We examine the phase diagram of starblock copolymers with monodisperse diblock arms. Within a self-consistent-field theory, we calculate the phase diagrams for starblocks with equal Kuhn lengths for all monomers, and = 1,3, 5, and 9 arms. For = 1 and 5, we also consider the effect of asymmetric Kuhn lengths. We find all phase diagrams to be topologically identical to that of diblocks (Af = 1). In each case, the lamellar, gyroid, hexagonal, and cubic phases are found to be stable. The region of stability of the gyroid phase is found to increase as the number of arms is increased. Regions in which the double-diamond and catenoid-lamellar phases are nearly stable are also located.

We study the microphases of linear multiblock copolymers formed from monodisperse Aand B-type blocks in the limit in which the number of blocks is large. We find the lamellar, gyroid, hexagonal, and cubic microphases to be stable. Monocontinuous catenoid-lamellar and bicontinuous double-diamond phases are nearly stable in the region between the lamellar and hexagonal phases where the gyroid phase is stable. In the weak-segregation limit, the gyroid phase is not stable, and along the lamellar to hexagonal boundaries a bicontinuous catenoid-lamellar phase is close to stability. In the strong-segregation limit, we can examine only the lamellar phase, and we determine the scaling behavior of its period and interfacial width. We conclude that multiblocks exhibit identical scaling exponents as diblocks.

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