1
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Lequieu J. Combining particle and field-theoretic polymer models with multi-representation simulations. J Chem Phys 2023; 158:244902. [PMID: 37377157 DOI: 10.1063/5.0153104] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Accepted: 05/30/2023] [Indexed: 06/29/2023] Open
Abstract
Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.
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Affiliation(s)
- Joshua Lequieu
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA
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2
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Angelopoulou PP, Moutsios I, Manesi GM, Ivanov DA, Sakellariou G, Avgeropoulos A. Designing high χ copolymer materials for nanotechnology applications: A systematic bulk vs. thin films approach. Prog Polym Sci 2022. [DOI: 10.1016/j.progpolymsci.2022.101625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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3
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Zhao F, Dong Q, Li Q, Liu M, Li W. Emergence and Stability of Exotic “Binary” HCP-Type Spherical Phase in Binary AB/AB Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Fengmei Zhao
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Qingshu Dong
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Qingyun Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Meijiao Liu
- Department of Chemistry, Zhejiang Sci-Tech University, Hangzhou 310018, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
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4
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Chen D, Quah T, Delaney KT, Fredrickson GH. Investigation of the Self-Assembly Behavior of Statistical Bottlebrush Copolymers via Self-Consistent Field Theory Simulations. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01622] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Duyu Chen
- Materials Research Laboratory, University of California, Santa Barbara, California93106, United States
| | - Timothy Quah
- Department of Chemical Engineering, University of California, Santa Barbara, California93106, United States
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California93106, United States
| | - Glenn H. Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, California93106, United States
- Department of Chemical Engineering, University of California, Santa Barbara, California93106, United States
- Materials Department, University of California, Santa Barbara, California 93106, United States
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5
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Mueller AJ, Lindsay AP, Jayaraman A, Weigand S, Lodge TP, Mahanthappa MK, Bates FS. Tuning Diblock Copolymer Particle Packing Symmetry with Variable Molecular Weight Core-Homopolymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Andreas J. Mueller
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
| | - Aaron P. Lindsay
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
| | - Ashish Jayaraman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
| | - Steven Weigand
- DND-CAT, Advanced Photon Source, 9700 South Cass Ave, Argonne, Illinois 60439-4857, United States
| | - Timothy P. Lodge
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Mahesh K. Mahanthappa
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 United States
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6
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Zhou D, Xu M, Ma Z, Gan Z, Zheng J, Tan R, Dong XH. Discrete Diblock Copolymers with Tailored Conformational Asymmetry: A Precise Model Platform to Explore Complex Spherical Phases. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dongdong Zhou
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
- College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu 610065, China
| | - Miao Xu
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Zhuang Ma
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Zhanhui Gan
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Juncheng Zheng
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Rui Tan
- College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China
| | - Xue-Hui Dong
- South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
- Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
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7
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Chen P, Mahanthappa MK, Dorfman KD. Stability of cubic single network phases in diblock copolymer melts. JOURNAL OF POLYMER SCIENCE 2022. [DOI: 10.1002/pol.20220318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Pengyu Chen
- Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis Minnesota USA
| | - Mahesh K. Mahanthappa
- Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis Minnesota USA
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis Minnesota USA
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8
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Li SF, Muthukumar M. Theory of Microphase Separation in Concentrated Solutions of Sequence-Specific Charged Heteropolymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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9
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Liberman L, Coughlin ML, Weigand S, Bates FS, Lodge TP. Phase Behavior of Linear-Bottlebrush Block Polymers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00337] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lucy Liberman
- Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - McKenzie L. Coughlin
- Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Steven Weigand
- Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439 United States
| | - Frank S. Bates
- Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Timothy P. Lodge
- Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
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10
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Seeger SC, Dorfman KD, Lodge TP. Free Energy Trajectory for Escape of a Single Chain from a Diblock Copolymer Micelle. ACS Macro Lett 2021; 10:1570-1575. [PMID: 35549128 DOI: 10.1021/acsmacrolett.1c00508] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We use umbrella sampling to compute the free energy trajectory of a single chain undergoing expulsion from an isolated diblock copolymer micelle. This approach elucidates the experimentally unobservable transition state, identifies the spatial position of the maximum free energy, and reveals the chain conformation of a single chain as it undergoes expulsion. Combining umbrella sampling with dissipative particle dynamics simulations of A4B8 micelles reveals that the core block (A) of the expelled chain remains partially stretched at the transition state, in contrast with the collapsed state assumed in some previous models. The free energy barrier increases linearly with the Flory-Huggins interaction parameter χ up to large interaction energies, where the structure of the otherwise spherical core apparently deforms near the transition state.
