Simple Calibration of Block Copolymer Melt Models

Abstract

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.

References in corpus (6)

• Universality of Block Copolymer Melts
• Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts
• Renormalized one-loop theory of correlations in polymer blends
• On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends
• Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers
• Dissipative Particle Dynamics for Directed Self-Assembly of Block Copolymers