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

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.