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Affiliation(s)
- Sarah C. Seeger
- Department of Chemical Engineering and Materials Science, University of Minnesota − Twin Cities, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota − Twin Cities, Minneapolis, Minnesota 55455, United States
| | - Timothy P. Lodge
- Department of Chemical Engineering and Materials Science, University of Minnesota − Twin Cities, Minneapolis, Minnesota 55455, United States
- Department of Chemistry, University of Minnesota − Twin Cities, Minneapolis, Minnesota 55455, United States
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11
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Cheong GK, Dorfman KD. Disordered Micelle Regime in a Conformationally Asymmetric Diblock Copolymer Melt. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
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12
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Affiliation(s)
- Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
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13
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Xie J, Li Y, Shi A. Binary Blends of Diblock Copolymers: An Efficient Route to Complex Spherical Packing Phases. MACROMOL THEOR SIMUL 2021. [DOI: 10.1002/mats.202100053] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Jiayu Xie
- Department of Physics and Astronomy McMaster University 1280 Main Street West Hamilton Ontario L8S 4M1 Canada
| | - Yu Li
- Department of Physics and Astronomy McMaster University 1280 Main Street West Hamilton Ontario L8S 4M1 Canada
| | - An‐Chang Shi
- Department of Physics and Astronomy McMaster University 1280 Main Street West Hamilton Ontario L8S 4M1 Canada
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14
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Lindsay AP, Cheong GK, Peterson AJ, Weigand S, Dorfman KD, Lodge TP, Bates FS. Complex Phase Behavior in Particle-Forming AB/AB′ Diblock Copolymer Blends with Variable Core Block Lengths. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01290] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Aaron P. Lindsay
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Austin J. Peterson
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Steven Weigand
- DND-CAT Synchrotron Research Center, Northwestern University, APS/ANL Building 432-A004, 9700 South Cass Avenue, Argonne, Illinois 60439, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Timothy P. Lodge
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
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15
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Lindsay AP, Jayaraman A, Peterson AJ, Mueller AJ, Weigand S, Almdal K, Mahanthappa MK, Lodge TP, Bates FS. Reevaluation of Poly(ethylene- alt-propylene)- block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth. ACS NANO 2021; 15:9453-9468. [PMID: 33886269 DOI: 10.1021/acsnano.1c02420] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Reanalysis of an asymmetric poly(ethylene-alt-propylene)-block-polydimethylsiloxane (PEP-PDMS) diblock copolymer first investigated in 1999 has revealed a rich phase behavior including a dodecagonal quasicrystal (DDQC), a Frank-Kasper σ phase, and a body-centered cubic (BCC) packing at high temperature adjacent to the disordered state. On subjecting the sample to large amplitude oscillatory shear well below the σ-BCC order-order transition temperature (TOOT), small-angle X-ray scattering evidenced the emergence of a twinned BCC phase that, on heating, underwent a phase transition to an unusually anisotropic DDQC state. Surprisingly, we observe no evidence of this apparent epitaxy on heating or cooling through the equilibrium σ-BCC transition. We rationalize these results in terms of a shear-induced order-order transition and an apparent BCC-DDQC epitaxy favored by micelle translation-mediated ordering dynamics far below TOOT.
