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Hard-surface effects in polymer self-consistent field calculations
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10.1063/1.2740633
/content/aip/journal/jcp/126/23/10.1063/1.2740633
http://aip.metastore.ingenta.com/content/aip/journal/jcp/126/23/10.1063/1.2740633
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Pressure field for confined homopolymer melts, with the linear profile P1 used in the surface layer. , , and .

Image of FIG. 2.
FIG. 2.

Pressure field for confined homopolymer melts, where and the values are chosen to give the same in all cases: (a) The quadratic profile P2 and the cosine profile COS are used in the surface layer, respectively. and . In the P2 case, two data points located around with values less than are not shown. (b) The fifth-order polynomial P5 is used in the surface layer. . (c) The profile EXP is used in the surface layer. For the case of and , a minimum located around with value about is not shown.

Image of FIG. 3.
FIG. 3.

Influence of spatial-domain discretization on the accuracy of free-energy calculations for confined homopolymers. and . The values are given in the caption of Fig. 2. Here we approximate the exact value of (obtained when ) by that calculated with the largest , .

Image of FIG. 4.
FIG. 4.

Reduced distributions of (a) the end segments and (b) the middle segments in confined homopolymer melts, where , , and . The values are given in the caption of Fig. 2. The results of using COS profile are hardly distinguishable from those of using EXP, thus not shown. In the log-log plot shown in part (a), the curves approach a slope of as . In part (b), the curves are symmetric about . Under the bulk condition a constant value of 1 is expected for these distributions.

Image of FIG. 5.
FIG. 5.

Free-energy differences between parallel and perpendicular lamellae of symmetric diblock copolymers ( and ) between two neutral surfaces separated at . Here we use (with ) such that adjusting from 0 to 1 changes from 1 to COS profile, and accordingly the Neumann boundary conditions in the direction. The dot at represents calculated using the Dirichlet boundary conditions, where the fast sine transforms are used accordingly.

Image of FIG. 6.
FIG. 6.

Reduced distributions of (a) ends and (b) joints in parallel lamellae of symmetric diblock copolymers ( and ) of 1.5 periods confined between two neutral surfaces separated at . Here we compare the case of hard-surface confinement (EXP profile with ) with that under the bulk condition . The -end distribution can be obtained by the symmetry between and .

Image of FIG. 7.
FIG. 7.

Reduced distributions of (a) ends and (b) joints in perpendicular lamellae of symmetric diblock copolymers ( and , microphase separated along the direction) confined between two neutral surfaces separated at . Here we compare the case of hard-surface confinement (EXP profile with ) with that under the bulk condition . The -end distribution can be obtained by the symmetry between and . In the legend, the -rich domain corresponds to a value where reaches a maximum of 0.9403, the -rich domain corresponds to a value where reaches a minimum of 0.0597, and the interface is where .

Image of FIG. 8.
FIG. 8.

Free-energy differences between parallel and perpendicular cylinders of asymmetric diblock copolymers confined by EXP profile between two neutral surfaces separated at . , 4.1266, 4.2832, and 4.4068 for , 0.25, 0.28, and 0.3, respectively. The data points are actual calculations, and the curves are guide to the eyes only. and (for perpendicular cylinders) are used in our calculations.

Image of FIG. 9.
FIG. 9.

interfaces [where ] in (a) parallel cylinders (whose axis is along the direction) and (b) perpendicular cylinders of asymmetric diblock copolymers ( and ) confined between two neutral surfaces separated at . The solid curves show the results under confinement by EXP profile , and the dotted curves show corresponding results under the bulk condition . and (for perpendicular cylinders) are used in our calculations.

Image of FIG. 10.
FIG. 10.

Reduced distributions of (a) ends, (b) ends, and (c) joints in parallel cylinders of asymmetric diblock copolymers ( and ) confined between two neutral surfaces separated at . In parts (a) and (b) we compare the case of hard-surface confinement (EXP profile with ) with that under the bulk condition , and use two values corresponding to Fig. 9(a). In part (c) only the results of hard-surface confinement are shown for clarity. Part (d) shows these distributions in perpendicular cylinders, where represents the average over directions, and under the bulk condition a constant value of 1 is expected for these distributions. In all cases, the distributions are symmetric about , and and (for perpendicular cylinders) are used in our calculations.

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/content/aip/journal/jcp/126/23/10.1063/1.2740633
2007-06-19
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hard-surface effects in polymer self-consistent field calculations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/126/23/10.1063/1.2740633
10.1063/1.2740633
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