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Soft particle model for block copolymers
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Image of FIG. 1.
FIG. 1.

Schematic illustration of the Gaussian disphere model.

Image of FIG. 2.
FIG. 2.

Comparison between the conditional probability based on the Gaussian approximation [Eq. (9)] (continuous curves) with Monte Carlo data for symmetric chains with . To display the dependence on , averages have been taken over eight successive intervals, see text. Different curves refer to the first five of these intervals. With increasing values, distributions shift towards larger values. The inset shows, in a semilogarithmic representation, the results for the smallest and largest of these eight intervals, confirming that the Gaussian approximation is satisfactory as long as .

Image of FIG. 3.
FIG. 3.

Simulated structure factor in the disordered phase for different with ; . Continuous curves are fits to Eq. (13).

Image of FIG. 4.
FIG. 4.

Normalized inverse maximum of the structure factor vs for three different chain lengths.

Image of FIG. 5.
FIG. 5.

Spherically averaged structure factor in ordered phases. Lamellar phase with (a) (weak segregation) and (b) (strong segregation), displaying the third-order peak. (c) Cylindrical phase with and , with marked higher-order peaks.

Image of FIG. 6.
FIG. 6.

Averaged stretching parameter (full symbols) compared to averaged radii of gyration (light symbols), cf. Eq. (9), vs .

Image of FIG. 7.
FIG. 7.

Scaling plot of lamellar distance depending on and extending to the strong segregation regime. The dashed straight line has a slope . Data points for are continued to the disordered phase. In these simulations, averages were taken over three independent runs.

Image of FIG. 8.
FIG. 8.

Normalized diffusion coefficient as well as anisotropic diffusion coefficients and in the lamellar phase vs . The vertical dashed-dotted line separates isotropic from anisotropic diffusion. Its position agrees with estimates for the ordering transition based on equilibrium simulations (Sec. III A).

Image of FIG. 9.
FIG. 9.

(a) Wall-induced molecular orientation (circles) and normalized radius of gyration (squares) of blocks across the slab for . The horizontal dotted line corresponds to random orientation, . The grid size along the axis is . Chosen parameters are , , and . (b) Time evolution of circularly averaged structure factor after averaging over . Note the appearance of the third-order peak in the final equilibrated state.

Image of FIG. 10.
FIG. 10.

(a) Time evolution of the -monomer density in a film of thickness with -attractive walls for . (b) Same, but with -attractive left and neutral right walls.

Image of FIG. 11.
FIG. 11.

Time evolution of the structure factor in the presence of a stripe-patterned wall near for . The pattern periodicity is , and the film thickness . The lateral system size is . (a) MCSs, (b) MCSs, and (c) MCSs.

Image of FIG. 12.
FIG. 12.

Same as Fig. 11, but , and MCSs in (c).

Image of FIG. 13.
FIG. 13.

Same as Fig. 11, but , and MCSs in (c).

Image of FIG. 14.
FIG. 14.

Circularly and -averaged structure factor from the same simulation data as in Fig. 13.


Generic image for table
Table I.

Parameters for fitting the generalized Leibler function [Eq. (13)] to structure factor data in Fig. 3.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Soft particle model for block copolymers