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Affiliation(s)
- Aaron P Lindsay
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Ashish Jayaraman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Austin J Peterson
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Andreas J Mueller
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Steven Weigand
- DND-CAT Synchrotron Research Center, Northwestern University, APS/ANL Building 432-A004, 9700 South Cass Avenue, Argonne, Illinois 60439, United States
| | - Kristoffer Almdal
- Department of Chemistry, Technical University of Denmark, Kemitorvet 207, 2800 Kongens Lyngby, Denmark
| | - Mahesh K Mahanthappa
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Timothy P Lodge
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Frank S Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
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16
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Quantitatively unravel the effect of chain length heterogeneity on polymer crystallization using discrete oligo l-lactide. POLYMER 2021. [DOI: 10.1016/j.polymer.2021.123746] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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17
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Barbon SM, Song JA, Chen D, Zhang C, Lequieu J, Delaney KT, Anastasaki A, Rolland M, Fredrickson GH, Bates MW, Hawker CJ, Bates CM. Architecture Effects in Complex Spherical Assemblies of (AB) n-Type Block Copolymers. ACS Macro Lett 2020; 9:1745-1752. [PMID: 35653677 DOI: 10.1021/acsmacrolett.0c00704] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Molecular architecture plays a key role in the self-assembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB)n radial star copolymers with n = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions (fA < 0.5), namely, σ and A15, but with differences in the location of order-order phase boundaries that are not anticipated by mean-field self-consistent field theory simulations. These results expand the palette of polymer architectures that readily self-assemble into complex TCP structures and suggest important design considerations when targeting specific phases of interest.
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Affiliation(s)
| | | | | | - Cheng Zhang
- Australian Institute for Bioengineering and Nanotechnology and ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, University of Queensland, Brisbane, Queensland 4072, Australia
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18
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Chang AB, Bates FS. Impact of Architectural Asymmetry on Frank-Kasper Phase Formation in Block Polymer Melts. ACS NANO 2020; 14:11463-11472. [PMID: 32820895 DOI: 10.1021/acsnano.0c03846] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In recent decades, the discoveries of complex low-symmetry phases in soft matter have inspired advances in molecular and materials design. However, understanding the mechanisms underlying symmetry selection across soft matter remains an important challenge in materials science. Block polymers represent attractive model materials because they permit wide synthetic tunability and provide access to multiple length scales (1-100 nm). However, to date the block polymer design space has been largely limited to variations in molecular weight, block volume fraction, and conformational asymmetry. The molecular architecture-the way in which chains are connected-offers rich potential but remains relatively unexplored in experimental block polymers. Our work bridges this gap, connecting molecular architecture, space-filling demands, and symmetry selection in block polymer self-assembly. Three series of block polymers were synthesized by living polymerization, tuning the architectural asymmetry across the linear-b-linear and linear-b-bottlebrush limits. The bottlebrush architecture amplifies two key ingredients for the formation of Frank-Kasper phases: high conformational asymmetry and high self-concentration. Analysis by small-angle X-ray scattering provides insight into the impact of architectural asymmetry on block polymer self-assembly. Increasing the asymmetry between blocks opens the complex phase window, expanding opportunities to tune symmetry selection in block polymer melts.
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Affiliation(s)
- Alice B Chang
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Frank S Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
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19
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Lewis RM, Jackson GL, Maher MJ, Kim K, Narayanan S, Lodge TP, Mahanthappa MK, Bates FS. Grain Growth and Coarsening Dynamics in a Compositionally Asymmetric Block Copolymer Revealed by X-ray Photon Correlation Spectroscopy. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01676] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Grayson L. Jackson
- Department of Chemistry, University of Wisconsin−Madison, Madison, Wisconsin 53706, United States
| | | | | | - Suresh Narayanan
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60349, United States
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20
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Cheong GK, Bates FS, Dorfman KD. Symmetry breaking in particle-forming diblock polymer/homopolymer blends. Proc Natl Acad Sci U S A 2020; 117:16764-16769. [PMID: 32636255 PMCID: PMC7382261 DOI: 10.1073/pnas.2006079117] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank-Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank-Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank-Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank-Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.
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Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
| | - Frank S Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
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21
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Park SJ, Kim JU. Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory. SOFT MATTER 2020; 16:5233-5249. [PMID: 32458920 DOI: 10.1039/d0sm00620c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.
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Affiliation(s)
- So Jung Park
- Department of Physics, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea.
| | - Jaeup U Kim
- Department of Physics, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea.
