Universality of block copolymer melts

Simulations of five different coarse-grained models of symmetric diblock copolymers are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy and order-disorder transition (ODT) on the invariant degree of polymerization N̄. The actual values of χN at the ODT approach predictions of the Fredrickson-Helfand (FH) theory for N̄104 but significantly exceed FH predictions at lower values characteristic of most experiments. The FH theory fails for modest N̄ because the competing phases become strongly segregated near the ODT, violating an underlying assumption of weak segregation.