Micelles ellipsoidal

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

The early Hartley model [2, 3] of a spherical micellar stmcture resulted, in later years, in some considerable debate. The self-consistency (inconsistency) of spherical symmetry witli molecular packing constraints was subsequently noted [4, 5 and 6]. There is now no serious question of tlie tenet tliat unswollen micelles may readily deviate from spherical geometry, and ellipsoidal geometries are now commonly reported. Many micelles are essentially spherical, however, as deduced from many light and neutron scattering studies. Even ellipsoidal objects will appear... 

Numerous books and reviews have been published on this subject (e.g. Fendler and Fendler, 1975 Mittal, 1977). Therefore, the structural characteristics of micelles will be presented only to the extent that is necessary for the subsequent discussions. These surfactants form micelles at concentrations above the cmc (critical micelle concentration). Such micelles have average radii of 12-30 A and contain 20-100 surfactant molecules. The hydrophobic part of the aggregate forms the core of the micelle while the polar head groups are located at the micellar surface. Micelles at concentrations close to their cmc are assumed to possess spherical and ellipsoidal structures (Tanford, 1973, 1978). A schematic representation of a spherical ionic micelle is shown in Fig. 1. 

As mentioned earlier, surfactants aggregate to form micelles, which may vary in size (i.e., number of monomers per micelle) from a few to over a thousand monomers. However, surfactants can form, besides simple micellar aggregates (i.e., spherical or ellipsoidal), many other structures also when mixed with other substances. The curved micelle aggregates are known to change to planar interfaces when additives, the so-called cosurfactants, are added. A reported recipe consists of... 

At relatively low concentrations of surfactant, the micelles are essentially the spherical structures we discussed above in this chapter. As the amount of surfactant and the extent of solubilization increase, these spheres become distorted into prolate or oblate ellipsoids and, eventually, into cylindrical rods or lamellar disks. Figure 8.8 schematically shows (a) spherical, (b) cylindrical, and (c) lamellar micelle structures. The structures shown in the three parts of the figure are called (a) the viscous isotropic phase, (b) the middle phase, and (c) the neat phase. Again, we emphasize that the orientation of the amphipathic molecules in these structures depends on the nature of the continuous and the solubilized components. 

Fig. 4.27 SAXS intensity as a function of wavevector for a PS-P1 diblock (Mw = 60 kg mol-1, 17wt% PS) (points) in dibutyl phthalate with a polymer volume fraction

Soft-core reverse micelles are spherical or ellipsoidal aggregates consisting of a water core separated from a continuous apolar phase by a surfactant shell. It is well known that in the absence of water, some surfactants such as sodium bis(2-ethylhexyl) sulfosuccinate (AOT) can form dry aggregates, while others such as sodium dodecyl sulfate (SDS) or hexadecyl-trimethylamonium bromide (CTAB) need a cosurfactant, e.g., a short chain alcohol, to form micelles. 

Only a small quantity of an amphiphilic lipid dispersed in water can form a monolayer (unless the water is spread as a very thin film), in which case the bulk of the lipid will form soluble micelles. Micelles can take a variety of forms, each satisfying the hydrophobic effect. Fig. 6-2 shows one such form, representing a spherical micelle, although ellipsoidal, diskoidal, and cylindrical variations are possible. 

The hydrophobic part of the aggregate molecules forms the core of the micelle while the polar head groups are located at the micelle-water interface in contact with the water molecules. Such micelles usually have average radii of 2... 4 nm and contain 50... 100 monomers in water. Their geometric structure is usually roughly spherical or ellipsoidal. In non-aqueous nonpolar solvents, the micellar structures are generally the inverse of those formed in water. In these solvents, the polar head groups form the interior of the micelle while the hydrocarbon chains of the ions are in contact with the nonpolar solvent. 

Disordered solutions of spherical micelles are not particularly viscoelastic, or even viscous, unless the volume fraction of micelles becomes high, greater than 30% by volume. Figure 12-7, for example, shows the relative viscosity (the viscosity divided by the solvent viscosity) as a function of micellar volume fraction for a solution of hydrated micelles of lithium dodecyl sulfate in water. Qualitatively, these data are reminiscent of the viscosity-volume-fraction relationship for suspensions of hard spheres, shown as a dashed line (see Section 6.2.1). The micellar viscosity is higher than that of hard-sphere suspensions because of micellar ellipsoidal shape fluctuations and electrostatic repulsions. 

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