Test of a scaling hypothesis for the structure factor of disordered diblock copolymer melts

TL;DR

This study tests a universal scaling hypothesis for the structure factor of disordered diblock copolymer melts across different simulation models, confirming the hypothesis's validity even for short chains.

Contribution

It provides empirical evidence supporting a two-parameter scaling law for the structure factor in diblock copolymer melts, validated across multiple simulation models with different interaction details.

Findings

Strong support for the scaling hypothesis across models

Validation of universal behavior for short chains

Methods developed to test scaling without detailed interaction models

Abstract

Coarse-grained theories of dense polymer liquids such as block copolymer melts predict a universal dependence of equilibrium properties on a few dimensionless parameters. For symmetric diblock copolymer melts, such theories predict a universal dependence on only chi N and Nbar, where chi is an effective interaction parameter, N is a degree of polymerization, and Nbar is a measure of overlap. We test whether simulation results for the structure factor S(q) obtained from several different simulation models are consistent with this two-parameter scaling hypothesis. We compare results from three models: (1) a lattice Monte Carlo model, the bond-fluctuation model, (2) a bead-spring model with harsh repulsive interactions, similar to that of Kremer and Grest, and (3) a bead-spring model with very soft repulsion between beads, and strongly overlapping beads. We compare results from pairs of simulations of different models that have been designed to have matched values of Nbar, over a range of values of chi N and N, and devise methods to test the scaling hypothesis without relying on any prediction for how the phenomenological interaction parameter chi depends on more microscopic parameters. The results strongly support the scaling hypothesis, even for rather short chains, confirming that it is indeed possible to give an accurate universal description of simulation models that differ in many details.