The inverted hexagonal phase ▫${(\rm H}_{\rm II})$▫ belongs to the biologically most significant nonlamellar lipid phases in biomembranes. Hence the geometric properties and conditions of transition ...to the ▫${(\rm H}_{\rm II})$▫ phase are nowadays widely studied. In this chapter we offer a brief overview on the mechanics of the ▫${(\rm H}_{\rm II})$▫ lipid phase. In our derivation of the free energy of lipid monolayers, we assume that lipid molecules are in general anisotropic with respect to the axis perpendicular to the membrane plane. In our model the expression for the lipid monolayer free energy consists of two energy contributions: the bending energy which involves also a deviatoric term, and the interstitial energy which describes the deformation energy due to stretching of the phospholipid molecule chains.On the basis of the derived expression for the lipid monolayer free energy, we theoretically predict optimal geometry and physical conditions for the stability of the inverted hexagonal phase. Using the Monte Carlo simulated annealing method, we theoretically describe first steps in the ▫${\rm L}_\alpha - {(\rm H}_{\rm II})$▫ phase transition, which may contribute to a better understanding of different biologically important processes within biomembranes.
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