Aggregation number measurement

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

Other solubilization and partitioning phenomena are important, both within the context of microemulsions and in the absence of added immiscible solvent. In regular micellar solutions, micelles promote the solubility of many compounds otherwise insoluble in water. The amount of chemical component solubilized in a micellar solution will, typically, be much smaller than can be accommodated in microemulsion fonnation, such as when only a few molecules per micelle are solubilized. Such limited solubilization is nevertheless quite useful. The incoriDoration of minor quantities of pyrene and related optical probes into micelles are a key to the use of fluorescence depolarization in quantifying micellar aggregation numbers and micellar microviscosities [48]. Micellar solubilization makes it possible to measure acid-base or electrochemical properties of compounds otherwise insoluble in aqueous solution. Micellar solubilization facilitates micellar catalysis (see section C2.3.10) and emulsion polymerization (see section C2.3.12). On the other hand, there are untoward effects of micellar solubilization in practical applications of surfactants. Wlren one has a multiphase... 

Section 4.2.2 discussed the use of methods other than F-N curves for determining aggregate risk. An aggregate risk measure can be calculated for Example 10 by multiplying each incident frequency by the expected number of serious injuries or fatalities. This results in a parameter of "fatalities per year."... 

Fluorescence spectroscopy is also particularly well-suited to clarify many aspects of polymer/surfactant interactions on a molecular scale. The technique provides information on the mean aggregation numbers of the complexes formed and measures of the polarity and internal fluidity of these structures. Such interactions may be monitored by fluorescence not only with extrinsic probes or labelled polymers, but also by using fluorescent surfactants. Schild and Tirrell [154] have reported the use of sodium 2-(V-dodecylamino) naphthalene-6-sulfonate (SDN6S) to study the interactions between ionic surfactants and poly(V-isopropylacrylamide). 

Translational diffusion times of micelles can be measured by FCS, which allows calculation of the aggregation number (see Box 11.2). 

Critical Micelle Concentration (cmc) is the surfactant concentration below which the formation of reverse micelles does not occur, while the number of surfactant molecules per micelle is referred to as the aggregation number, n. The cmc is obtained through physical measurements, and varies from 0.1-1.0 mmol dm in water or the nonpolar solvents. 

Turro and Yekta [142] discussed a simple method for measuring aggregation number by steady-state fluorescence. In this method, the decrease of the fluorescence intensity of a micelle-bound probe is monitored as a function of the quencher concentration and is fitted to the equation [143]... 

Instead, optical measurement was applied to clarify the formation mechanism of Agl nanoparticles in diluted suspensions. Figure 4.4.10A shows the absorption spectra of the 1-day aged suspension containing 3.33 X 10-4 M Ag+ and 6.67 X 10-4 M I- as a function of RSH concentration. When the content of RSH increased from 0 to 6.67 X I0-3 M (curves a-d), the absorption spectra of Agl particles blue-shifted, suggesting the quantum size effect. The relationship between the particle diameter, d (A), and the concentration of RSH, c (A/), was plotted in the inset, which shows the double-logarithmic linear line of d versus c. The aggregation number is found to be proportional to the cube of the size. The same relationship was reported on the formation of CdS nanoparticles (37). These correlations indicate that Agl and CdS have the same ionic nature and have the same reaction modules of thiols. 

The only uncertainty about the nature of active centers that remains, concerns their aggregation state. In order to measure the aggregation number, we have performed viscometric measurements on the polymer solutions in benzene, before and after deactivation of the active species. 

Regarding the liquid/liquid extraction from the metal standpoint is rather different. This is the classical approach of coordination chemistry (most of the publications in this area). Today, it is still difficult to establish a direct link between the two descriptions of the organic extractant phases. To better understand liquid/ liquid extraction, the aggregation number and coordination number must be measured separately for each system and set of initial conditions. This is the only way to determine the role of the aggregates in the extraction efficiency. This important point was emphasized by Yaita et al. (61). In this way, Gannaz et al. has used an approach combining studies on both supramolecular and molecular speciation of extractant systems of the DIAMEX-SANEX process (36). 

The methods mentioned above do not measure the micellar aggregation number itself but rather some micellar size. A direct determination of aggregation numbers can be performed by analysing some physico-chemical parameter in terms of the equilibria involved equilibrium analyses on the basis of potentiometric data have been pioneered by Danielsson and co-workers who studied short-chain, not typically micelle-forming, amphiphiles in the presence of added electrolyte (see above). 

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