Micelles geometrical considerations

The effect characteristic of a multi-chain hydrophobe, that is, increase in the cmc and simultaneous decrease in the cloud point, appears to be inconsistent with the well-known HLB concept in surfactants. Tanford has pointed out that based on geometric considerations of micellar shape and size, amphiphilic molecules having a double-chain hydrophobe tend to form a bilayer micelle more highly packed rather than those of single-chain types ( ). In fact, a higher homologue of a,a -dialkylglyceryl polyoxyethylene monoether has been found to form a stable vesicle or lamellar micelle (9 ). Probably, the multi-chain type nonionics listed in... 

The important role played by the curve Tc can also be understood in terms of these geometrical considerations. Indeed, it would clearly be impossible to form the spherical core of a micelle using rigid chains (when T < Tc). Observing that Fig. 4.2 corresponds to the lower right part of Fig. 4.3 rotated by 90°, we find that appearance of micelles does indeed coincide with Tc at low dilutions. 

The experimental determination of an unequivocal shape for small micelles such as those formed by ionic surfactants in the absence of added electrolyte and close to the CMC has not yet proved feasible. Although for the purposes of interpretation of experimental data it is usual to assume micellar sphericity, several authors [66-69] have shown from geometrical considerations that most of the common surfactants with a single unbranched hydrocarbon chain cannot... 

The Triton X-100 micelle is considered by many workers to be spherical [70,71]. From geometrical considerations, Robson and Dennis [72] have shown, however, that a spherical micelle would be possible only if several oxyethylene chains were embedded in the hydrophobic core (Fig. 3.3a). These authors consider that an oblate (Fig. 3.3b) rather than prolate (Fig. 3.3c) micelle would be most consistent with intrinsic viscosity measurements and volume calculations. Small-angle X-ray scattering measurements [73], conductivity and viscosity measurements [74] were also more consistent with an oblate ellipsoid of revolution rather than a prolate equivalent. 

For the polyoxyethylated ether type of non-ionic surfactant, increase of the length of the polyoxyethylene chain caused an increase in the CMC and a decrease in the micelle size (Table 3.6). Increasing the polyoxyethylene chain length makes the monomer more hydrophilic and the CMC increases. The same effect may be partially responsible for the decrease in micellar size with the increased chain length, but other factors, including possible geometric considerations of the packing of the monomer into the micelles may be involved. 

Unlike aqueous surfactant solutions in which micellar size and shape may vary considerably, small spherical micelles appear to be the most favored, especially when the reduction of solvent-polar group interactions is important. In much the same way as in water-based systems, geometric considerations often play an important role in determining micelle size and shape. Many materials that commonly form nonaqueous micellar solutions possess large, bulky hydrocarbon tails with a cross-sectional area significantly greater than that of the polar head group. Typical examples of such materials are sodium di-2-ethylhexylsulfosuccinate and sodium dinonylnaphthalene sulfonate ... 

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