Simple Calibration of Block Copolymer Melt Models

According to the universality hypothesis, the phase behavior of different block copolymer melt models having a fixed chain architecture depends solely on two parameters: the invariant chain length N̅ and the effective interaction parameter χN. If models behave universally, they can be compared to each other and can predict experiments quantitatively. The majority of simulations, however, do not use the Flory–Huggins parameter χ directly but instead operate with the exchange energy α = ϵAB– (ϵAA+ ϵBB)/2, where ϵxy is the interaction energy between monomers of type x and y. The simplest Flory-like definition of χ is a standard linear relation: χ ∝ α; however, previous studies have shown that the universality hypothesis does not hold for all models using this approximation. Here, we analyzed the behavior of more than 30 coarse-grained symmetric diblock copolymer melt models. We discovered that the phase behavior of a wide family of models depends only on two parameters, N̅ and χN, if the simple linear definition of χ is imposed. This family is comprised of the models in which the monomer interaction potential energy z has a near-symmetric distribution around its mean. This phenomenon could be explained by the coincidence of normalized peak scattering intensity at the same χN and N̅, which was observed for selected models with symmetric z-distribution when the χ ∝ α expression was used. Our results indicate that the main parameter controlling the symmetry of the z-distribution is the monomer density ρ. Above certain ρ, models have symmetric z-distributions, and their order–disorder transition points follow a master curve similar to the one predicted by Fredrickson–Helfand theory in the experimentally relevant N̅ > 102 range. On the other hand, low-ρ models exhibit skewed z-distributions, and the simple χ ∝ α formula is no longer universally applicable to them. We provided a table containing the linear χ(α) mapping; if that mapping is used, all models with a symmetric z-distribution have the phase behavior depending solely on N̅ and χN. Our results will enable a simple comparison between a broad family of coarse-grained models and experiments and can guide block copolymer model building. This, in turn, will facilitate the screening of new block copolymer morphologies and support material design.