Bending frustration of lipid-water mesophases based on cubic minimal surfaces

Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures an d consist of a lipid bilayer forming a cubic minimal surface, thereby divid ing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a mini mal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we c alculate for seven different structures (G, D, P, I-WP, C(P), S, and F-RD). We show that the free-energy densities of the structures G, D, and P are c onsiderably lower than those of the other investigated structures due to th eir narrow distribution of Gaussian curvature. The Bonnet transformation be tween G, D, and P implies that these phases coexist along a triple line, wh ich also includes an excess water phase. Our model includes thermal membran e undulations. Our qualitative predictions remain unchanged when higher ord er terms in the curvature energy are included. Calculated phase diagrams ag ree well with the experimental results for 2:1 lauric acid/dilauroyl phosph atidylcholine and water.