First discovered in surfactant-water liquid crystalline systems, so-called ‘bicontinuous cubic phases’ have the property that hydropnilic and lipophilic microdomains form interpenetrating networks conforming to cubic lattices on the scale of nanometers. Later these same structures were found in star diblock copolymers, where the simultaneous continuity of elastomeric and glassy domains gives rise to unique physical properties. Today it is well-established that the symmetry and topology of such a morphology are accurately described by one of several triply-periodic minimal surfaces, and that the interface between hydrophilic and hydrophobic, or immiscible polymer, domains is described by a triply-periodic surface of constant, nonzero mean curvature. One example of such a dividing surface is shown in figure 5.The study of these structures has become of increasing importance in the past five years for two reasons:1)Bicontinuous cubic phase liquid crystals are now being polymerized to create microporous materials with monodispersed pores and readily functionalizable porewalls; figure 3 shows a TEM from a polymerized surfactant / methylmethacrylate / water cubic phase; and2)Compelling evidence has been found that these same morphologies describe biomembrane systems in a wide range of cells.
Translation covers of some triply periodic Platonic surfaces
