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Phase segregation of a symmetric diblock copolymer in constrained space with a square-pillar array
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10.1063/1.3685220
/content/aip/journal/jcp/136/7/10.1063/1.3685220
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/7/10.1063/1.3685220

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of 3D square lattices of square pillars. (a) Vertical view of this confinement uncovered by the substrate above composed of a 3D normal square-pillar array. (b) Lateral view of 3D normal square-pillar array. (c) Vertical view of 3D rotated square-pillar array. The blue components represent the square pillars (P), and the parallel yellow substances represent the substrates (S). The variables D, W(G), Z, and L represent the pillar pitch, the gap between two nearest neighboring square pillars, the copolymer film thickness, and the side length of the pillar, respectively.

Image of FIG. 2.
FIG. 2.

Lamellar structures found in normal square-pillar array. The color bars in Fig. 2(a) represent the component density profiles above 0.40 (the density has been normalized to 0.00–1.00). The red region represents the A block, and the green region represents another block. For simplicity and analysis, the listed values of the parameters Z, D, and W are rescaled in units of R 0 in a later figure. Parallel lamellae: (a) symmetric lamellae () (Z = 0.9, W = 0.36, and D = 0.52); (b) antisymmetric lamellae () (Z = 1.5, W = 0.36, and D = 0.52); (c) symmetric lamellae () (Z = 1.81, W = 0.36, and D = 0.52). Perpendicular lamellae: (d) simple lamellae (L ) (Z = 0.47, W = 0.55, and D = 0.78); (e) diagonal wavy lamellae () (Z = 0.45, W = 0.9, and D = 1.29); (f) knitting-pattern lamellae () (Z = 0.47, W = 0.62, and D = 1.55); (g) square lamellae () (Z = 0.47, W = 0.78, and D = 1.55); (h) semi-circle-section lamellae () (Z = 0.47, W = 0.93, and D = 1.55); (i) wavy-circle-section lamellae () (Z = 0.47, W = 1.09, and D = 1.55).

Image of FIG. 3.
FIG. 3.

Square lattices of perpendicular cylinders found in normal square-pillar array. (a) Alternating cross-shaped cylinders () (Z = 0.23, W = 0.21, and D = 0.52); (b) cross-shaped cylinders () (Z = 0.21, W = 0.41, and D = 1.03); (c) simple cylinders (C ) (Z = 0.21, W = 0.62, and D = 1.03); (d) elliptical cylinders () (Z = 0.26, W = 0.77, and D = 1.29).

Image of FIG. 4.
FIG. 4.

Comparison between the modified strong segregation theory (curve lines) and the simulation results (symbols). The inset is a vertical view of the unit cell of the alternating cross-shaped cylindrical structure (). The SST1, SST2, and SST3 curves illustrate the structural transformations between the three types of the parallel lamellar structures, i.e., the , , and , and alternating cross-shaped cylindrical structure (), respectively.

Image of FIG. 5.
FIG. 5.

Possible structures at Z = 1.50 and D = 0.52. (a) Asymmetric parallel lamellae and its lateral view (); (b) antisymmetric parallel lamellae (); (c) alternating circle-shaped perpendicular lamellae (); (d) alternating cross-shaped cylinders ().

Image of FIG. 6.
FIG. 6.

Bicontinuous structures found in normal square-pillar array. Double-cylinder network structure (): (a) theat Z = 0.93, W = 0.72, and D = 1.03; (a-1) the A structure of the ; (b) the at Z = 1.81, W = 0.72, and D = 1.03; (b-1) the A structure of the . Pseudo-lamellae (): (c) the at Z = 0.93, W = 1.09, and D = 1.55; (c-1) the A structure of the ; (d) the at Z = 1.78, W = 1.09, and D = 1.55; (d-1) the A structure of the .

Image of FIG. 7.
FIG. 7.

