Program Asymmetric Binary Packing Lattices of AB₁CB₂ Tetrablock Terpolymers

ABC-type block terpolymers have great potential to self-assemble into rich ordered nanostructures, e.g., binary cylindrical structures. Recent experiments observed novel binary cylindrical structures in AB1CB2 linear tetrablock terpolymers, which have a high coordination number of A cylinder (CNA = 8). To elucidate the formation mechanism of high-CNA binary cylindrical phases and thus to stabilize more high-CNA phases, we investigate the self-assembly of AB1CB2 block copolymers, focusing on the exploration of distinct high-CNA cylindrical phases. We introduce a polygonal tiling approach to divide the planar space into different regions for two B blocks to fill through local separation. Based on this approach, the transition mechanism between different binary phases is clarified. Following the transition mechanism, we predict a multitude of high-CNA binary cylindrical phases by tailoring the key architectural parameters such as the volume fraction or the conformational parameter of the A block, including those with CNA = 6, 7, 8, 9, 10, and 12. Our theoretical prediction of so many novel binary cylindrical phases is expected to promote further experimental studies on the self-assembly of ABC-type block copolymers.