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22
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Qiang Y, Li W, Shi AC. Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures. ACS Macro Lett 2020; 9:668-673. [PMID: 35648571 DOI: 10.1021/acsmacrolett.0c00193] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
It is generally believed that the spherical domains self-assembled from AB-type block copolymers are composed of the minority A blocks with a volume fraction of fA < 1/2. Breaking this generic rule so that the spherical domains are formed by the majority A blocks (fA > 1/2) requires mechanisms to drastically expand the stable region of spherical packing phases. Self-consistent field theory predicts that dendron-like AB-type block copolymers, composed of G - 1 generations of A blocks connected with the outermost generation of B blocks, exhibit a stable region of spherical packing phases extending to fA ∼ 0.7. The extremely expanded spherical regions shed light on the mechanisms governing the self-assembly of amphiphilic macromolecules, as well as provide opportunities to engineer complex spherical packing phases.
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Affiliation(s)
- Yicheng Qiang
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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23
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Mueller AJ, Lindsay AP, Jayaraman A, Lodge TP, Mahanthappa MK, Bates FS. Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends. ACS Macro Lett 2020; 9:576-582. [PMID: 35648489 DOI: 10.1021/acsmacrolett.0c00124] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
The observation of complex, Frank-Kasper (FK) particle packings in diblock polymer melts has until recently been limited to low molecular weight, conformationally asymmetric polymers. We report temperature-dependent small-angle X-ray scattering (SAXS) studies of blends of a sphere-forming poly(styrene-block-1,4-butadiene) (SB) diblock polymer (Mn = 33.3 kg/mol, Đ = Mw/Mn = 1.08, fB = 0.18) with two different poly(1,4-butadiene) (B) homopolymer additives. When the B additive Mn is the same as that of the diblock core-forming B segment, these blends remarkably form tetrahedrally close-packed FK σ and Laves C14 and C15 phases with increasing B content. However, binary blends in which the B additive Mn is 60% of that of the diblock B segment form only the canonical body-centered cubic (BCC) particle packing and hexagonally-packed cylinders (HEXc). The observed phase behavior is rationalized in terms of "wet" and "dry" brush blending, whereby higher B Mn drives stronger localization of the homopolymer in the particle cores while preserving the interfacial area per SB diblock chain. The consequent packing constraints in these blends destabilize the BCC packing, and FK phases emerge as optimal minimal surface solutions to filling space at constant density while maximizing local particle sphericity.
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Abstract
This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.
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Affiliation(s)
- M W Matsen
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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25
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Cheong GK, Chawla A, Morse DC, Dorfman KD. Open-source code for self-consistent field theory calculations of block polymer phase behavior on graphics processing units. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:15. [PMID: 32086593 DOI: 10.1140/epje/i2020-11938-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
Self-consistent field theory (SCFT) is a powerful approach for computing the phase behavior of block polymers. We describe a fast version of the open-source Polymer Self-Consistent Field (PSCF) code that takes advantage of the massive parallelization provided by a graphical processing unit (GPU). Benchmarking double-precision calculations indicate up to 30× reduction in time to converge SCFT calculations of various diblock copolymer phases when compared to the Fortran CPU version of PSCF using the same algorithms, with the speed-up increasing with increasing unit cell size for the diblock polymer problems examined here. Where double-precision accuracy is not needed, single-precision calculations can provide speed-up of up to 60× in convergence time. These improvements in speed within an open-source format open up new vistas for SCFT-driven block polymer materials discovery by the community at large.
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Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, 55455, Minneapolis, MN, USA
| | - Anshul Chawla
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, 55455, Minneapolis, MN, USA
| | - David C Morse
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, 55455, Minneapolis, MN, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota - Twin Cities, 421 Washington Avenue SE, 55455, Minneapolis, MN, USA.
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Lindsay AP, Lewis RM, Lee B, Peterson AJ, Lodge TP, Bates FS. A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends. ACS Macro Lett 2020; 9:197-203. [PMID: 35638682 DOI: 10.1021/acsmacrolett.9b01026] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A renewed focus on the phase behavior of nominally single-component, compositionally asymmetric diblock copolymers has revealed a host of previously unanticipated Frank-Kasper (FK) and quasicrystalline phases. However, these periodic and aperiodic particle packings have thus far only been reported in low molecular weight, highly conformationally asymmetric diblock copolymers, leaving researchers with a relatively small library of polymers in which these phases can be studied. In this work, we report on a simple approach to access these morphologies: blending two diblock copolymers with the same corona block length and varied core block lengths. Compositionally symmetric and asymmetric polystyrene-b-1,4-polybutadiene (SB) diblock copolymers with constant corona block lengths were blended together and shown via small-angle X-ray scattering and transmission electron microscopy to order into the FK A15 and σ phases, as well as a dodecagonal quasicrystal, providing a route to various particle packings in high molecular weight diblock copolymer melts.
