Hierarchical Bicontinuous Primitive Phases via an Order–Order Transition in Miktoarm Star Quaterpolymers

Despite the considerable technological potential of bicontinuous network structures, achieving spontaneous formation of double primitive (DP) phases from the self-assembly of neat flexible block copolymers remains a great challenge. We demonstrate through simulations that miktoarm star quaterpolymers (μ-ABCDs) with two pairs of equal-length arms can spontaneously self-assemble into hierarchical DP phases. In these structures, the two interpenetrating networks are each formed by a chemically distinct arm, while the matrix domain consists of alternately packed spheres or stripes. Notably, these DP phases consistently emerge via an order–order transition from double gyroid (DG) phases that formed spontaneously at relatively higher temperatures. Our quantitative analyses reveal that these DP phases form under conditions of strong pairwise incompatibility, and the pair of majority arms exhibits maximum immiscibility. The structure stabilization mechanisms of DP phases involve (1) all arms being stretched excessively to minimize interfacial energy, thereby lowering the enthalpy, which effectively compensates for the entropy penalty due to the excessive chain stretching, and (2) a large volume fraction of the network-forming arms alleviating the packing frustration. To the best of our knowledge, this is the first reported instance of various hierarchical phases, including three DP and DG phases, four cylindrical-type structures, and one lamellar-type structure in block copolymer systems. Our results may provide guidance for the formation of these hierarchical phases and enhance the understanding of the phase behavior of μ-ABCDs.