Order-Disorder Transitions and Free Energies in Asymmetric Diblock Copolymers

Simulations of simple bead-spring models of asymmetric diblock copolymers are used to study the dependence of order-disorder transitions and free energies upon the invariant degree of polymerization (N) over bar and the fraction f of beads in the minority block. Well-tempered metadynamics is used to determine values of (chi N) ODT along the lamellar-disorder and hexagonaldisorder transitions over the range 0.1875 = f = 0.5 for two models with different values of (N) over bar = 480 and 1920, where chi is an effective Flory-Huggins interaction parameter, N is the degree of polymerization, and (chi N)(ODT) is a value of chi N at the order-disorder transition (ODT). More extensive studies are performed for systems with f = 1/4, which undergo a hexagonal-disorder transition. Equivalent results for both phase boundaries and free energies are obtained for one pair of systems with different numbers of beads per chain but matched values of f = 1/4 and (N) over bar, in agreement with the corresponding state hypothesis. Comparison of results for ((N) over bar) ODT for systems with f = 1/4 and several values for (N) over bar show a systematic decrease in ((N) over bar) ODT with an increase N<overline>, consistent with the expected approach to the self-consistent field (SCFT) prediction as (N) over bar -> infinity. Results for the free energy per chain in the disordered and hexagonal phases of systems with f = 1/4 show that SCFT gives rather accurate predictions for the free energy in the ordered hexagonal phase but that the random-mixing approximation underlying SCFT significantly overestimates the free energy of the disordered phase.