cation influence the state of aggregation. This topic is discussed further in Section 1.1.3. 

Experiments made at higher degrees of aggregation have provided strong evidence192 for ring-like structures for mixed neutral clusters. For example, under a wide variety of experimental conditions, mixed cluster ions display a maximum intensity atm = 2(n + 1) whenn<5 for (NH3)II (M)mH+, andm = n + 2 whenn<4 for (H20)B(M)mH+ M is a proton acceptor such as acetone, pyridine, and trimethy-lamine. These findings reveal that the cluster ions with these compositions have stable solvation shell structures as discussed above. 

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