Microphase and macrophase separations in binary blends of diblock copolymers

Phase behavior of blends of two AB diblock copolymers, with the long one at relatively strong segregation, is studied using the self-consistent field theory, focusing on the effect of compositions of the two block copolymers and their length ratio. In order to carry out extensive calculations on the large parameter space, a unit-cell approximation is employed, in which the mean-field equations are solved using a Bessel function expansion. Phase diagrams are constructed for four typical series of blends by comparing the free energies of the different ordered phases including lamellae, cylinders, and spheres. The results reveal that the competition between macro- and microphase separation leads to complex phase behavior. When the length ratio of the two block copolymers is small, the short copolymers tend to segregate to the A/B interfaces, inducing multiple order-order phase transitions including reentrant phase transitions in some blends. When the length ratio of the two diblock copolymers is sufficiently large, macrophase separation may take place. The predicted phase diagrams are compared with available experiments. Density profiles of typical ordered structures are presented to understand the self-organization of the polymer chains. The energetics of the blends is introduced to account for the appearance of the macro- and microphase separations.