Effect of architectural asymmetry of hyperbranched block copolymers on their phase boundaries

Asymmetric architecture of AB-type block copolymers can induce additional spontaneous curvature to the A/B interface, accordingly deflecting the phase boundaries. However, it is often difficult to determine or compare the asymmetric effects of different asymmetric architectures. In this work, we proposed to use the equivalent arm number n_equ, which was originally defined as n_equ = n/iĐ for AB with unequal B-arms and iĐ being the intramolecular polydispersity of these B-arms, to quantify the asymmetric effect of various linear-hyperbranched copolymers. For each linear-hyperbranched copolymer, n_equ is estimated by matching its phase boundaries on the side with expanded spherical phase region with those of AB with unequal B-arms but tunable iĐ. Our results suggest that the addition of B-blocks at the further location from the A-B joint point has less influence on n_equ, i.e. the asymmetric effect, because these B-blocks can access more space. For the linear-dendrimer copolymers, n_equ changes from 2 to about 3.8 when the overall generation number of the copolymer increases from 2 to 5. In other words, the asymmetric effect of these linear-dendrimer copolymers is intermediate between those of AB₂ and AB₄ miktoarm star copolymers. In brief, n_equ can effectively describe the asymmetric effect on the interfacial curvature of complex asymmetric architectures.