Submicellar aggregates

Onset of micellization is detected by sharp changes in such properties as surface tension, refractivity or conductivity (of ionic micelles). To a first approximation the solution is assumed to contain monomeric amphiphiles, whose concentration is given by the cmc, and fully formed micelles, with submicellar aggregates playing a minor role. 

Two other general ways of treating micellar kinetic data should be noted. Piszkiewicz (1977) used equations similar to the Hill equation of enzyme kinetics to fit variations of rate constants and surfactant concentration. This treatment differs from that of Menger and Portnoy (1967) in that it emphasizes cooperative effects due to substrate-micelle interactions. These interactions are probably very important at surfactant concentrations close to the cmc because solutes may promote micellization or bind to submicellar aggregates. Thus, eqn (1) and others like it do not fit the data for dilute surfactant, especially when reactants are hydrophobic and can promote micellization. 

Key questions in these treatments are the constancy of a (or P) and the nature of the reaction site at the micellar surface. Other questions are less troubling for example the equations include a term for the concentration of monomeric surfactant which is assumed to be given by the cmc, but cmc values depend on added solutes and so will be affected by the reactants. In addition submicellar aggregates may form at surfactant concentrations near the cmc and may affect the reaction rate. But these uncertainties become less important when [surfactant] > cmc and kinetic analyses can be made under these conditions. In addition, perturbation of the micelle by substrate can be reduced by keeping surfactant in large excess over substrate. 

Quantitative fits of the rate constant to concentrations of surfactant or reagent are sometimes poor when [surfactant] is close to the cmc. Several factors can be involved here (l) the kinetic cmc can be lower than that in water because the reagents promote micellization (ii) reaction is promoted by submicellar aggregates or (iff) the simplifying assumptions involved in the kinetic equations (2-6) may be invalid when concentrations of substrate and micellized surfactant are similar (Romsted, 1984). 

Rate constants of bimolecular, micelle-assisted, reactions typically go through maxima with increasing concentration of inert surfactant (Section 3). But a second rate maximum is observed in very dilute cationic surfactant for aromatic nucleophilic substitution on hydrophobic substrates. This maximum seems to be related to interactions between planar aromatic molecules and monomeric surfactant or submicellar aggregates. These second maxima are not observed with nonplanar substrates, even such hydrophobic compounds as p-nitrophenyl diphenyl phosphate (Bacaloglu, R. 1986, unpublished results). 

This very simplified model of micellization is illustrated in scheme 4 for a cationic surfactant. At concentrations below the cmc only monomeric surfactant is present, but at higher concentration the solution contains micelle, free surfactant and counterions which escape from the micelle. It is assumed that submicellar aggregates are relatively unimportant for normal micelles in water, although, as we shall see, this assumption fails in some systems. However it is probably reasonable for relatively dilute surfactant, although at high surfactant concentration, and especially in the presence of added salt, the micelle may grow, and eventually, new organized assemblies form, for example, liquid crystals are often detected in relatively concentrated surfactant [1]. However, this discussion will focus on the relatively dUute surfactant solutions in which normal micelles are present. 

Eqn. 3 adequately fits data for unimolecular tnicellar-catalyzed reactions [66,68], and for micellar-inhibited reactions, where for bimolecular reactions, is usually small so that the second term in the numerator of Eqn. 3 can be neglected [70]. In some cases, for example with very hydrophobic substrates, micellar rate effects are observed at [D] < cmc, so that in these cases we cannot equate the concentration of monomeric surfactant with the cmc, probably because the substrate promotes micellization or interacts with submicellar aggregates, and modified forms of Eqn. 3 have been used [71]. 

Both explanations are reasonable. Critical micelle concentrations are decreased by addition of both electrolytes and hydrophobic non-ionic solutes to water [15]. But submicellar aggregates could coexist in solution with monomeric and micellized surfactant, although their concentration is probably low [2,23]. They could interact with, and be stabilized by, hydrophobic substrates. 

FIGURE 15.6. Micelle formation is a rapid and dynamic process involving continuous movement of surfactant molecules into and out of the micelle and, perhaps, submicellar aggregates. The residence time of a given molecule in a micelle is estimated to be between 10 and 10 s. 

I/X2. Similar results were reported for the SDS/PVP sys-tem.2 2 These variations are probably related to the decrease of the surfactant aggregation number upon increasing polymer concentration and the corresponding changes in the micelle size distribution curve when the surfactant aggregates on the polymer.The submicellar aggregates at the minimrun of the distribution curve may be stabihzed when forming on the polymer. 

In both of these models, the effects of intermicellar distance as well as the distance between submicellar aggregates have not been taken into ac-... 

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