Simple Calibration of Block Copolymer Melt Models

According to the universality hypothesis, the phase behavior of different block copolymer melt models having fixed composition depends solely on two parameters: the invariant chain length $\bar{N}$ and the effective interaction parameter $\chi N$. If models behave universally, they can be compared to each other and can predict experiment quantitatively. Here, we present a simple way to achieve this universality for coarse-grained models. Our method relies on the properties of the monomer interaction potential energy $z$ distribution. In particular, models having near-symmetric $z$-distributions exhibit universal phase behavior using the standard linear definition of the Flory-Huggins parameter $\chi\propto\alpha$, where $\alpha = \epsilon_{AB}-(\epsilon_{AA}+\epsilon_{BB})/2$, and $\epsilon_{xy}$ is the interaction energy between monomers of type $x$ and $y$. Previously, universality had been achieved using a nonlinear $\chi(\alpha)$ function which is difficult to obtain and interpret physically. The main parameter controlling the symmetry of the $z$-distribution is the monomer density $\rho$. Above certain $\rho$, models have symmetric $z$-distributions, and their order-disorder transition points follow the universal curve predicted by Fredrickson-Helfand theory in the experimentally relevant $\bar{N} > 10^2$ range. On the other hand, low-$\rho$ models exhibit skewed $z$-distributions, and the simple $\chi\propto\alpha$ formula is no longer universally applicable to them. Our results can be used for correct block copolymer model building leading to a simple and direct comparison of simulations to experiments, which will facilitate the screening of new block copolymer morphologies and support materials design.