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Stable Frank–Kasper phases of self-assembled, soft matter spheres
Single molecular species can self-assemble into Frank–Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling sph...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
National Academy of Sciences
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6187128/ https://www.ncbi.nlm.nih.gov/pubmed/30249659 http://dx.doi.org/10.1073/pnas.1809655115 |
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author | Reddy, Abhiram Buckley, Michael B. Arora, Akash Bates, Frank S. Dorfman, Kevin D. Grason, Gregory M. |
author_facet | Reddy, Abhiram Buckley, Michael B. Arora, Akash Bates, Frank S. Dorfman, Kevin D. Grason, Gregory M. |
author_sort | Reddy, Abhiram |
collection | PubMed |
description | Single molecular species can self-assemble into Frank–Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise measure of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which a minimal interblock area competes with a minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium [Formula: see text] lattice but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness increases the sensitivity of the intradomain chain configurations and the asymmetry of local domain packing. These findings shed light on the role of volume exchange on the formation of distinct FK phases in copolymers and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry. |
format | Online Article Text |
id | pubmed-6187128 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | National Academy of Sciences |
record_format | MEDLINE/PubMed |
spelling | pubmed-61871282018-10-15 Stable Frank–Kasper phases of self-assembled, soft matter spheres Reddy, Abhiram Buckley, Michael B. Arora, Akash Bates, Frank S. Dorfman, Kevin D. Grason, Gregory M. Proc Natl Acad Sci U S A Physical Sciences Single molecular species can self-assemble into Frank–Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise measure of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which a minimal interblock area competes with a minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium [Formula: see text] lattice but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness increases the sensitivity of the intradomain chain configurations and the asymmetry of local domain packing. These findings shed light on the role of volume exchange on the formation of distinct FK phases in copolymers and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry. National Academy of Sciences 2018-10-09 2018-09-24 /pmc/articles/PMC6187128/ /pubmed/30249659 http://dx.doi.org/10.1073/pnas.1809655115 Text en Copyright © 2018 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/ This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) . |
spellingShingle | Physical Sciences Reddy, Abhiram Buckley, Michael B. Arora, Akash Bates, Frank S. Dorfman, Kevin D. Grason, Gregory M. Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title | Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title_full | Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title_fullStr | Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title_full_unstemmed | Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title_short | Stable Frank–Kasper phases of self-assembled, soft matter spheres |
title_sort | stable frank–kasper phases of self-assembled, soft matter spheres |
topic | Physical Sciences |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6187128/ https://www.ncbi.nlm.nih.gov/pubmed/30249659 http://dx.doi.org/10.1073/pnas.1809655115 |
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