The impact of intramolecular polydispersity on the self-assembly of ABn miktoarm star copolymers

The self-assembly behaviors of ABn miktoarm star copolymers as one typical type of asymmetric architecture have been studied well in the past few decades due to their deflected phase boundaries. In particular, recently, they have attracted renewed theoretical interest due to their expanded spherical phase region that stabilizes complex Frank–Kasper spherical phases. However, previous theoretical studies have never considered ABn copolymers with unequal arm lengths, which is more or less the case for synthesized copolymers. In this work, we investigate the self-assembly behaviors of ABn miktoarm star copolymers with unequal B-arms using self-consistent field theory. We propose an intramolecular polydispersity index (iĐ) to quantify the distribution of unequal B-blocks. Accordingly, we further propose a simple quantity of an effective arm number nequ = n/iĐ for quantitatively comparing the phase boundaries between various ABn copolymer samples with different arm numbers or different distributions of B-blocks. Our results indicate that different ABn copolymers with equal nequ exhibit similar phase diagrams. On the other hand, we also found that the phase boundaries of two different samples with same nequ are not exactly overlapped. We speculate that the effect of spontaneous curvature may be mainly controlled by nequ, but the packing frustration of B-blocks may also be dependent on the other quantities that are closely related to the shape of the distribution of B-arms, such as higher order polydispersity indexes.