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Lachmayr KK, Sita LR. Small‐Molecule Modulation of Soft‐Matter Frank–Kasper Phases: A Method for Adding Function to Form. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.201915416] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Kätchen K. Lachmayr
- Department of Chemistry and BiochemistryUniversity of Maryland College Park MD 20742 USA
| | - Lawrence R. Sita
- Department of Chemistry and BiochemistryUniversity of Maryland College Park MD 20742 USA
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Lachmayr KK, Sita LR. Small‐Molecule Modulation of Soft‐Matter Frank–Kasper Phases: A Method for Adding Function to Form. Angew Chem Int Ed Engl 2020; 59:3563-3567. [DOI: 10.1002/anie.201915416] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Indexed: 01/27/2023]
Affiliation(s)
- Kätchen K. Lachmayr
- Department of Chemistry and BiochemistryUniversity of Maryland College Park MD 20742 USA
| | - Lawrence R. Sita
- Department of Chemistry and BiochemistryUniversity of Maryland College Park MD 20742 USA
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29
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Levi AE, Fu L, Lequieu J, Horne JD, Blankenship J, Mukherjee S, Zhang T, Fredrickson GH, Gutekunst WR, Bates CM. Efficient Synthesis of Asymmetric Miktoarm Star Polymers. Macromolecules 2020; 53:702-710. [PMID: 32489220 PMCID: PMC7266137 DOI: 10.1021/acs.macromol.9b02380] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Asymmetric miktoarm star polymers comprising an unequal number of chemically-distinct blocks connected at a common junction produce unique material properties, yet existing synthetic strategies are beleaguered by complicated reaction schemes that are restricted in both monomer scope and yield. Here, we introduce a new synthetic approach coined "μSTAR" - Miktoarm Synthesis by Termination After Ring-opening metathesis polymerization - that circumvents these traditional synthetic limitations by constructing the block-block junction in a scalable, one-pot process involving (1) grafting-through polymerization of a macromonomer followed by (2) in-situ enyne-mediated termination to install a single mikto-arm with exceptional efficiency. This modular μSTAR platform cleanly generates AB n and A(BA') n miktoarm star polymers with unprecedented versatility in the selection of A and B chemistries as demonstrated using many common polymer building blocks: poly(siloxane), poly(acrylate), poly(methacrylate), poly(ether), poly(ester), and poly(styrene). The average number of B or BA' arms (n) is easily controlled by the molar equivalents of macromonomer relative to Grubbs catalyst in the initial ring-opening metathesis polymerization step. While these materials are characterized by dispersity in n that arises from polymerization statistics, they self-assemble into mesophases that are identical to those predicted for precise miktoarm stars as evidenced by small-angle X-ray scattering experiments and self-consistent field theory simulations. In summary, the μSTAR technique provides a significant boost in design flexibility and synthetic simplicity while retaining the salient phase behavior of precise miktoarm star materials.
