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Phase behaviors and ordering dynamics of diblock copolymer self-assembly directed by lateral hexagonal confinement
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Image of FIG. 1.
FIG. 1.

(a) Density plots of stable morphologies observed in the cylinder-forming diblock copolymer melts, with fixed f = 0.26 and χN = 20, under the confinement of two-dimensional hexagons with varying diagonal size of D, in units of the bulk cylinder-to-cylinder distance of L0; (b) stable phase sequence of morphologies as a function of D/L0; (c) density plots of observed metastable 2D morphologies.

Image of FIG. 2.
FIG. 2.

(a) Isosurface density plots and the density profiles of cross section of three-dimensional morphologies. The major component inside the green isosurface is A block indicated by red-color region in the cross section profiles. (b) Stable phase sequence as a function of D/L0 identified by considering both 2D and 3D phases.

Image of FIG. 3.
FIG. 3.

Free-energy comparisons between all candidate 2D and 3D morphologies for hexagons with the diagonal size between L0 and 6L0. For the reason of clarity, the free energy relative to that of a selected reference phase is plotted, and the plot is divided into four pieces along the size.

Image of FIG. 4.
FIG. 4.

Typical snapshots of density isosurfaces at t = 5 × 104Δt (a), t = 105Δt (b), and t = 2 × 105Δt, respectively, for the diagonal size of the hexagon, D/L0 = 15.

Image of FIG. 5.
FIG. 5.

Histogram plots of the distributions of the ordering time for the diagonal size of D/L0 = 13 (a) and D/L0 = 15 (b), respectively. The Poisson distribution is used to fit the results. (a) The time interval is chosen as δt = 104 time steps, and the Poisson distribution curves of three parameters of λ = 3, 4, and 5, are plotted; (b) The time interval is chosen as δt = 3 × 104, and λ = 2, 3, and 4, respectively.

Image of FIG. 6.
FIG. 6.

Ordering time as a function of the diagonal size of hexagons, plotted in a double-logarithm plot. The solid line is obtained by a linear fitting. Note that, the filled symbol for D = 19L0 indicates that the ordering time is beyond 106 time steps in one or more runs of our simulated eight samples.

Image of FIG. 7.
FIG. 7.

(a) The time evolution of the space fluctuation of bonds, θ, for D/L0 = 21. (b) Four typical snapshots of the structures are shown for t = 50 × 104, t = 77 × 104, t = 78 × 104, and t = 85 × 104, respectively (indicated by color circles and numbers 1, 2, 3, and 4) (a link to the corresponding movie of the structure evolution is provided at the end of this figure caption). (c) The corresponding distributions of bonds with respect to their positions are presented for the above four times. The bond length is indicated by both the filled circle size and the color spectrum. However, for the reason of clarity, different length ranges are used in the four plots: L/L0 ≈ 0.794–1.158 (c1), 0.714–1.050 (c2), 0.976–1.077 (c3), and 0.982–1.030 (c4), respectively (enhanced online). [URL: http://dx.doi.org/10.1063/1.4765098.1]10.1063/1.4765098.1



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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase behaviors and ordering dynamics of diblock copolymer self-assembly directed by lateral hexagonal confinement