Scattering patterns of self-assembled gyroid cubic phases in amphiphilic systems

We present scattering patterns (with surface contrast) for five triply periodic minimal surfaces of the Ia3̄d cubic symmetry. We obtain a very good agreement between the numerically obtained spectrum and experimental patterns for the simple gyroid G structure. We show the scattering patterns for four gyroid GX1, GX2, GX3, and GX5 structures of a complex topology. We show how the scattering patterns change with increasing complexity of the unit cell of the structure. The spectra of the complex structures can give wrong estimates about the cubic cell parameter and even wrong establishment of the space symmetry group. Thus the correct recognition of the structure present in the system requires the analysis of the intensities of the peaks and comparison with numerically obtained spectra.