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Affiliation(s)
- Adam E. Levi
- Department of Chemistry & Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Liangbing Fu
- School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive NW, Atlanta, Georgia 30332, United States
| | - Joshua Lequieu
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Jacob D. Horne
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
| | - Jacob Blankenship
- Department of Chemistry & Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Sanjoy Mukherjee
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
| | - Tianqi Zhang
- School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive NW, Atlanta, Georgia 30332, United States
| | - Glenn H. Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Department, University of California, Santa Barbara, California 93106, United States
| | - Will R. Gutekunst
- School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive NW, Atlanta, Georgia 30332, United States
| | - Christopher M. Bates
- Department of Chemistry & Biochemistry, University of California, Santa Barbara, California 93106, United States
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Materials Department, University of California, Santa Barbara, California 93106, United States
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30
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Lachmayr KK, Wentz CM, Sita LR. An Exceptionally Stable and Scalable Sugar–Polyolefin Frank–Kasper A15 Phase. Angew Chem Int Ed Engl 2019. [DOI: 10.1002/ange.201912648] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Kätchen K. Lachmayr
- Department of Chemistry and Biochemistry University of Maryland College Park MD 20742 USA
| | - Charlotte M. Wentz
- Department of Chemistry and Biochemistry University of Maryland College Park MD 20742 USA
| | - Lawrence R. Sita
- Department of Chemistry and Biochemistry University of Maryland College Park MD 20742 USA
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31
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Lachmayr KK, Wentz CM, Sita LR. An Exceptionally Stable and Scalable Sugar-Polyolefin Frank-Kasper A15 Phase. Angew Chem Int Ed Engl 2019; 59:1521-1526. [PMID: 31703151 DOI: 10.1002/anie.201912648] [Citation(s) in RCA: 49] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Revised: 11/06/2019] [Indexed: 11/08/2022]
Abstract
"One-component" soft material Frank-Kasper (FK) phases are an intriguing structural form of matter that possess periodically ordered structures arising from the self-reconfiguration and close packing of an initial assembly of identical "deformable" spheres into two or more size- or shape-distinct sets of particles. Significant challenges that must still be addressed to advance the field of soft matter FK phases further, however, include their rare and unpredictable occurrence, uncertain mechanisms of solid-state assembly, and low thermodynamic stability. Here we show that a readily-accessible sugar-polyolefin conjugate quantitatively produces an exceptionally stable solid-state FK A15 phase through a rapid and irreversible thermotropic order-order transition, which contrary to other prevailing proposed mechanisms, does not require mass transfer between particles or large structural reorganization in the bulk to establish unit cell non-equivalency. Our results provide the basis for a realistic strategy for obtaining practical and scalable quantities of a diverse range of sugar-polyolefin FK A15 phases with unique intrinsic physical properties and chemical reactivities not previously seen in such systems.
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Affiliation(s)
- Kätchen K Lachmayr
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, 20742, USA
| | - Charlotte M Wentz
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, 20742, USA
| | - Lawrence R Sita
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, 20742, USA
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32
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Zhu HY, Tian F, Li XH, Qiu HB, Wang J. Crystallization and Phase Behavior in Block Copolymer Solution: An in Situ Small Angle X-ray Scattering Study. CHINESE JOURNAL OF POLYMER SCIENCE 2019. [DOI: 10.1007/s10118-019-2258-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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33
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Early JT, Lodge TP. Fragmentation of 1,2-Polybutadiene-block-Poly(ethylene oxide) Micelles in Imidazolium-Based Ionic Liquids. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01530] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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34
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Bates MW, Lequieu J, Barbon SM, Lewis RM, Delaney KT, Anastasaki A, Hawker CJ, Fredrickson GH, Bates CM. Stability of the A15 phase in diblock copolymer melts. Proc Natl Acad Sci U S A 2019; 116:13194-13199. [PMID: 31209038 PMCID: PMC6613078 DOI: 10.1073/pnas.1900121116] [Citation(s) in RCA: 107] [Impact Index Per Article: 21.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)-block-poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 - 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15-disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.
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Affiliation(s)
- Morgan W Bates
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
| | - Joshua Lequieu
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
| | - Stephanie M Barbon
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
| | - Ronald M Lewis
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
| | - Kris T Delaney
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
| | - Athina Anastasaki
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
| | - Craig J Hawker
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
- Department of Materials, University of California, Santa Barbara, CA 93106
| | - Glenn H Fredrickson
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106
- Department of Chemical Engineering, University of California, Santa Barbara, CA 93106
| | - Christopher M Bates
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106;
- Department of Materials, University of California, Santa Barbara, CA 93106
- Department of Chemical Engineering, University of California, Santa Barbara, CA 93106
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35
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Wei X, Luo T. Chain length effect on thermal transport in amorphous polymers and a structure–thermal conductivity relation. Phys Chem Chem Phys 2019; 21:15523-15530. [DOI: 10.1039/c9cp02397f] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
The physics of thermal transport in polymers is important in many applications, such as in heat exchangers and electronics packaging.
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Affiliation(s)
- Xingfei Wei
- Department of Aerospace and Mechanical Engineering
- University of Notre Dame
- Notre Dame IN 46556
- USA
| | - Tengfei Luo
- Department of Aerospace and Mechanical Engineering
- University of Notre Dame
- Notre Dame IN 46556
- USA
- Department of Chemical and Biomolecular Engineering
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