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,... 

The relation between head-group area and extended chain length and volume of the apolar groups favors formation of vesicles or bilayers from these twin-tailed surfactants. However, it seems that DDDAOH forms vesicles only in dilute solution, because the solution becomes viscous with increasing [surfactant] which is incompatible with the presence of approximately spherical vesicles. It appears that the solution then contains long, non-vesicular aggregates (Ninham et al., 1983). 

The order parameter is directly available from the calculations and the SCF results are given in Figure 17. The absolute values of the order parameter are a strong function of head-group area. Unlike in most SCF models, we do not use this as an input value it comes out as a result of the calculations. As such, it is somewhat of a function of the parameter choice. The qualitative trends of how the order distributes along the contour of the tails are rather more generic, i.e. independent of the exact values of the interaction parameters. The result in Figure 17 is consistent with the simulation results, as well as with the available experimental data. The order drops off to a low value at the very end of the tails. There is a semi-plateau in the order parameter for positions t = 6 — 14,... 

What is the total charge on a CTAB micelle if the head-group area is 45 A and the micelle is 40 A in diameter ... 

In addition to its simplicity, such a geometric argument can also be used to predict the changes in the structure of the aggregates as variables such as pH, charge, electrolyte concentration, and chain length of the tail are varied. The importance of the relative effects of the head group area and the size of the tails was first emphasized by Tatar (1955), and the details were developed subsequently by Tanford (1980) and others (see Wennerstrom and... 

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. 

The most problematic quantity in the definition of the surfactant parameter is the head group area. For ionic surfactants a a depends on both the electrolyte and the surfactant concentration. In this case the surfactant parameter is only of limited usefulness for a quantitative... 

Example 12.2. The head group area of SDS in water (no additional background salt) is 0.62 nm2. This leads to a surfactant parameter of... 

Bilayers are preferentially formed for Ns = 0.5...1. Lipids that form bilayers cannot pack into micellar or cylindrical structures because of their small head group area and because their alkyl chains are too bulky to fit into a micelle. For bilayer-forming lipids this requires that for the same head group area a a, and chain length Lc, the alkyl chains must have twice the volume. For this reason lipids with two alkyl chains are likely to form bilayers. Examples are double-chained phospholipids such as phophatidyl choline or phophatidyl ethanolamine. Lipids with surfactant parameters slightly below 1 tend to form flexible bilayers or vesicles. Lipids with Ns = 1 form real planar bilayers. At high lipid concentration this leads to a so-called lamellar phase. A lamellar phase consist of stacks of roughly parallel planar bilayers. In some cases more complex, bicontinuous structures are also formed. As indicated by the name, bicontinuous structures consist of two continuous phases. 

Surfactants with very small head group areas such as cholesterol tend to form inverted micelles (Fig. 12.7). Their head groups point into the center of the micelle while the hydrophobic tails form the continuous, hydrophobic outer region. Inverted structures such as inverted liposomes, are also formed in nonpolar solvents such as toluene, benzene, cyclohexane instead of water [534]. 

Comparing CMCs of a nonionic and an ionic surfactant with approximately equal head-group area (C12E08, C12Pyr and C12E02S0y) makes it apparent that the CMC of the nonionic surfactant is the lowest. It also demonstrates the effect of electrostatic repulsion. While hydrophobic interactions drive micellization, they are counteracted by steric and electrostatic interactions of the headgroups, both of which limit the coverage of the interface with surfactant molecules. 

Spherical micelles are formed where the value of surfactant packing parameter is less than 1/3 (single chain surfactants with large head group areas such as anionic surfactants). The spherical aggregates are extremely small and their radius is approximately equal to the maximum stretched out length of the surfactant molecule. 

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