1
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Shi J, Zhou J, Liu L, Miao C. Molecular dynamics simulations of single polyethylene chain folding during fast quenching using all-atom and united-atom models. Phys Chem Chem Phys 2024; 26:24995-25004. [PMID: 39300936 DOI: 10.1039/d4cp02746a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2024]
Abstract
Molecular dynamics simulations have been employed to investigate the folding behavior of a single linear polyethylene (PE) chain containing 1000 backbone carbon atoms under fast quenching based on all-atom and united-atom models. The single-chain folding characteristics were studied in detail for six different force fields by analyzing the evolution of chain conformations, folded structure characterisation, free energy and crystallisation. The results show that the all-trans chain undergoes a similar two-stage chain collapse mechanism during isothermal relaxation at T = 500 K, transitioning from local collapse to global collapse into a molten globule state under different force fields. During fast quenching at 100 K ns-1, the molten globule of all-atom model transitions into a folded, significantly anisotropic ordered structure under AMBER-AA or OPLS-AA force fields, while that of the united-atom model remains unchanged in its globular structure. The chain crystallization evolution indicates that the single chain folds into ordered lamellar structures with higher crystallinity under AMBER-AA and OPLS-AA force fields. In contrast, under the other four force fields, the single chain remains in a stable amorphous state.
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Affiliation(s)
- Jingfu Shi
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150001, P. R. China.
| | - Jianqiu Zhou
- Institute of Basic Medical Sciences, Harbin Medical University, Harbin, 150086, P. R. China.
| | - Lei Liu
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150001, P. R. China.
| | - Changqing Miao
- National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150001, P. R. China.
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2
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Le Brun AP, Gilbert EP. Advances in sample environments for neutron scattering for colloid and interface science. Adv Colloid Interface Sci 2024; 327:103141. [PMID: 38631095 DOI: 10.1016/j.cis.2024.103141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 03/27/2024] [Accepted: 03/27/2024] [Indexed: 04/19/2024]
Abstract
This review describes recent advances in sample environments across the full complement of applicable neutron scattering techniques to colloid and interface science. Temperature, pressure, flow, tensile testing, ultrasound, chemical reactions, IR/visible/UV light, confinement, humidity and electric and magnetic field application, as well as tandem X-ray methods, are all addressed. Consideration for material choices in sample environments and data acquisition methods are also covered as well as discussion of current and potential future use of machine learning and artificial intelligence.
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Affiliation(s)
- Anton P Le Brun
- Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation (ANSTO), New Illawarra Road, Lucas Heights, NSW 2234, Australia
| | - Elliot Paul Gilbert
- Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation (ANSTO), New Illawarra Road, Lucas Heights, NSW 2234, Australia.
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3
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Jin F, Huang Z, Zheng Y, Sun C, Kafle N, Ma J, Pan P, Miyoshi T. Impact of Entanglement on Folding of Semicrystalline Polymer during Crystallization. ACS Macro Lett 2023; 12:1138-1143. [PMID: 37503873 DOI: 10.1021/acsmacrolett.3c00364] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Upon cooling, semicrystalline polymers experience crystallization and form alternatively stacked layers consisting of thin crystal lamellae and amorphous ones. The unique morphology, crystallinity, and crystallization kinetics highly depend on the molecular weight. Therefore, it is deduced that entanglement impacts crystallization kinetics, as well as hierarchically crystalline structures. However, the impact of entanglement on folded crystalline chains has not been well understood due to experimental difficulties. In this work, chain-folding structures for seven 13C CH3 labeled poly(l-lactic acid)s with various molecular weights (Mws) were investigated by 13C-13C double quantum NMR spectroscopy. As a result, chain-folding events were categorized into three different Mw regimes: (i) The lowest Mw sample (2K g/mol) adopts an extended chain conformation (folding number, n = 0) (regime I); (ii) Intermediate Mw ones possess mixtures of non- and once-folded structures, and the once-folded fraction suddenly increases above the entanglement length (Me), up to Mw = 45K g/mol (regime II); (iii) The high Mw ones (Mw > 45K g/mol) adopt the highest chance for an adjacent re-entry structure with n = 1.0 in the well-developed entangled network (regime III). It was suggested that entanglement induces folding of the semicrystalline polymer.
