Driving force for liquid crystalline phases formation

Except for the lamellar phase, which is symmetrical around the middle of the bilayer, the different structures have a reversed counterpart in which the polar and nonpolar parts have changed roles. For example, a hexagonal phase is built up of hexagonally packed water cylinders surrounded by the polar head groups of the surfactant molecules and a continuum of the hydrophobic parts. Similarly, reversed (micellar-type) cubic phases and reversed micelles consist of globular water cores surrounded by surfactant molecules. The radii of the water cores are typically in the range 2-10 nm. 

6 Driving force for liquid crystalline phases formation 

One of the simplest methods for predicting the shape of an aggregated structure is based on the critical packing parameter P [30]. 

For a spherical micelle with radius r and containing n molecules each with volume 

The cross-sectional area of the hydrocarbon tail a is given by 

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