Micelle ellipsoidal structure

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. 

At higher surfactant concentrations the ratio of alcohol to surfactant molecules does not exceed 2 at the phase boundary, and it appears that the alcohols promote structural changes of the micelles, for example from spherical to rodlike or ellipsoidal structures. This structural change is dependent both on the surfactant concentration and on the amount of solute, which is apparent from the study carried out by Backlund and co-workers who mapped the whole LI-phase of the SDS-1-hexanol and C gBr-l-hexanol systems demonstrating regions in the phase diagram relating to spherical micelles, spherical swollen micelles, and rodlike micelles. 

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. 

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. 

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. 

At the present time, the major types of micelles appear to be (1) relatively small, spherical structures (aggregation number <100), (2) elongated cylindrical, rodlike micelles with hemispherical ends (prolate ellipsoids), (3) large, flat lamellar... 

The early Hartley model [2, 3] of a spherical micellar structure resulted, in later years, in some considerable debate. The self-consisteney (inconsisteney) of spherical symmety with molecular packing constraints was subsequently noted [4, 5 and 6]. There is now no serious question of the tenet that imswollen micelles may readily deviate from spherical geometiy, 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... 

When amphipathic molecules are dispersed in water, their hydrophobic parts (i.e., hydrocarbon chains) aggregate and become segregated from the solvent. This is a manifestation of the hydrophobic effect which comes about because of exclusion and hence ordering of water at the interface between these distinct types of molecule. Aggregates of amphipathic molecules can be located at a water-air boimdary (monolayers) (Fig. 3-24) however, only a small quantity of an amphipathic lipid dispersed in water can form a monolayer (unless the water is spread as a very thin film). The bulk of the lipid must then be dispersed in water as micelles (Fig. 3-24). In both of these structures the polar parts, or heads (O), of the lipid make contact with the water, while the nonpolar parts, or tails (=), are as far from the water as possible. Micelles can be spherical as shown in Fig. 3-24, but can also form ellipsoidal, discoidal, and cylindrical stmctures. 

FIGURE 15.3. Of the many theoretically possible hquid crystal structures, five are most commonly encountered in surfactant systems. The lamellar phase (a) is simply alternating layers of surfactant molecules. The hexagonal phases (fe,c) are infinite hexagonal close-packed structures of normal and inverted cylindrical micelles. The most complicated, and difficult to visualize and shown schematically here, are the cubic bicontinuous (or interpenetrating) network d) and the cubic close packed ellipsoidal or finite cylindrical arrays (e). 

Although the classic picture of a micelle is that of a sphere, most evidence suggests that spherical micelles are not the rule and may in fact be the exception. Due to geometric packing requirements (to be discussed below) ellipsoidal, disk-shaped, and rodlike structures may be the more commonly encountered micellar shapes (Fig. 15.8). However, from the standpoint of providing... 

Extension of the concepts of molecular geometry and aggregate structure has led to its use in predicting not only the structure to be expected (the shape to be expected (micelle, vesicle, extended bilayer, etc.), but also the size, size distribution, shape (spherical, ellipsoidal, disk, or rod-shaped), dispersity (or size distribution), critical micelle concentration, average aggregation number, and other such characteristics. The rules of association derived from the geometric analysis of molecular structure are summarized in Figure 15.11. 

Under these considerations, the analysis of the energetics of size and shape of the micelles becomes of interest. The spherical shape would be the most stable structure if the monomers aggregate with a minimum of other constraints needed to satisfy the forces as described under Chap. 2.3, because this gives the minimum surface area of contact between the micelle and the solvent. On the other hand, if large constraints exist, other possible shapes, e.g. ellipsoids, cylinders or bilayers would be present [1,4]. It is obvious that micelles as formed by non-linear surfactants, e.g. bile salts etc., can not be analyzed by these theories, because steric hinderance gives rise to rather small aggregation numbers [1,3,4, 12,32,33,34,35,36,37,38,39,40]. In the case of spherical micelles of linear alkyl chain surfactants, with aggregation numberm, the radius, R, and total volume, V, and micellar surface area, A, we have ... 

A common feature of all amphiphiles is their tendency to seif-assemble in aqueous solutions above a critical concentration, denoted as the critical aggregation concentration or, for micelle-forming amphiphiles (surfactants), the critical micellar concentration, abbreviated cmc [1-3], The structure of the resultant aggregates depends on the molecular geometry of the amphiphiles and varies from micelles of various geometries (e.g., spheres, ellipsoids, or rods) to bilayers, cubic, or hexagonal phases [4,5],... 

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