Stability of Complex Spherical Packing Phases in Low-Molecular-Weight Diblock Copolymers

Block copolymers are known for their ability to self-assemble into an array of ordered structures. Of special interest are the spherical packing phases due to their similarity to the atomic crystals. Until the past decade, the packing arrangement was believed to be primarily body-centered cubic for diblock copolymers. However, recent experimental and theoretical studies have revealed the emergence of various complex spherical phases including the Frank-Kasper phases. Qualitatively, the agreement between experimental and theoretical phase behaviour of diblocks is remarkable. On the other hand, quantitative differences still exist. These discrepancies could be due to numerous factors, such as polydispersity and the non-Gaussian nature of low-molecular-weight polymers used in experiments. In this work, we examine the formation of complex spherical phases for low-molecular-weight polymers with conformational asymmetry. Using the self-consistent field theory applied to freely-joint polymer chains, we model the conformational asymmetry by a difference in the bond lengths of the A and B blocks. Our results indicate that, consistent with the experiments, the inclusion of polydispersity and short-chain statistics leads to a shift of the phase boundaries between different ordered phases.