Statistical honeycomb

The shapes of these self-assemblies are as varied as the capacity of the molecules to weave through space will allow. The accessible interfacial geometries span a rich range of structures from spheres and planes to highly intercormected bicontinuous honeycombs. So how are the structures of these complex liquid crystalline and disordered assemblies best described and understood Typically, the problem is tackled by recourse to thermodynamic principles. A complete statistical mechanical treatment is out of the question. (The difficulty is a fundamental one. We do not yet know how to write down a partition faction that describes the full ensemble of possible aggregate shapes and their associated free energies.)... 

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