Three types of triply periodic minimal surfaces (TPMSs), gyroid (G), diamond (D), and primitive (P) TPMSs, are frequently observed in natural and artificial material systems. Inverse bicontinuous cubic (QII) phase of a lyotropic liquid crystals is one of the examples, in which bilayer membrane of amphiphile molecules resides on the TPMSs.

Recently, I am trying to aplly X-ray crystallography to the single crystal regions of the QII phases. In this talk I will outiline the method and present the result of structural analyses of the QII phases in monoolein/water systems.

Electron density maps of the monolein/water systems showed that the lipid bilayer structures were located on the TPMSs. It was also found unexpectedly that the electron densities of bilayer membranes varied depending on the Gaussian curvatures of TPMSs. This could be interpreted that the fluctuation of the position of the bilayer membrane depends on the Gaussian curvature: the fluctuation becomes smaller as the Gaussian curvature is close to 0, that is, the larger the Gaussian curvature is.