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Affiliation(s)
- Fan Jin
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Zheng Huang
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Ying Zheng
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
- State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China
- Institute of Zhejiang University-Quzhou, 99 Zheda Road, Quzhou 324000, China
| | - Chenxuan Sun
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
- State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China
- Institute of Zhejiang University-Quzhou, 99 Zheda Road, Quzhou 324000, China
| | - Navin Kafle
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Jiayang Ma
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Pengju Pan
- State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China
- Institute of Zhejiang University-Quzhou, 99 Zheda Road, Quzhou 324000, China
| | - Toshikazu Miyoshi
- School of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325-3909, United States
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4
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Song Y, Ma Z, Zhang W. Manipulation of a Single Polymer Chain: From the Nanomechanical Properties to Dynamic Structure Evolution. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00076] [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)
- Yu Song
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Ziwen Ma
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Wenke Zhang
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
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5
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Yuan S, Schmidt-Rohr K. Immobilized 13C-labeled polyether chain ends confined to the crystallite surface detected by advanced NMR. SCIENCE ADVANCES 2020; 6:eabc0059. [PMID: 32917712 PMCID: PMC7486094 DOI: 10.1126/sciadv.abc0059] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
A comprehensive 13C nuclear magnetic resonance (NMR) approach for characterizing the location of chain ends of polyethers and polyesters, at the crystallite surface or in the amorphous layers, is presented. The OH chain ends of polyoxymethylene are labeled with 13COO-acetyl groups and their dynamics probed by 13C NMR with chemical shift anisotropy (CSA) recoupling. At least three-quarters of the chain ends are not mobile dangling cilia but are immobilized, exhibiting a powder pattern characteristic of the crystalline environment and fast CSA dephasing. The location and clustering of the immobilized chain ends are analyzed by spin diffusion. Fast 1H spin diffusion from the amorphous regions shows confinement of chain ends to the crystallite surface, corroborated by fast 13C spin exchange between chain ends. These observations confirm the principle of avoidance of density anomalies, which requires that chains terminate at the crystallite surface to stay out of the crowded interfacial layer.
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Affiliation(s)
- Shichen Yuan
- Department of Chemistry, Brandeis University, Waltham, MA 02453, USA
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6
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Ma Z, Yang P, Zhang X, Jiang K, Song Y, Zhang W. Quantifying the Chain Folding in Polymer Single Crystals by Single-Molecule Force Spectroscopy. ACS Macro Lett 2019; 8:1194-1199. [PMID: 35619456 DOI: 10.1021/acsmacrolett.9b00607] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Chain folding is a motif of polymer crystallization, which is essential for determining the crystallization kinetics. However, the experimental quantification of the chain folding remains a challenge because of limited instrumental resolution. Here, we quantify chain folding in solution-grown single crystals by using atomic force microscopy (AFM)-based single-molecule force spectroscopy. The fingerprint spectrum of force-induced chain motion allows us to decipher the adjacent and nonadjacent re-entry folding with spatial resolution of subnanometers. The average fractions of adjacent re-entry folds ⟨f⟩ are in the range 91-95% for polycaprolactone, poly-l-lactic acid, and polyamide 66, which is higher than the values determined by other classical technologies. The established single-molecule method is applicable to a broad range of crystalline polymer systems with different chain conformations or compositions.
