Systematic approach to bicontinuous cubic phases in ternary amphiphilic systems

The Fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures i n the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both single and double structures are investigated; they correspond to sys tems with one or two monolayers in a unit cell, respectively. We shaw how a nd why single structures can be made to approach triply periodic minimal su rfaces very closely, and give improved nodal approximations for G, D, I-WP, and P surfaces. We demonstrate that the relative stability of the single s tructures can be calculated from the geometrical properties of their interf aces only. The single gyroid G turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity. The representations are us ed to calculate distributions of the Gaussian curvature and H-2-nuclear-mag netic-resonance band shapes for C(P), C(D), S,C(Y), and F-RD surfaces. [S10 63-651X(99)01005-3].