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Discovery of a Frank-Kasper σ Phase in Sphere-Forming Block Copolymer Melts

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Science  15 Oct 2010:
Vol. 330, Issue 6002, pp. 349-353
DOI: 10.1126/science.1195552

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Abstract

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 σ 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.

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