Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

Proceedings of the National Academy of Sciences of the United States of America - Tập 111 Số 50 - Trang 17723-17731 - 2014
Sangwoo Lee1,2, Chris Leighton1, Frank S. Bates1
1Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455;
2Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180; and

Tóm tắt

Significance Understanding how particles fill space has challenged mathematicians, scientists, and technologists since antiquity. This article rationalizes the spontaneous organization of single-component diblock copolymers into multimolecular nanoscale domains that order into a low-symmetry Frank–Kasper (FK) phase with short-range tetrahedral close packing and a giant unit cell that contains 30 particles. This class of crystal structures bridges conventional periodic crystals and low symmetry aperiodic crystals often termed “quasicrystals.” Surprising analogies are thus drawn between the heretofore unexplained formation of FK structures in soft materials, and in certain elemental metals (including manganese and uranium), alloys, and intermetallic compounds, highlighting opportunities to better understand space filling in hard and soft materials by investigation of block polymers with precisely tuned molecular architectures.

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Tài liệu tham khảo

10.1103/PhysRevLett.53.2477

10.1103/PhysRevLett.53.1951

10.1107/S0365110X58000487

10.1107/S0365110X59001499

10.6028/jres.106.049

10.1103/RevModPhys.64.3

10.1021/ic2005024

10.1103/PhysRevB.80.134122

10.1021/ic202479y

10.1103/PhysRevB.68.014407

10.1103/PhysRevB.68.014408

10.1107/S0108768187009406

10.1126/science.1078849

10.1021/la9701844

10.1103/PhysRevLett.98.195502

10.1073/pnas.1008695108

10.1039/b502443a

10.1038/nature02368

10.1021/ja301770v

P Alexandridis, B Lindman Amphiphilic Block Copolymers: Self-Assembly and Applications (Elsevier, Amsterdam, Netherlands, 2000).

10.1126/science.1082193

10.1146/annurev.pc.41.100190.002521

10.1126/science.1195552

10.1002/aic.14023

10.1201/9781420018271

10.1063/1.1750872

10.1017/CBO9780511534874

10.1021/ma991862r

10.1021/ma021009j

10.1038/35081021

10.1063/1.882522

10.1063/1.473153

10.1016/j.physrep.2006.08.001

10.1021/jp010944q

E Helfand, ZR Wasserman, Microdomain structure and the interface in block copolymers. Developments in Block Copolymers - 1, ed I Goodman (Applied Science, New York), pp. 99–125 (1982).

10.1021/ma047990j

G Pólya Induction and Analogy in Mathematics (Princeton Univ Press, Princeton, NJ, 1954).

10.1126/science.1220869

10.1038/nature12938

10.1038/nature08439

10.1021/jp709616c

10.1021/jp7120577

10.1103/PhysRevLett.102.057801

10.1039/C0SM00944J

10.1038/ncomms1974

JW Christian The Theory of Transformations in Metals and Alloys (Pergamon Press, Oxford, 1965).

10.1038/374524a0

10.1103/PhysRevB.31.1909

NF Mott, H Jones The Theory of the Properties of Metals and Alloys (Clarendon Press, Oxford, 1936).

SL Altmann Band Theory of Metals: The Elements (Pergamon Press, Oxford, 1970).

10.1103/PhysRevLett.41.702

10.1103/PhysRev.129.625

10.1103/PhysRevLett.107.136401

10.1525/9780520911482

10.1063/1.3328198

10.1080/0895795032000102441

10.1002/chem.201203758

Y Ishii, T Fujiwara, Electronic structures and stability mechanism of quasicrystals. Handbook Metal Physics, eds Y Ishii, T Fujiwara (Elsevier, Oxford), pp. 171–208 (2008).

10.1126/science.1215368

10.1038/nature03977

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Proceedings of the National Academy of Sciences of the United States of America

Tập 111 Số 50

17723-17731

Thông tin tác giả