Shapes of micelles

As is the case for all macromolecules, the analyses of the size and shapes of micelles become of importance, when considering their colligative properties. Since the interfacial area between the macromolecule and the solvent determines the interactions between these species, it is obvious that the shape attained under given temperature and pressure will be determined by the lowest free energy of the macromolecule in solvent phase. These considerations have been the subject of analyses in various literature reports [27,311. 

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  

In recent studies the micelles have been considered as comprised of hydrocarbon and polar groups regions [1,4,41]. In the case of spherical micelles it is reasonable to accept that the hydrocarbon interior would also be of spherical shape. Thus the hydrocarbon 

One can determine whether the hydrocarbon core is spherical or ellipsoidal from these relations. 

The data for various ionic and nonionic (Triton X-100) surfactants are given in Table 1 as examples [4). It is conclusively observed that ionic micelles (e.g. n-CgSO Na, 

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The size and shape of micelles also are affected by fluormation Whereas hydrocarbon surfactants usually form spbencal micelles, linear fluorocarbon surfactants tend to produce larger rodhke speacs [31, 32 This is attnbuted to two inherent charac-tenshcs of the (CF2) chain (1) it adopts a hehcal rather than a linear zigzag conformation [dd 34, 35, 36], and (2) it is much suffer than the (CH2) cham [d5 37, 38] The relatively sbff, helical (CFj) chains thus prefer cylindrical to sphencal packing... 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

MOLECULAR ARCHITECTURE OF SURFACTANTS, PACKING CONSIDERATIONS, AND SHAPES OF MICELLES... 

Another possible mechanism involves the effect of saponins on micelle formation. Saponins are known to alter the size or shape of micelles (Oakenfull, 1986 Oakenfull and Sidhu, 1983), an observation that is consistent with decreased bile acid absorption (Stark and Madar, 1993) and increased fecal bile acid excretion (Malinow et al., 1981 Nakamura et al.,1999). Saponins may also directly bind bile acids (Oakenfull and Sidhu, 1989), which would presumably interfere with micelle formation and decrease cholesterol absorption. Other studies have found that saponins decrease the absorption of fat-soluble vitamins (Jenkins and Atwal, 1994) and triglycerides (Han et al., 2002 Okuda and Han, 2001), indicating decreased micelle formation. However, direct evidence showing impaired micelle formation in vivo is lacking. Moreover, Harwood et al. (1993) reported no change in bile acid absorption or interruption of the enterohepatic circulation of bile acids in hamsters fed tiqueside, despite significant reductions in cholesterol absorption. 

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. 

Two other shapes of micelles may be considered, namely, the rod-shaped micelle suggested by Debye and Anacker and the lamellar micelle suggested by McBain. The rod-shaped micelle was suggested to account for the light-scattering results of cetyl trimethyl ammonium bromide in KBr solutions, whereas the lamellar micelle was considered to account for the X-ray results in soap solutions. A schematic picture of the three type of micelles is shown in Fig. 2. 

FIGURE 2 Various shapes of micelles following McBain (II). [Adapted from Hartley (1936) and Debye and Anaker (1951).]... 

We have already alluded to geometric limitations which place restrictions on the allowed shapes of micelles, and it is clear that packing constraints must be invoked for a proper treatment of self-assembly, for, in the absence of any such restrictions, spherical micelles will always be thermodynamically favoured over other shapes like cylindrical micelles or bilayers. There must then be some overriding factor that... 

In Fig. 2, a variety of micelle structures are shown. Typical shapes of micelles are spherical, rod-like, and worm-like. At high concentrations of surfactant or at high concentrations of counterions, liquid crystals are usually formed. Hexagonal, cubic, and lamellar are common liquid crystal phases that occupy much of a... 

It is also known that additives may change the size and shape of micelles.At a certain point, as the surfactant or additive concentrations change, ionic micelles may change shape from spherical or nearly spherical to rodlike or other elongated forms. This may also affect the solubilization of the additive. It appears that alkane solubilization increases as the micelles become large, rodlike aggregates, whereas for polar additives like alcohols the solubilization decreases. ... 

Nelson et al. used Monte Carlo techniques and were able to obtain the equilibrium shape of micelles with various amounts of solubilized oil. However, their surfactant and oil molecules had fewer segments than those in the work just described. 

The Dill-Flory model may be considered as a more rigorous version of the Hartley model (30). Both models are readily applied to other shapes of micelles, such as rods, discs, bilayers, and vesicles. Also, it follows that diameters of spherical, rodlike, and disclike micelles cannot exceed the total length of two hydrocarbon chains in all-trans conformation. The number of entities in one micelle, i.e. the aggregation number s, is therefore readily estimated for any given chain length r. Assuming equal densities p (= 0.777 g/cm ) for micelles and solid n-alkanes, r may be obtained from the volume v and the constant cross section A (= 2.385 x 10 cm ) of alkane chains ... 

The size and shape of micelles are determined by a delicate balance between various factors, such as chemical constitution, electrical repulsion of head groups, amphiphile and solute concentration, and temperature. The addition of electrolytes will in general raise aggregation numbers of ionic micelles and may even induce sphere-rod transitions. Temperature has an enormous influence on aggregation numbers of nonionic micelles, but only a little effect on those of ionic and amphoteric micelles. There is a vast literature covering the subject (24,25,36). 

Due to the d3mamic nature and to the small micellization enthalpies (25), micelles and other aggregates of amphiphilic molecules are sensitive in shape and size to various additives. It has been known for a long time that the addition of salt to solutions of ionic spherical micelles induces the formation of rodlike aggregates (144), but also the solubilization of alcohols, alkanes, and aromatic liquids (36,145-147) has consequences on aggregation numbers and on shapes of micelles. 

An extension of the Tanford s (1980) treatment of the shapes of micelles, based on the molecular-shape analysis and the concept of the shape parameter (ratio between the nonpolar and polar cross-section areas), was introduced by Israelachvili (1991) for a qualitative understanding of the topology of lipid aggregates with different lipid compositions. However, the liposome models are approximate, and a rigorous thermodynamic analysis fails because liposomes are not at the thermodynamic equilibrium. The rigorous analysis would yield a very narrow size distribution, which is never observed in practice, as well as the spontaneous formation, while a high-energy process is typically needed to produce liposomes. 

As mentioned earlier, studies of simple linear surfactants in a solvent (i.e, those without any third component) allow one to examine the sufficiency of coarse-grained lattice models for predicting the aggregation behavior of micelles and to examine the limits of applicability of analytical lattice approximations such as quasi-chemical theory or self-consistent field theory (in the case of polymers). The results available from the simulations for the structure and shapes of micelles, the polydispersity, and the cmc show that the lattice approach can be used reliably to obtain such information qualitatively as well as quantitatively. The results are generally consistent with what one would expect from mass-action models and other theoretical techniques as well as from experiments. For example. Desplat and Care [31] report micellization results (the cmc and micellar size) for the surfactant h ti (for a temperature of = ksT/tts = /(-ts = 1-18 and... 

To investigate the shape of micelles in EG,/Sii4C3EO systems, SAXS measurements were performed at 60 °C. The scattered intensities I q) are shown in Figure 10.4. The concentration of SiuCsEOn in EG, is fixed to 2 wt96. 

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