Logarithmic plot of the bulk lamellar period L 0 of symmetric DBC as a function of χN. The SCF results are shown in curves, where “Standard” denotes the “standard” model, and the FOMC results for the DPD model are shown in symbols.
Comparisons of the ensemble-averaged profiles of (a) the relative fraction of A segments in the direction (denoted by x) perpendicular to the lamellar interfaces, , and (b) the total segmental density in the x-direction, ϕ(x) ≡ ⟨ϕA(x) + ϕB(x)⟩, obtained from our SCF calculations and FOMC simulations of the DPD model at χN = 30π ( in the simulations), where the bulk lamellar period L 0/R e, 0 = 2.658 in the SCF calculations and 2.497 ± 0.002 in the FOMC simulations.
Differences in the free energy per chain βf c of various ordered phases from that of the disordered phase obtained from our SCF calculations of the DPD model at (a) f = 0.4 and (b) f = 0.3. The inset of part (a) uses the free energy per chain of S, , as the reference, and the inset of part (b) shows the difference in the free energy per chain between L and C.
(a) Reprinted Fig. 9 with permission from R. D. Groot and T. J. Madden, J. Chem. Phys.108, 8713 (Year: 1998)10.1063/1.476300. . (b) Hexagonal packing of cylinders in any x-y cross section of the cubic simulation box shown in part (a). (c) Reprinted lower-right panel of Fig. 6 with permission from R. D. Groot and T. J. Madden, J. Chem. Phys.108, 8713 (Year: 1998)10.1063/1.476300. . (d) Hexagonal packing of cylinders in any x-y cross section of the cubic simulation box shown in part (c). See text for more details.
Mean-field ODT and the corresponding bulk lamellar period (shown in parentheses) of symmetric DBC for four combinations of chain model with non-bonded interaction potential, obtained from RPA. The upper-left corresponds to the “standard” model and the lower-right to the DPD model system.
ODT χ*N and the corresponding bulk lamellar period of symmetric DBC for the DPD model at given segment number density ρ0σ3, obtained from FOMC simulations. The corresponding values of the invariant degree of polymerization , the Flory-Huggins parameter χ e , and that corrected for the fluctuation effects based on FH theory χ e, f are also listed. See main text for more details.
Comparisons of the bulk period from SCF calculations L 0, MF, that from variable-box FOMC simulations L 0, and the period from fixed-box simulations L for lamellae (at f = 0.5 and 0.4) and hexagonally packed cylinders (at f = 0.3) obtained with various parameters.
Stable regions in χN of various ordered phases obtained from the SCF calculations of the DPD and the “standard” models; results for the latter model are provided by Mark Matsen. For each A-block volume fraction in the copolymer f, the stable phase (having the lowest Helmholtz free energy per chain) is replaced by that in a lower row at higher χN. The last column lists the χN-values at which the DPD simulations 15,17 were performed; the morphology obtained from the DPD simulations is given in parentheses if it is different from the SCF prediction. See main text for more details.
Article metrics loading...
Full text loading...