Polar-Nonpolar Interfaces of Inverse Bicontinuous Cubic Phases in Phytantriol/Water System are Parallel to Triply Periodic Minimal Surfaces

We investigated two distinct lyotropic liquid crystal inverse bicontinuous cubic phases of phytantriol/water mixtures by small-angle X-ray crystallography of the single-crystal regions. Reconstructed electron density maps revealed hydrophilic head and hydrophobic tail regions of the phytantriol bilayer membranes and water regions. The bilayer membranes are shown to be located on the D and gyroid triply periodic minimal surfaces. To investigate the structures of the polar-nonpolar interfaces, we optimized two models: a parallel surface model and a constant mean curvature surface model. The parallel surface model agreed well with the X-ray data, and the R factors, which show the degree of agreement between those structural models and the data, were less than 0.04. In stark contrast, the constant mean curvature surface model deviated significantly from the data, and the R factors were around 0.15. We therefore conclude that the polar-nonpolar interface of the inverse bicontinuous cubic phase of the phytantriol/water system is close to a parallel surface to a triply periodic minimal surface.