Discovery of a Frank-Kasper σ phase in sphere-forming block copolymer melts

Sangwoo Lee, Michael J. Bluemle, Frank S. Bates

Research output: Contribution to journalArticlepeer-review

212 Scopus citations


Sphere-forming block copolymers are known to self-assemble into body-centered cubic crystals near the order-disorder transition temperature. Small-angle x-ray scattering and transmission electron microscopy experiments on diblock and tetrablock copolymer melts have revealed an equilibrium phase characterized by a large tetragonal unit cell containing 30 microphase-separated spheres. This structure, referred to as the sigma (σ) phase by Frank and Kasper more than 50 years ago, nucleates and grows from the body-centered cubic phase similar to its occurrence in metal alloys and is a crystal approximant to dodecagonal quasicrystals. Formation of the s phase in undiluted linear block copolymers (and certain branched dendrimers) appears to be mediated by macromolecular packing frustration, an entropic contribution to the interparticle interactions that control the sphere-packing geometry.

Original languageEnglish (US)
Pages (from-to)349-353
Number of pages5
Issue number6002
StatePublished - Oct 15 2010

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