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Affiliation(s)
- Ziwen Ma
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Peng Yang
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Xiaoye Zhang
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Ke Jiang
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Yu Song
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
- Institute of Theoretical Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China
| | - Wenke Zhang
- State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, P. R. China
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7
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Wang S, Yuan S, Wang K, Chen W, Yamada K, Barkley D, Koga T, Hong YL, Miyoshi T. Intramolecular and Intermolecular Packing in Polymer Crystallization. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00702] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Shijun Wang
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Shichen Yuan
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Kun Wang
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Wei Chen
- National Synchrotron Radiation Lab, CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, P. R. China
| | - Koji Yamada
- Advanced Processing Technology Unit, Research Center, Toyobo Co., Ltd. 2-1-1 Katata, Otsu, Shiga 520-0292, Japan
| | | | | | - You-lee Hong
- RIKEN CLST-JEOL Collaboration Center, RIKEN, Yokohama, Kanagawa 230-0045, Japan
| | - Toshikazu Miyoshi
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
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8
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Wang S, Hong YL, Yuan S, Chen W, Zhou W, Li Z, Wang K, Min X, Konishi T, Miyoshi T. Chain Trajectory, Chain Packing, and Molecular Dynamics of Semicrystalline Polymers as Studied by Solid-State NMR. Polymers (Basel) 2018; 10:E775. [PMID: 30960700 PMCID: PMC6403921 DOI: 10.3390/polym10070775] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2018] [Revised: 07/13/2018] [Accepted: 07/13/2018] [Indexed: 01/05/2023] Open
Abstract
Chain-level structure of semicrystalline polymers in melt- and solution-grown crystals has been debated over the past half century. Recently, 13C⁻13C double quantum (DQ) Nuclear Magnetic Resonance (NMR) spectroscopy has been successfully applied to investigate chain-folding (CF) structure and packing structure of 13C enriched polymers after solution and melt crystallization. We review recent NMR studies for (i) packing structure, (ii) chain trajectory, (iii) conformation of the folded chains, (iv) nucleation mechanisms, (v) deformation mechanism, and (vi) molecular dynamics of semicrystalline polymers.
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Affiliation(s)
- Shijun Wang
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
| | - You-Lee Hong
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
- RIKEN CLST-JEOL Collaboration Center, RIKEN, Yokohama, Kanagawa 230-0045, Japan.
| | - Shichen Yuan
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
| | - Wei Chen
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
- State Key Lab of Pollution Control and Resource Reuse Study, College of Environmental Science and Engineering, Tongji University, Shanghai 200092, China.
| | - Wenxuan Zhou
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
| | - Zhen Li
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
| | - Kun Wang
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
| | - Xu Min
- School of Physics and Materials Science & Shanghai Key Laboratory of Magnetic Resonance, East China Normal University, Shanghai 200062, China.
| | - Takashi Konishi
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
- Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan.
| | - Toshikazu Miyoshi
- Department of Polymer Science, The University of Akron, Akron, OH 44325-3909, USA.
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9
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Liu F, Sun T, Tang P, Zhang H, Qiu F. Understanding chain folding morphology of semicrystalline polymers based on a rod-coil multiblock model. SOFT MATTER 2017; 13:8250-8263. [PMID: 29071322 DOI: 10.1039/c7sm01892d] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We employ a rod-coil multiblock molecular chain model to investigate chain folding behavior, which is a significant characteristic in semicrystalline polymers, by using the method of self-consistent field theory (SCFT). Polymer chains with different conformations in crystalline and amorphous regions are described by rigid rod chains and flexible Gaussian chains, respectively. At present, we concentrate on the thermodynamic behaviors of polymer semi-crystals after the formation of the initial lamellar crystals. A new mechanism for lamellar thickening is proposed to realize that the end of lamellar thickening depends on the crystallinity degree. In other words, it is impossible for lamellae to develop into extended-chain crystals by means of lamellar thickening if crystallinity is limited to a certain degree. We further discuss the competition between crystalline and amorphous regions and its influence on crystallization behaviors, such as the formation of double lamellae, chain tilt, the anomalies and adjacent re-entry. The synergistic influences of the driving force of crystallization, interfacial energy and crystallinity degree on chain folding behavior are also investigated when the density anomalies in amorphous regions are excluded. Our model demonstrates advantages in accurately describing the mesoscopic layered structures of semicrystalline polymers based upon a microscopic chain model and provides at least a semi-quantitative thermodynamic picture for chain folding.
