Quasicrystals and Their Approximants in a Crystalline–Amorphous Diblock Copolymer

Andreas J. Mueller, Aaron P. Lindsay, Ashish Jayaraman, Timothy P. Lodge, Mahesh K. Mahanthappa, Frank S. Bates

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29 Scopus citations


Discoveries of Frank-Kasper phases and closely related dodecagonal quasicrystals (DDQCs) in soft, mesoscopic systems have galvanized efforts to unveil the fundamental mechanisms that drive the formation of these remarkably complex micellar packings. Toward this end, we report temperature-dependent small-angle X-ray scattering analyses of a crystalline-amorphous poly(ethylene oxide)-block-poly(2-ethyl hexylacrylate) (OA) diblock copolymer with Mn = 8300 g/mol, C = Mw/Mn = 1.10, and volume composition fO = 0.21. On heating at ambient temperature, this polymer assembles sequentially into five distinct morphologies prior to melt disordering at TODT = 69 °C: semicrystalline lamellae (Lc), a liquid-like packing (LLP) of particles lacking translational order, an aperiodically ordered DDQC, a periodic FK σ phase, and a body-centered cubic (BCC) packing of particles. Detailed investigations of thermal processing conditions that foster DDQC formation reveal that this metastable morphology only forms in melts exhibiting LLP characteristics arising from either melting the Lc phase at low temperature or quenching a high-temperature disordered state, and that this DDQC eventually evolves into a σ approximant phase. Cooling a well-ordered BCC phase induces direct formation of a σ phase with no evidence of DDQC formation, suggesting the critical importance of particle size distribution of the disorganized yet segregated LLP state in triggering the emergence of a DDQC.

Original languageEnglish (US)
Pages (from-to)2647-2660
Number of pages14
Issue number6
StatePublished - Mar 3 2021

Bibliographical note

Funding Information:
Financial support for this work was provided by National Science Foundation grants DMR-1801993 (A.J.M., A.P.L., and F.S.B.) and CHE-1807330 (A.J. and M.K.M.) and a National Science Foundation Graduate Research Fellowship under grant no. 00039202 (A.P.L.). SAXS experiments were carried out at Sector 12 and Sector 5 of the Advanced Photon Source (APS). The Sector 5 DuPont-Northwestern-Dow Collaborative Access Team (DND-CAT) was 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 U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under contract no. DE-AC02-06CH11357. Parts of this work, including lab source SAXS analyses, were carried out in the Characterization Facility at the University of Minnesota, which receives partial support from NSF through the UMN MRSEC (DMR-1420013 and DMR-2011401). H NMR spectra used in this study were collected on a Bruker Avance II HD 400 MHz spectrometer purchased by the Office of the Vice President of Research, the College of Science of and Engineering, and the Department of Chemistry at the University of Minnesota. MALDI-ToF data were obtained at the Mass Spectroscopy Laboratory located in the Chemistry Department at the University of Minnesota, supported by the Office of the Vice President of Research, the College of Science and Engineering, and the Department of Chemistry at the University of Minnesota, as well as The National Science Foundation (NSF, award CHE-1336940). 1

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