Micelle Dill model

Figure 4 A cross-sectional schematic of the Dill model for the micelle. Counterions are not shown. (From Ref. 2 with permission.)...

In the model of micelle proposed by Dill et al. [21], the hydrocarbon chains of the surfactants are more randomly distributed, bearing in mind statistical considerations (Fig. 4). A considerable number of hydrocarbon chains are exposed to the water at the surface. 

The models of Fromherz and Dill allow the solubilization of hydrophobic solutes near the surface of the micelle and explain how these solutes (in addition to part of the hydrocarbon chains of the surfactants) can be in contact with the water when they are associated with the micelle. However, the debate concerning the structure of the clusters is not yet finished and research on the subject continues. 

Dill, K.A., Flory, P.J. (1981). A stereochemical model of spherical micelles, Proc. Natl. Acad. Sci USA 78 676. 

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 standard picture of ionic micelles forms a common starting point for three recent attempts at modelling the state of the chains in amphiphilic aggregates Dill and Flory s lattice model [15, 16], Fromherz surfactant-block model [18] and a model devised by the present author [19-21]. For each of these models, it is necessary to make further assumptions which are not part of the standard picture. These further assumptions are necessary in order to render the models soluble. 

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