Optimal Surface to Tail Volume Ratio

It is evident that the optimal interface between the water and amphiphilic molecules is the surface area of the hydrophilic part. The shapes in which the molecules arrange themselves depend partly on the optimal siuface area, as well as partly on the fluid volume of the hydrocarbon chains and the maximum length at which they can still be considered fluid. Although many structures can fit the geometry, one is usually best from a thermodynamic perspective. Large structures create too much order, while small structures cause the surface area to be larger than optimal, so a medimn-sized structure usually wins out. 

The interfacial curvature is determined by the effective area of the head group, a, with respect to length I and occupied voliune V of the hydrophobic tale. Their ratio determines the surfactant packing parameter as N,. = 

The association number p (the number of molecules forming a micelle) for spherical micelle can be expressed by simple geometrical arguments as  

A spherical micelle. The packing of amphiphilic moleciiles is controlled by the effective cross-sectional area of the head group, a and the hydrophobic chain of length, I and volume, V. These quantities define the surfactant packing parameter. 

In this expression, R ,isthe radius of the micelle. Similarly, we can express p as  

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