Analytical Weak-Segregation Theory of Bicontinuous Phases in Diblock Copolymers

Abstract

We compute phase diagrams for diblock copolymers in the mean-field weak- segregation regime as a function of the fraction f of A-monomers and the repulsive interaction XN. We include the ordered bicontinuous double-diamond (OBDD) phase (space group Pn3m) and the gyroid phase (space group Ia3d) as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and larnellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher (220) reflections in addition to the (211) fundamental. The gyroid free energy is favored by terms of the form ~(~~~j ~bj220j and ~b(~i~j~bj220j; the analogous terms are not permitted for OBDD.