Origins of low-symmetry phases in asymmetric diblock copolymer melts

Kyungtae Kim; Akash Arora; Ronald M. Lewis; Meijiao Liu; Weihua Li; An Chang Shi; Kevin D. Dorfman; Frank S. Bates

doi:10.1073/pnas.1717850115

Origins of low-symmetry phases in asymmetric diblock copolymer melts

Kyungtae Kim, Akash Arora, Ronald M. Lewis, Meijiao Liu, Weihua Li, An Chang Shi, Kevin D. Dorfman, Frank S. Bates

Chemical Engineering and Materials Science

Research output: Contribution to journal › Article › peer-review

118 Scopus citations

Abstract

Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (T_ODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the T_ODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEX_C) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

Original language	English (US)
Pages (from-to)	847-854
Number of pages	8
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	115
Issue number	5
DOIs	https://doi.org/10.1073/pnas.1717850115
State	Published - Jan 30 2018

Bibliographical note

Funding Information:
Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–Northwestern–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada.

Funding Information:
APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–North-western–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada.

Funding Information:
ACKNOWLEDGMENTS. Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the

Keywords

Frank–Kasper phases
block copolymers
fluctuating disorder
sphere-forming diblocks
structured liquids

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10.1073/pnas.1717850115

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title = "Origins of low-symmetry phases in asymmetric diblock copolymer melts",

abstract = "Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.",

keywords = "Frank–Kasper phases, block copolymers, fluctuating disorder, sphere-forming diblocks, structured liquids",

author = "Kyungtae Kim and Akash Arora and Lewis, {Ronald M.} and Meijiao Liu and Weihua Li and Shi, {An Chang} and Dorfman, {Kevin D.} and Bates, {Frank S.}",

note = "Funding Information: Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–Northwestern–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada. Funding Information: APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–North-western–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada. Funding Information: ACKNOWLEDGMENTS. Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the",

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T1 - Origins of low-symmetry phases in asymmetric diblock copolymer melts

AU - Kim, Kyungtae

AU - Arora, Akash

AU - Lewis, Ronald M.

AU - Liu, Meijiao

AU - Li, Weihua

AU - Shi, An Chang

AU - Dorfman, Kevin D.

AU - Bates, Frank S.

N1 - Funding Information: Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–Northwestern–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada. Funding Information: APS, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. Part of this work was performed at the DuPont–North-western–Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University. Parts of the computations were made possible by the Minnesota Supercomputing Institute at University of Minnesota, as well as the facilities of the Shared Hierarchical Academic Research Computing Network (www.sharcnet.ca) and Compute/ Calcul Canada. Funding Information: ACKNOWLEDGMENTS. Byeongdu Lee is acknowledged for his help with experiments conducted at Beamline 12-ID-B at the Advanced Photon Source (APS). Marc Hillmyer provided a valuable review of the manuscript. This research was supported by the National Science Foundation under Grants DMR-1104368 and DMR-1333669, the National Science Foundation of China under Grants 21774025 and 21320102005, and the Natural Science and Engineering Research Council of Canada. The work was enabled by resources at the

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Y1 - 2018/1/30

N2 - Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

AB - Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

KW - Frank–Kasper phases

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KW - fluctuating disorder

KW - sphere-forming diblocks

KW - structured liquids

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Origins of low-symmetry phases in asymmetric diblock copolymer melts

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