Dodecagonal quasicrystalline order in a diblock copolymer melt

Timothy M. Gillard, Sangwoo Lee, Frank S. Bates

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131 Scopus citations


We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (TODT = 66 °C) using small-angle X-ray scattering (SAXS) measurements. Between TODT and the order-order transition temperature TOOT = 42 °C, an equilibrium body-centered cubic (BCC) structure forms, whereas below TOOT the Frank-Kasper σ phase is the stable morphology. At T < 40 °C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35 °C and more than 10 and 200 d at 25 °C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state,whereas the σ phase grows directly when the BCC phase is cooled below TOOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40 °C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.

Original languageEnglish (US)
Pages (from-to)5167-5172
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
StatePublished - May 10 2016

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation (NSF) under Award 1104368. Portions of this work were performed at the DuPont-Northwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Use of the APS, an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the US DOE under Contract DE-AC02-06CH11357.


  • Block polymers
  • Frank-Kasper phases
  • Quasicrystals

How much support was provided by MRSEC?

  • Shared

PubMed: MeSH publication types

  • Journal Article
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.


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