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Strong stretching theory for diblock copolymers in thin films under application of electric fields
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10.1063/1.4738594
/content/aip/journal/jcp/137/4/10.1063/1.4738594
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/4/10.1063/1.4738594

Figures

Image of FIG. 1.
FIG. 1.

Example for the discretization of the interface between the A and B domain. This figure explains also the notation used in Eq. (15).

Image of FIG. 2.
FIG. 2.

Example for the phase: A thin film containing two rows of hexagons. The deformation of the inner hexagons is quantified by the parameter h, the side length of the hexagons is . The horizontal semi-axes of the outer and inner elliptical A-domains a can be varied. The outer hexagons contain more volume than the inner hexagons, the slope p can be varied.

Image of FIG. 3.
FIG. 3.

Example for the phase: A thin film containing lamellae at the film boundaries and hexagons in the center. In this instance, we have diverted some volume to the inner hexagon, such that each lamellae is slightly smaller than 1.5 hexagons. The lamellae can be undulated, and the amplitude varied.

Image of FIG. 4.
FIG. 4.

Example for : A thin film containing two rows of hexagons. The height of the vertical hexagon-boundary is given by l o (can be varied independently for outer and inner hexagons), the width of the hexagons by w. The horizontal semi-axis a and vertical height l i of the A-domain can be varied independently for outer and inner domains.

Image of FIG. 5.
FIG. 5.

Example for : A thin film containing three rows of hexagons. Only the lower half of the symmetric configuration is shown. All hexagons have the same vertical height 2l o , the lower (upper) half of lower (upper) outer hexagon is converted to a rectangular shape while keeping the same volume. The horizontal semi-axis a and vertical height l i of the A-domains can be varied independently for outer and inner hexagons. The outer hexagons have two independently adjustable vertical parts of the A-domain.

Image of FIG. 6.
FIG. 6.

Different configurations of the hexagonal cell and A-domain with resulting minimal free energy densities for a volume fraction of f = 0.13. Light gray: perfectly circular/hexagonal, dark gray: C ∥,hs, black: C ∥,vs.

Image of FIG. 7.
FIG. 7.

Phase diagram for volume fraction f = 0.13 and E = 0.0. For the C ∥,vs phase, the gray shades indicate the percentage to which the walls are wetted by the A domain.

Image of FIG. 8.
FIG. 8.

Phase diagrams for E = 0.0 and volume fractions f = 0.13, f = 0.2, and f = 0.27.

Image of FIG. 9.
FIG. 9.

Phase diagrams for E = 1.66 and volume fractions f = 0.13, f = 0.2, and f = 0.27.

Image of FIG. 10.
FIG. 10.

Phase diagrams for E = 3.33 and volume fractions f = 0.13, f = 0.2, and f = 0.27.

Image of FIG. 11.
FIG. 11.

Phase diagrams for E = 5.0 and volume fractions f = 0.13, f = 0.2, and f = 0.27.

Image of FIG. 12.
FIG. 12.

Ratio of electrostatic energies of three parallel phases with the C phase, for eight different values of λ, and for f = 0.2. The three parallel phases are shown in the pictures on the left. The gray shades indicate undeformed C ∥,vs (, light gray), vertically stretched C ∥,vs (, dark gray), and L (black) phases.

Image of FIG. 13.
FIG. 13.

Analytical approximation of the electrostatic energies for C and S in a cube of unit volume for a volume fraction of f = 0.13 with a field strength E 0.

Tables

Generic image for table
Table I.

Wetting capabilities of undeformed C , C , and S, with C stacked hexagonally and S in a bcc lattice.

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/content/aip/journal/jcp/137/4/10.1063/1.4738594
2012-07-31
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Strong stretching theory for diblock copolymers in thin films under application of electric fields
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/4/10.1063/1.4738594
10.1063/1.4738594
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