A The Packing Parameter

The shape of the micelle produced in aqueous media is of importance in determining various properties of the surfactant solution, such as its viscosity, its capacity to solubilize water-insoluble material (Chapter 4), and its cloud point (Chapter 4, Section IIIB). 

At the present time, the major types of micelles appear to be (1) relatively small, spherical structures (aggregation number 100), (2) elongated cylindrical, rodlike micelles with hemispherical ends (prolate ellipsoids), (3) large, flat lamellar 

In aqueous media, the surfactant molecules are oriented, in all these structures, with their polar heads predominantly toward the aqueous phase and their hydro-phobic groups away from it. In vesicles, there will also be an aqueous phase in the interior of the structure. In ionic micelles, the aqueous solution-micelle interfacial region contains the ionic head groups, the Stern layer of the electrical double layer with the bound counterions, and water. The remaining counterions are contained in the Gouy-Chapman portion of the double layer that extends further into the aqueous phase. For POE nonionics the structure is essentially the same, except that the outer region contains no counterions, but includes coils of hydrated POE chains. 

The interior region of the micelle, containing the hydrophobic groups, has a radius approximately equal to the length of the fully extended hydrophobic chain. The aqueous phase is believed to penetrate into the micelle beyond the hydrophobic head groups, and the first few methylene groups of the hydrophobic chain adjacent to the hydrophobic head are often considered in the hydration sphere. It is therefore useful to divide the interior region into an outer core that may be penetrated by water and an inner core from which water is excluded (Muller, 1972). 

In nonpolar media, the structure of the micelle is similar but reversed, with the hydrophilic heads comprising the interior region surrounded by an outer region containing the hydrophobic groups and nonpolar solvent (Hirschhom, 1960). Dipole-dipole interactions hold the hydrophilic heads together in the core (Singleterry, 1955). 

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