Block copolymer microstructures in the intermediate-segregation regime

A detailed examination of the intermediate-segregation regime of diblock copolymer melts is presented using the incompressible Gaussian chain model and self-consistent field theory (SCFT). We find that the competition between interfacial tension and chain stretching used to describe behavior in the strong-segregation regime also explains behavior in this regime. Phase transitions from lamellae (L) to cylinders (C) to spheres (S) occur due to the spontaneous curvature produced as the asymmetry in the diblock composition increases. Complex phases, gyroid (G), perforated lamellar (PL), and double diamond (D), have curvatures between those of L and C, and therefore they compete for stability along the L/C boundary. Nevertheless, only G exhibits a region of stability. To explain why, we recognize that interfacial tension prefers the formation of constant mean curvature (CMC) surfaces to reduce interfacial area, and chain stretching favors domains of uniform thickness so as to avoid packing frustration. While the classical structures, L, C, and S, are successful at doing both simultaneously, the complex phases are not. Of the complex phases, G is the least frustrated and consequently is stable at intermediate degrees of segregation. However, G becomes unstable in the strong-segregation regime because the relative penalty for packing frustration increases with segregation. The PL and D structures are simply too frustrated, and therefore are never stable.