(415f) 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).