Rods, micelle shapes

The determination of the molecular weight was complicated by the lack of data at low angles, and a simple Zimm plot analysis of the curve (Kc/Rq)c=0 could not be performed in a straightforward way (as suggested by Eq. 4), since it would lead to an underestimated value of the micelle molecular weight. However, from the downward curvature of these different plots we were able to deduce that the scattering particles present in solution had a rod-like shape. 

Given that micelles are present in solution above the CMC, the most important consideration for the liquid crystal phases is the micelle shape. There are three major types, namely spheres, rods and discs . They can be described by using the packing constraint concepts (5, 41, 42). These give a simple description of the relationship between micelle shape and molecular shape. The micelles are assumed to be smooth, with only the hydrophobic volume in the micelle interior. The main molecular parameters are the hydrophobic group volume, usually taken as being equal to the alkyl chain volume (u), the area that the molecule occupies at the... 

The micelle shape is determined by the molecular structure as described above (see equations (21.5-21.8) and Table 21.1). There is a critical volume fraction (concentration) above which random (disordered) solutions cannot occur for each of the shapes, i.e. spheres, rods and discs (bilayers). An ordered state (liquid crystal) must form at some higher concentrations if the surfactant is sufficiently soluble. Thus the general scheme is as follows ... 

Micelles with platelet or rod-like shapes were obtained in supersaturated aqueous solution containing a surfactant and an aromahc compound. In particular, chiral surfactants are known to produce enantiomeric precipitahon, while most of the others give symmetric micelles [45-47]. 

FIGURE 15.8. The most important micelle shapes include (a) normal spherical, (b) lamellar, (c) inverted spherical, (d) oblate ellipsoidal, and (e) prolate cylindrical or rod-shaped. 

The structure in the micellar region of the phase diagrams of potassium soaps has been analysed by Reiss-Husson and Luzzati (1969) using X-ray methods. A common feature in soaps of saturated fatty acids is that spherical micelles exist at low concentrations, and at increased concentrations a transition into rod micelles occurs. Sodium oleate, however, was found to give rod-shaped micelles at all concentrations. The micellar association and phase behaviour have been reviewed by Wenner-strom and Lindman (1979) and Lindman and Wennerstrom (1980). 

At low concentration of amphiphiles micelles are usually formed. Micelles typically contain some 20-100 monomeric molecules. In most cases they are spherical, but sometimes they adopt a rod-like shape. In the latter case, they contain more monomers. The radius of the sphere or the cylindrical, more or less worm-like, rod is comparable to the length of the apolar parts of the amphiphilic molecule, which is usually in the range of a few nanometers. Spherical micelles are extensively studied and well understood. 

Micelle shapes are determined to a large extent by a packing factor p) defined as p = v/a l, where v is hydrodynamic volume of surfactant molecule, 4 is the length of the tail, and is the head group cross-section area (see Figure 13.1). Whenp is equal to 1/3 or less, the surfactant will be cone shape and the micelles will be spherical. This is the most commonly encountered micelle shape. For p close to or equal to 1/2, the micelles are of cylindrical shape (rod like). Figure 13.1 shows different micelle shapes and the corresponding p values. 

The formation of CTAB rod-like micelles with molecular weight of 10 in the presence of KBr was reported by Debye and Anacker [42], About a decade ago, the salt-induced sphere-rod transition of alkyltrimethy-lammonium halides was extensively studied with the use of static light scattering and viscometry [43-46]. The formation of surfactant micelles in low-molecular electrolyte solution has been described as a two-step process at first, primary spherical micelles were formed and then, with further increase of salt concentration, micelles reorganized to the secondary rod-like shape [47]. It was also concluded that the salt-induced sphere-rod transition of the surfactant micelles is not caused by the change in water structure [48]. 

The hydrophilic-hydrophobic nature of amphiphilic molecules leads to their self-assembly into a variety of structures in aqueous solution, as will be discussed further in Section 4.10.2. Micelles are one of the main types of structure formed by the association of amphiphiles. They consist of a core of hydrophobic chains (often alkyl chains) shielded from contact with water by hydrophilic head groups, which may be ionic or nonionic. The hydrophilic units of surfactants form a micellar corona. Micelles can either be spherical or extended into an ellipsoidal or rod-like shape. This depends on the packing of the molecules, as discussed further in Section 4.10.1. In this section we consider spherical micelles, since these are usually the type formed at the critical micelle concentration. A spherical micelle is sketched in Fig. 4.14. Unassociated molecules coexisting with micelles are often called unimers, and this nomenclature is used here. 

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