Analytical weak-sagregation theory of bicontinuous phases in diblock copolymers

Scott T. Milner, Peter D. Olmsted

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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 languageEnglish (US)
Pages (from-to)249-255
Number of pages7
JournalJournal de Physique I
Issue number2
StatePublished - Dec 1 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Engineering


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