Contour Length Fluctuations and Melt Density Control the Universality of Block Copolymers

Melts of block copolymers can form nanostructured materials serving as next-generation platforms in nanotechnology applications. Theoretical modeling is a promising tool to accelerate the discovery in this field. However, it is challenging to guide experiments precisely by using simulations because it is very hard to correctly relate simulation model parameters to real quantities such as temperature, polymer length, and density. We describe how to build block copolymer melt models to make this mapping especially easy and universal. In particular, we discovered a wide family of block copolymer melt models that exhibit universal behavior at the order-disorder transition (ODT) using the standard simple definition of the Flory-Huggins parameter χ ∝ α, where α=ε_AB-(ε_AA+ε_BB)/2, and ε_xy is the interaction energy between monomers of type x and y. The classic Fredrickson-Helfand theory predicts the ODT point location for these models correctly for experimentally relevant invariant chain lengths Ñ>10² far outside the assumed validity range of the theory Ñ>10⁴. The models in the discovered class have high polymer density and small fluctuations of contour length, which led to the observed universality. Our work describes how to build block copolymer models to compare simulation results to experiments easily and directly.