Effects of Polydispersity on the Stability of Complex Spherical Packing Phases in Diblock Copolymers

The effects of polydispersity on the relative stability of complex spherical packing phases, i.e., the Frank-Kasper phases, self-assembled from conformationally asymmetric AB diblock copolymers are studied using the self-consistent field theory (SCFT). Previous experimental and theoretical studies have revealed that the Frank-Kasper σ-phase could be stabilized by the conformational asymmetry between the A- and B-blocks. The current SCFT results reveal that polydispersity in the minority A-blocks could enhance the stability of the complex spherical packing phases, resulting in a wider stable region of the Frank-Kasper σ-phase in the phase diagram. Furthermore, the effects of polydispersity on the formation of the Frank-Kasper σ-phase depend on the chain length distribution of the polymers. Different chain length distributions with a given polydispersity index could have very different effects on the stability region of the Frank-Kasper σ-phase. The mechanisms of stabilizing the complex spherical packing phases are analyzed by examining the chain-length driven local segregation of the block copolymers.