Largely Tunable Asymmetry of Phase Diagrams of A(AB)_<i>n</i> Miktoarm Star Copolymer

Abstract

Topological asymmetry is an important factor to change the phase diagram of AB-type block copolymer with respect to the volume fraction of A-blocks from symmetric to asymmetric. However, many topology-asymmetric AB-type block copolymers can only produce limited effects on the asymmetry of phase diagrams, such as (AB)n star and ABn miktoarm star copolymers. In this work, we investigate the self-assembly behavior of an A1(A2B)n miktoarm star copolymer composed of one A1-arm and n A2B-arms using self-consistent field theory, aiming to demonstrate that the asymmetry of the phase diagram can be largely tuned by controlling n and the ratio of the volume fraction fA1 of A1-block to the total volume fraction f of A-blocks, τ = fA1/f. Note that this copolymer with τ = 0 is reduced to (AB)n star copolymer while it is reduced to ABn miktoarm star copolymer with τ = 1. For n ≥ 2, the asymmetry of the phase diagram changes nonmonotonically and exhibits a maximum as τ increases from 0 to 1, and the maximal degree of asymmetry increases with increasing n. In the phase diagram of maximal asymmetry with n = 5, the phase boundaries of A-sphere/A-cylinder and A-gyroid/lamella are deflected to f ≈ 0.56 and f ≈ 0.76 at a moderate segregation strength, respectively. As a result, the regions of both Frank–Kasper σ and A15 phases are dramatically expanded in such a highly asymmetric phase diagram. Moreover, the gyroid region exhibits a very complex changing trend with increasing τ, even vanishing in a certain range of τ for n ≥ 3. Surprisingly, the A1(A2B)3 copolymer with an optimized τ ≈ 0.6 exhibits the largest gyroid region with a width of about ΔfG ≈ 0.187 at χN = 60, which is about 4 times that at τ = 0 and 13 times that at τ = 1. The gyroid morphology with the volume fraction of channels ranging from f ≈ 0.54 to f ≈ 0.73 is promising in applications.