Unifying weak- and strong-segregation block copolymer theories

A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (Q<Im(3)over bar m>), close-packed spheres (CPS), and the bicontinuous cubic network with <Ia(3)over bar d> symmetry (Q(<Ia(3)over bar d>)). The CPS phase exists in narrow regions along the order-disorder transition for chi N greater than or equal to 17.67. Results suggest that the Q<Ia(3)over bar d> phase is not stable above chi N similar to 60. Along the L/Q<Ia(3)over bar d> phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (Q<Pn(3)over bar m>) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and comparisons are made with our more accurate calculation.