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Macromolecules, Vol.29, No.4, 1091-1098, 1996
Unifying Weak-Segregation 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), close-packed spheres (CPS), and the bicontinuous cubic network with symmetry (Q()). 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 phase is not stable above chi N similar to 60. Along the L/Q phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (Q) 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.
Keywords:DENSITY-FUNCTIONAL THEORY;MICROPHASE-SEPARATION TRANSITION;MOLECULAR-WEIGHT DEPENDENCE;CATENOID-LAMELLAR PHASE;MEAN-FIELD-THEORY;DIBLOCK-COPOLYMER;MICRODOMAIN MORPHOLOGY;IMMISCIBLE POLYMERS;THIN-FILMS;MELTS