Understanding Fluctuation/Correlation Effects on the Order-Disorder Transition of Symmetric Diblock Copolymers with a Density-Functional Theory

How fluctuations change the order-disorder transition (ODT) of symmetric diblock copolymers (DBC) 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). } Taking a model system of discrete Gaussian chains interacting with soft, finite-range repulsions as commonly used in dissipative-particle dynamics simulations we formulate a density-functional theory (DFT) based on the polymer integral equation theories,\footnote{\textit{D. Chandler and H. C. Andersen,}~\textbf{J. Chem. Phys.},~\textbf{57}, 1930 (1972);~\textit{K. S. Schweizer and J. G. Curro},~\textbf{Phys. Rev. Lett.},~\textbf{58},~246, (1987).} which includes the system fluctuations and correlations neglected by the mean-field theory (i.e., the widely applied self-consistent field theory) and can be reduced to the latter under the mean-spherical approximation. We then unambiguously reveal the fluctuation/correlation effects on the ODT of symmetric DBC by direct comparisons among the mean-field theory, DFT, and fast off-lattice Monte Carlo simulations,\footnote{\textit{Q. Wang and Y. Yin}, \textbf{J. Chem. Phys., 130}, 104903 (2009).} all using exactly the same model system (Hamiltonian) and thus without any parameter-fitting.