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.¹ While it is qualitatively known that fluctuations change ODT to a weak first-order phase transition and increase the ODT temperature, their effects have not been ambiguously quantified as a function of the invariant degree of polymerization  controlling the system fluctuations. Although many groups addressed this problem with molecular simulations, they were hindered by the difficulty of accurately locating ODT in the simulations and the use of different model systems in the simulations and mean-field theory.

Here we unambiguously quantify the fluctuation effects by direct comparisons between fast off-lattice Monte Carlo (FOMC) simulations² 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. Such soft potentials give much better sampling of configuration space by allowing particle overlapping, and further enable the simulations to be performed at experimentally realistic -values not accessible by conventional molecular simulations using hard-core repulsions (such as in the Lennard-Jones potential or the self- and mutual-avoiding walk). The effects of chain discretization and finite-range interactions on ODT are properly accounted for in our mean-field theory.³ Our FOMC simulations are performed in a canonical ensemble with variable box lengths to eliminate the adverse effects of fixed box sizes on ODT.⁴ 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.

References:

[1]  L. Leibler, Macromolecules, 13, 1602 (1980); G. H. Fredrickson and E. Helfand, J. Chem. Phys., 87, 697 (1987).

[2]  Q. Wang and Y. Yin, J. Chem. Phys., 130, 104903 (2009).

[3]  Q. Wang, J. Chem. Phys., 129, 054904 (2008); 131, 234903 (2009).

[4]  Q. Wang et al., J. Chem. Phys., 112, 450 (2000).