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

How fluctuations change the order-disorder transition (ODT) of symmetric diblock copolymers is a classic yet unsolved problem in polymer physics.\footnote{\textit{L. Leibler}, \textbf{Macromolecules, 13}, 1602 (1980); \textit{G. H. Fredrickson and E. Helfand}, \textbf{J. Chem. Phys., 87}, 697 (1987).} Here we unambiguously quantify the fluctuation effects by direct comparisons between fast off-lattice Monte Carlo (FOMC) simulations\footnote{\textit{Q. Wang and Y. Yin}, \textbf{J. Chem. Phys., 130}, 104903 (2009).} and mean-field theory using exactly the same model system (Hamiltonian), thus without any parameter-fitting. The symmetric diblock copolymers are modeled as discrete Gaussian chains with soft, finite-range repulsions as commonly used in dissipative-particle dynamics simulations. The effects of chain discretization and finite-range interactions on ODT are properly accounted for in our mean-field theory.\footnote{\textit{Q. Wang}, \textbf{J. Chem. Phys.}, \textbf{129}, 054904 (2008); \textbf{131}, 234903 (2009).} Our FOMC simulations are performed in a canonical ensemble with variable box lengths to eliminate the adverse effects of fixed box sizes on ODT.\footnote{\textit{Q. Wang et al.}, \textbf{J. Chem. Phys.}, \textbf{112}, 450 (2000).} Furthermore, with a new order parameter for the lamellar phase, we use replica exchange and multiple histogram reweighting to accurately locate ODT in our simulations.