Optimal head group area

Larger aggregates seldom have spherical geometry, but tend to form cylindrical micelles. In this case, the diameter of the cylinders can usually be adjusted such that the head groups can cover their optimal head group area Uq, and the interaction free energy per surfactant reduces to the constant The size distribution for cylindrical micelles is then exponential in the limit of large N,... 

What is meant by the optimal head group area of a surfactant What is the packing parameter (P Explain how packing considerations can be used to determine the possible shapes of the micellar aggregates. 

These ideas can be formalised in terms of statistical mechanics to some extent, and an outline of the main ideas is given in the following section. We remark parenthetically that there are profound difficulties confronting the definition of an aggregate. The nature of the hydrophobic free energy of transfer of a hydrocarbon from water to the hydrophobic core of a micelle can be measured, but its temperature dependence is not understood because it depends on water, an unknown quantity. For the same reasons, solution theory, does not even tell us whether mole fractions or mole volumes are the correct ratios to use to determine entropy. However, provided certain assumptions are allowed [62-65], then simple rules emerge. The rules are if v is the hydrocarbon chain volume, a the head-group area, and 1 of an optimal... 

Here, v is the hydrocarbon chain volume, a<> is the optimal head group surface area, and is the critical chain length. For packing parameters between and 1, amphiphiles should form flexible bilayers (vesicles), or planar bilayers as the packing parameter approaches 1. On the contrary, a packing paramter less than j should hinder the formation of bilayers in particular, the theory predicts micelle formation. 

The optimal area Qq can be used as a practical criterion for the shape of the micelle versus the size of the head group and tail of the surfactant, assuming that the... 

Then, since there is an optimal area per head group ao, there is also an optimal aggregation number no and an optimal radius Rc,o at which /xJJ is a minimum ... 

If the optimal micelle core radius i c,o from Eq. (12-10) exceeds the maximum effective tail length Ic (i.e., if Rc,o/ic = vjaoic > 1), then optimally sized spherical micelles are not possible, and either the surface area per head group must deviate from its optimal value Up, or there will be a transition to a shape with a higher surface-to-volume ratio. 

At moderate surfactant concentration, the micelle shape is determined by the value of the surfactant packing parameter P=v/aol, where v and I are the volume and length of the hydrophobic moiety (alkyl chain), and Uq is the optimal surface area occupied by one surfactant at the micelle-water interface. - It is important to realize that the value of is determined by the cross-sectional area of the surfactant head group and also by the various interactions at play in micelle formation.Surfactants characterized by values of P<113 give rise to sphericall... 

In fact, the predominant forces determining association of amphiphiles in well defined structures (e.g., micellar, cylindrical, lamellar) are the hydrophobic effect, tending to associate chains together, and repulsions between head groups. The latter are of electrostatic origin for ionic surfactants and steric for non-ionic surfactants. These two forces tend respectively to diminish or increase the interfacial area per molecule at the water/chain interface. The result is an optimal interfacial area Uq. 

Fig. 15.4. ToF-SIMS images of three different ceii types prepared with the reported optimized ceiiuiar preparation procedure, in the left column are totai ioh images, in the right column composite images of potassium ion blue) and m/z = 184, a fragment of the phosphochoiine head group (red), (a and b) MCF7 human breast cancer cells, (c and d) MDCK canine kidney cells, and (e and f) NIFI/3T3 mouse fibroblast. Note the excellent localization of potassium in the area immediately surrounding the cells and the localization of phophocholine on the cellular region. Reproduced from (30) with permission from Elsevier Science.

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