Micellization length

Fig. B4.3.1. Schematic illustration of the average residence sites of the probes NOH (1), NSOH (2), NDSOH (3) in AOT reverse micelles. Length of the surfactant 11 A. Diameter of the water pool 18A at w = 3, 36A at w = 9. Largest dimension of the naphthol derivatives 9 A (adapted from Bardez et al.a ).

It is not difficult to carry out the statistical calculations for these two degrees of freedom (size and flexibility), since they are largely independent of one another. The energy AE endcap does not depend on micelle length, nor on the various bending configurations the micelle may explore. Statistical analysis shows that mean micelle size (L) varies in a continuous way [5.14], but very rapidly with AE endcap- In fact,... 

Zhong, X.F., Varshnay, S.K., and Eisenberg, A. (1992) Critical micelle lengths for ionic blocks in solutions of polystyrene-b-poly(sodium acrylate) ionomers. Macromolecules, 25,7160-7167. 

Turner and Cates assumed an exponential distribution of micelle lengths and a rate constant of breakdown of a micelle into two daughter micelles that is proportional to the mean micelle length . The resulting relaxation time is given by... 

Waton derived the general expression (3.24) for this relaxation time. This expression applies to different t3rpes of distribution of micelle lengths. ... 

In this equation kf is the mean rate constant of fission. Equation 3.24 yields Equation 3.23 in the case of an exponential distribution of micelle lengths. 

After reviewing various earlier explanations for an adsorption maximum, Trogus, Schechter, and Wade [244] proposed perhaps the most satisfactory one so far (see also Ref. 243). Qualitatively, an adsorption maximum can occur if the surfactant consists of at least two species (which can be closely related) what is necessary is that species 2 (say) preferentially forms micelles (has a lower CMC) relative to species 1 and also adsorbs more strongly. The adsorbed state may also consist of aggregates or hemi-micelles, and even for a pure component the situation can be complex (see Section XI-6 for recent AFM evidence of surface micelle formation and [246] for polymeric surface micelles). Similar adsorption maxima found in adsorption of nonionic surfactants can be attributed to polydispersity in the surfactant chain lengths [247], Surface-active impuri-... 

In some of these models (see Sec. Ill) the surfactants are still treated as flexible chains [24]. This allows one to study the role of the chain length and chain conformations. For example, the chain degrees of freedom are responsible for the internal phase transitions in monolayers and bilayers, in particular the hquid/gel transition. The chain length and chain architecture determine the efficiency of an amphiphile and thus influence the phase behavior. Moreover, they affect the shapes and size distributions of micelles. Chain models are usually fairly universal, in the sense that they can be used to study many different phenomena. 

In a class of reahstic lattice models, hydrocarbon chains are placed on a diamond lattice in order to imitate the zigzag structure of the carbon backbones and the trans and gauche bonds. Such models have been used early on to study micelle structures [104], monolayers [105], and bilayers [106]. Levine and coworkers have introduced an even more sophisticated model, which allows one to consider unsaturated C=C bonds and stiffer molecules such as cholesterol a monomer occupies several lattice sites on a cubic lattice, the saturated bonds between monomers are taken from a given set of allowed bonds with length /5, and torsional potentials are introduced to distinguish between trans and "gauche conformations [107,108]. 

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