Spherical micelles, cylinders, and bilayers

One characteristic property of surfactants is that they spontaneously aggregate in water and form well-defined structures such as spherical micelles, cylinders, bilayers, etc. (review Ref. [524]). These structures are sometimes called association colloids. The simplest and best understood of these is the micelle. To illustrate this we take one example, sodium dode-cylsulfate (SDS), and see what happens when more and more SDS is added to water. At low concentration the anionic dodecylsulfate molecules are dissolved as individual ions. Due to their hydrocarbon chains they tend to adsorb at the air-water interface, with their hydrocarbon chains oriented towards the vapor phase. The surface tension decreases strongly with increasing concentration (Fig. 3.7). At a certain concentration, the critical micelle concentration or... 

The most straightforward morphologies (i.e. spheres, cylinders and bilayers) are obtained by the combination of parameters given in Table 7.3. From this table it is evident that an increasing hydrophobic/hydrophilic ratio results in a change in aggregate morphology from spherical to rod-like micelles to vesicles. 

Spherical micelles have constant size and their spatial distribution is essentially that of a point particle gas, confined within the volume defined by the quantity of aqueous solvent. By their one- or two-dimensional nature, the long cylinders and bilayers are more complex. They possess internal degrees of freedom affecting structure and physical properties of the phases they make up. 

The previous discussion is grossly simplified. There are some surfactants, notably those that have two chains per head, which do not form micelles at all. Furthermore, at higher concentrations of conventional surfactants, it is possible to create cylinders and bilayers, rather than simple spherical micelles. Still, for most ordinary applications of surfactants, the normal trend is to avoid such high concentrations, which generate highly viscous systems that are more difficult to handle. 

It thus seems that the basic physics of the process of micellization is well understood, but one can hardly expect the theories to be terribly quantitative. Some properties, such as the dimensions of the micelle, are not overly sensitive to the details of the approximation scheme, but other properties, such as cmc, the aggregation number and the thermodynamics of micelle formation are much more volatile in their behaviour. The theories presented all assumed a monodisperse micelle distribution, but in fact one can use the methods to calculate the full distribution from equations (42) and (43), and indeed the distribution does turn out to be narrowly peaked. One can also use the theories to estimate the relative stabilities of spherical micelles vis-a-vis non-spherical micelles, infinite cylinders and bilayers, and preliminary studies indeed indicate the possibility of infinite cylinders at copolymer concentrations less than the cmc. The possible formation of these and other structures should be more thoroughly investigated. 

The structures formed by polystyrene-poly(propylene imine) dendrimers have also been analyzed. Block copolymers with 8, 16, and 32 end-standing amines are soluble in water. They have a critical micelle concentration of the order of 10"7 mol/1. At 3x10 4 mol/l they form different types of micelles. The den-drimer with eight amine groups (80% PS) form bilayers. The dendrimer with 16 amine groups (65% PS) forms cylinders and the dendrimer with 32 amine groups (50% PS) forms spherical micelles [38,130,131]. These are the classical lamellar, cylindrical, and spherical phases of block copolymers. However, the boundary between the phases occurs at very different volume fractions, due to the very different packing requirements of the linear polymer and spherical dendrimer at the interphase. 

Figure 3.1 (Top ) Schematic view of processes controlled by curvature in endocytosis. Adapted from [2]. (Bottom ) Representative of the simplest surfactant aggregates spherical micelles v/al between 1/3 (spheres) and 1/2 (cylinders) planar bilayers (v/al = 1) inverted micelles...

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 ... 

One can classify micelles into different types with morphologies varying from spherical to vesicular or other structures, such as bilayers, cylinders, and inverse micelles (Figure 2.1). 

Moreover, on the same basis, one can rather readily deal with the other geometries cylinders, planar bilayers, and curved bilayers, thus enabling theoretical calculations of the relative stabilities of spherical, rod-shaped, and disc-shaped micelles as well as geometrically closed vesicles [60]. 

Cubic phases are the third concentrated self-assembly state commonly formed by surfactants. They include a variety of structures, the simplest being analogous to atomic crystals but in which spherical micelles take the place of individual atoms on the lattice points. Other more complex structures are also known or postulated, including ordered, interpenetrating networks of branched cylinders and deformed bilayers which form... 

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