Universality of Block Copolymer Melts

Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy on the invariant degree of polymerization \(\overline{N}\), and to study universal properties of the order-disorder transition (ODT). The ODT appears to exhibit two regimes: Systems of very long chains (\(\overline{N} \gtrsim 10^{4}\)) are well described by the Fredrickson-Helfand theory, which assumes weak segregation near the ODT. Systems of smaller but experimentally relevant values, \(\overline{N} \lesssim 10^4\), undergo a transition between strongly segregated disordered and lamellar phases that, though universal, is not adequately described by any existing theory.