Stability of cubic single network phases in diblock copolymer melts

We used self-consistent field theory (SCFT) to examine the stability of three cubic single network structures, single gyroid, single diamond, and single primitive, in neat diblock copolymer melts. Arguments related to packing frustration, as measured by the standard deviation in the mean curvature of the interface relative to its mean, that explain the relative stability of double gyroid, double diamond and double primitive also extend to the relative stability of their single networks. However, this packing frustration measure fails to account for the relative stabilities of single and double networks, for example, single gyroid versus double gyroid, and arguments for a preferred curvature fail to explain the selection of double gyroid as the segregation strength increases. Rather, the larger interfacial areas per unit volume of single networks, arising from decreased domain sizes, are found to be a generic factor that leads to metastability of the cubic single networks relative to double gyroid in the network-forming region of the morphology diagram. These results clarify the origins of the metastability of single cubic network phases in neat diblock copolymer melts.