Analytical weak-sagregation theory of bicontinuous phases in diblock copolymers

Scott T. Milner; Peter D. Olmsted

Analytical weak-sagregation theory of bicontinuous phases in diblock copolymers

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Abstract

We compute phase diagrams for diblock copolymers in the mean-field weak-segregation regime as a function of the fraction f of A-monomers and the repulsive interaction _χN. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m] and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher [220] reflections in addition to the [211] fundamental. The gyroid free energy is favored by terms of the form ψ_[211]³ψ_[220] and ψ_[211]²ψ_[220]; the analogous terms are not permitted for OBDD.

Original language	English (US)
Pages (from-to)	249-255
Number of pages	7
Journal	Journal de Physique I
Volume	7
Issue number	2
State	Published - Dec 1 1997

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Engineering

Cite this

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abstract = "We compute phase diagrams for diblock copolymers in the mean-field weak-segregation regime as a function of the fraction f of A-monomers and the repulsive interaction χN. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m] and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher [220] reflections in addition to the [211] fundamental. The gyroid free energy is favored by terms of the form ψ[211]3ψ[220] and ψ[211]2ψ[220]; the analogous terms are not permitted for OBDD.",

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N2 - We compute phase diagrams for diblock copolymers in the mean-field weak-segregation regime as a function of the fraction f of A-monomers and the repulsive interaction χN. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m] and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher [220] reflections in addition to the [211] fundamental. The gyroid free energy is favored by terms of the form ψ[211]3ψ[220] and ψ[211]2ψ[220]; the analogous terms are not permitted for OBDD.

AB - We compute phase diagrams for diblock copolymers in the mean-field weak-segregation regime as a function of the fraction f of A-monomers and the repulsive interaction χN. We include the ordered bicontinuous double-diamond (OBDD) phase [space group Pn3m] and the gyroid phase [space group Ia3d] as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and lamellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher [220] reflections in addition to the [211] fundamental. The gyroid free energy is favored by terms of the form ψ[211]3ψ[220] and ψ[211]2ψ[220]; the analogous terms are not permitted for OBDD.

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Analytical weak-sagregation theory of bicontinuous phases in diblock copolymers

Abstract

All Science Journal Classification (ASJC) codes

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