Bicontinuous structures found in normal square-pillar array. (a) Similar pseudo-lamellae () (Z = 0.71, W = 0.90, and D = 1.29); (a-1) the A structure of the ; (b) perforated lamellae (BpL ×) (Z = 0.93, W = 0.62, and D = 1.55); (b-1) the A structure of the BpL ×and its cut view; (c) dislocation of the elliptical cylinders () (Z = 1.4, W = 0.62, and D = 1.55); (c-1) the A structure of the ; (d) curved-lamellae network (BclL ×) (Z = 0.7, W = 1.09, and D = 1.55); (d-1) vertical view of the A structure of the BclL ×; (e) diagonal-wavy-lamellae network () (Z = 0.89, W = 0.55, and D = 0.78); (e-1) vertical view of the A structure of the .

Image of FIG. 8.
FIG. 8.

Antisymmetric and cross-network bicontinuous structures found in normal square-pillar array. (a) Hybridization of the BpL × and the () (Z = 1.81, W = 0.77, and D = 1.29); (a-1) the A structure of the ; (a-2) the top part of the A structure; (a-3) the bottom part of the A structure; (b) cross-network (BcnL ×) (Z = 1.82, W = 0.39, and D = 0.78); (b-1) the A structure of the BcnL ×; (b-2) cut view of the A structure; (b-3) cut view of the A structure.

Image of FIG. 9.
FIG. 9.

Lamellar structures found in rotated square-pillar array. Parallel lamellae: (a) symmetric lamellae () (Z = 0.9, G = 0.29, and D = 0.52). Perpendicular lamellae: (b) simple lamellae (L ) (Z = 0.23, G = 0.43, and D = 0.78); (c) novel knitting-pattern lamellae () (Z = 0.26, G = 0.71, and D = 1.29); (d) wavy lamellae () (Z = 0.23, G = 0.85, and D = 1.55).

Image of FIG. 10.
FIG. 10.

Perpendicular cylinders found in rotated square-pillar array. (a) Alternating square-shaped cylinders () (Z = 0.23, G = 0.08, and D = 0.52); (b) alternating octagonal cylinders () (Z = 0.23, G = 0.23, and D = 0.52); (c) distorted cylinders (dC ) (Z = 0.23, G = 0.12, and D = 0.78); (d) simple cylinders (C ) (Z = 0.26, G = 0.32, and D = 1.29); (e) elliptical cylinders () (Z = 0.26, G = 0.58, and D = 1.29); (f) square-shaped cylinders () (Z = 0.23, G = 0.23, and D = 1.55).

Image of FIG. 11.
FIG. 11.

Comparison between the modified strong segregation theory (curve lines) and the simulation results (symbols). The inset is a vertical view of the unit cell of the alternating square-shaped or octagonal cylindrical structures. The SST1 and SST2 curves illustrate the structural transformations between the alternating cylindrical structure ( or ) and the parallel lamellar structures, i.e., and , respectively.

Image of FIG. 12.
FIG. 12.

Bicontinuous structures found in rotated square-pillar array. Double-cylinder network structure (): (a) the at Z = 0.93, G = 0.57, and D = 1.03; (a-1) the A structure of the ; (b) the at Z = 1.81, G = 0.57, and D = 1.03; (b-1) the A structure of the . Pseudo-lamellae (): (c) the at Z = 0.93, G = 0.85, and D = 1.55; (c-1) the A structure of the ; (d) the at Z = 1.78, G = 0.85, and D = 1.55; (d-1) the A structure of the . (e) Perforated lamellae (BpL ×) (Z = 0.93, G = 0.39, and D = 1.55); (e-1) the A structure of the BpL ×.

Tables

Generic image for table
Table I.

Structures in normal square-pillar array.

Generic image for table
Table II.

Free energies for several possible structures at Z = 1.5 and D = 0.52.

Generic image for table
Table III.

Structures in rotated square-pillar array.

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/content/aip/journal/jcp/136/7/10.1063/1.3685220
2012-02-17
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase segregation of a symmetric diblock copolymer in constrained space with a square-pillar array
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/7/10.1063/1.3685220
10.1063/1.3685220
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