Quantifying Fluctuation/Correlation Effects on the Order-Disorder Transition of Symmetric Diblock Copolymers

TL;DR

This study uses advanced Monte Carlo simulations to quantify how fluctuations and correlations shift the order-disorder transition point in symmetric diblock copolymers, revealing the impact of short-range correlations.

Contribution

First systematic quantification of the fluctuation-induced shift of the ODT in symmetric diblock copolymers using off-lattice Monte Carlo simulations.

Findings

The ODT shift scales with the invariant degree of polymerization.

Short-range correlations significantly influence the transition.

Simulation results match theoretical predictions for fluctuation effects.

Abstract

Using fast off-lattice Monte Carlo simulations with experimentally accessible fluctuations, we report the first systematic study unambiguously quantifying the shift of the order-disorder transition (ODT) $\chi^*$ of symmetric diblock copolymers from the mean-field prediction $\chi^*_{\rm MF}$. Our simulations are performed in a canonical ensemble with variable box lengths to eliminate the restriction of periodic boundary conditions on the lamellar period. Exactly the same model system (Hamiltonian) is used in both our simulations and mean-field theory; the ODT shift is therefore due to the fluctuations/correlations neglected by the latter. While $\chi^* / \chi^*_{\rm MF} - 1 \propto \bar{\mathcal{N}}^{-k}$ is found with $\bar{\mathcal{N}}$ denoting the invariant degree of polymerization, $k$ decreases around the $\bar{\mathcal{N}}$-value corresponding to the close packing of polymer segments as hard spheres, indicating the short-range correlation effects.