To highlight the importance of quantitative and parameter-fitting-free comparisons among different models/methods, we revisited the comparisons made by Groot and Madden [J. Chem. Phys. 108, 8713 (1998)] and Chen et al. [J. Chem. Phys. 122, 104907 (2005)] between their dissipative particle dynamics (DPD) simulations of the DPD model and the self-consistent field (SCF) calculations of the "standard" model done by Matsen and Bates [Macromolecules 29, 1091 (1996)] for diblock copolymer (DBC) A-B melts. The small values of the invariant degree of polymerization used in the DPD simulations do not justify the use of the fluctuation theory of Fredrickson and Helfand [J. Chem. Phys. 87, 697 (1987)] by Groot and Madden, and their fitting between the DPD interaction parameters and the Flory-Huggins χ parameter in the "standard" model also has no rigorous basis. Even with their use of the fluctuation theory and the parameter-fitting, we do not find the "quantitative match" for the order-disorder transition of symmetric DBC claimed by Groot and Madden. For lamellar and cylindrical structures, we find that the system fluctuations/correlations decrease the bulk period and greatly suppress the large depletion of the total segmental density at the A-B interfaces as well as its oscillations in A- and B-domains predicted by our SCF calculations of the DPD model. At all values of the A-block volume fractions in the copolymer f (which are integer multiples of 0.1), our SCF calculations give the same sequence of phase transitions with varying χN as the "standard" model, where N denotes the number of segments on each DBC chain. All phase boundaries, however, are shifted to higher χN due to the finite interaction range in the DPD model, except at f = 0.1 (and 0.9), where χN at the transition between the disordered phase and the spheres arranged on a body-centered cubic lattice is lower due to N = 10 in the DPD model. Finally, in 11 of the total 20 cases (f-χN combinations) studied in the DPD simulations, a morphology different from the SCF prediction was obtained due to the differences between these two methods.

Using fast off-lattice Monte Carlo simulations with experimentally accessible fluctuations, we reported the first systematic study unambiguously quantifying the shift of the order-disorder transition (ODT) χ* of symmetric diblock copolymers from the mean-field prediction χ(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, and give the most accurate data of χ* and bulk lamellar period reported to date. 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 χ*/χ(MF)*-1∝N(-k) is found with N denoting the invariant degree of polymerization, k decreases around the N-value corresponding to the face-centered cubic close packing of polymer segments as hard spheres, indicating the short-range correlation effects.

The parameter region in the Δχ−χSC plane where cononsolvency will (the shaded area) and will not (the blank area) occur with ϕP = 0.1.

No abstract