Spheres, micelle shapes

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 ... 

Israelachvili et al. [20] have considered the geometrical limitations that place restrictions on the allowed shape of a micelle. They gave a critical condition for the formation of rod and sphere micelles. The geometrical constant, /, is given as follows ... 

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. 

Figure 22.1 The amphiphilic nature of phospholipids in solution drives the formation of complex structures. Spherical micelles may form in aqueous solution, wherein the hydrophilic head groups all point out toward the surrounding water environment and the hydrophobic tails point inward to the exclusion of water. Larger lipid bilayers may form by similar forces, creating sheets, spheres, and other highly complex morphologies. In non-aqueous solution, inverted micelles may form, wherein the tails all point toward the outer hydrophobic region and the heads point inward forming hexagonal shapes.

One of the several shapes that micelles can take is laminar. Since the ends of such micelles have their lyophobic portions exposed to the surrounding solvent, they can curve upwards to form spherical structures called vesicles. Vesicles are spherical and have one or more surfactant bilayers surrounding an internal pocket of liquid. Multi-lamellar vesicles have concentric spheres of uni-lamellar vesicles, each separated from one another by a layer of solvent [193,876] (Figure 14.1). The bilayers are quite thin (-10 nm) and are stabilized by molecules such as phospholipids, cholesterol, or other surfactants (Figure 14.2). Vesicles made from phospholipid bi-layers are called liposomes. Liposomes can be made by dispersing phospholipids (such as lecithin) into water and then agitating with ultrasound. 

The size and shape of micelles have been a subject of several debates. It is now generally accepted that three main shapes of micelles are present, depending on the surfactant structure and the environment in which they are dissolved, e.g., electrolyte concentration and type, pH, and presence of nonelectrolytes. The most common shape of micelles is a sphere with the following properties (i) an association unit with a radius approximately equal to the length of the hydrocarbon chain (for ionic micelles) (ii) an aggregation number of 50-100 surfactant monomers (iii) bound counterions for ionic surfactants (iv) a narrow range of concentrations at which micellization occurs and (v) a liquid interior of the micelle core. 

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