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Affiliation(s)
- Faqiang Liu
- State Key Laboratory of Molecular Engineering of Polymers, Collaborative Innovation Center of Polymers and Polymer Composite Materials, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
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10
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Wang S, Yuan S, Chen W, He Q, Hong YL, Miyoshi T. Solid-State NMR Study of the Chain Trajectory and Crystallization Mechanism of Poly(l-lactic acid) in Dilute Solution. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01462] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shijun Wang
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Shichen Yuan
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Wei Chen
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
- State
Key Lab of Pollution Control and Resource Reuse Study, College of
Environmental Science and Engineering, Tongji University, Shanghai 200092, China
| | - Qiming He
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - You-lee Hong
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
- RIKEN
CLST-JEOL Collaboration Center, RIKEN, Yokohama, Kanagawa 230-0045, Japan
| | - Toshikazu Miyoshi
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
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11
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Hong YL, Chen W, Yuan S, Kang J, Miyoshi T. Chain Trajectory of Semicrystalline Polymers As Revealed by Solid-State NMR Spectroscopy. ACS Macro Lett 2016; 5:355-358. [PMID: 35614717 DOI: 10.1021/acsmacrolett.6b00040] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Over the last half century, a chain-folding structure of semicrystalline polymers has been debated in polymer science. Recently, 13C-13C double quantum (DQ) NMR spectroscopy combined with 13C selective isotope labeling has been developed to investigate re-entrance sites of the folded chains, mean values of adjacent re-entry number ⟨n⟩ and fraction ⟨F⟩ of semicrystalline polymers. This viewpoint highlights the versatile approaches of using solid-state (ss) NMR and isotope labeling for revealing (i) chain trajectory in melt- and solution-grown crystals, (ii) conformation of the folded chains in single crystals, (iii) self-folding in the early stage of crystallization, and (iv) unfolding of the folded chains under stretching.
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Affiliation(s)
- You-lee Hong
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Wei Chen
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Shichen Yuan
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Jia Kang
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Toshikazu Miyoshi
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
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12
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Hong YL, Koga T, Miyoshi T. Chain Trajectory and Crystallization Mechanism of a Semicrystalline Polymer in Melt- and Solution-Grown Crystals As Studied Using 13C–13C Double-Quantum NMR. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00079] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- You-lee Hong
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Tadanori Koga
- Department
of Materials Science and Engineering, Stony Brook University, Stony Brook, New York 11794-2275, United States
| | - Toshikazu Miyoshi
- Department
of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
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13
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Hong YL, Miyoshi T. Elucidation of the Chain-Folding Structure of a Semicrystalline Polymer in Single Crystals by Solid-State NMR. ACS Macro Lett 2014; 3:556-559. [PMID: 35590726 DOI: 10.1021/mz500196s] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Despite tremendous efforts over the last half-century to elucidate the chain-folding (CF) structure of semicrystalline polymers, the re-entrance sites of folded chains, the successive CF number n, and the adjacent re-entry fraction F have not been well characterized due to experimental limitations. In this report, 13C-13C double-quantum (DQ) NMR was used to determine for the first time the detailed CF structure of 13C CH3-labeled isotactic poly(1-butene) (iPB1) in solution-grown crystals blended with nonlabeled iPB1 across a wide range of crystallization temperatures (Tcs). Comparison of the results of DQ experiments and spin dynamics simulations demonstrated that the majority of individual chains possess completely adjacent re-entry structures at both Tc = 60 and ∼0 °C, as well as indicated that a low polymer concentration, not kinetics, leads to cluster formations of single molecules in dilute solution. The changes in crystal habits from hexagonal shapes at Tc = 60 °C to rounded shapes at ∼0 °C (kinetic roughness) are reasonably explained in terms of kinetically driven depositions of single molecule clusters on the growth front.
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Affiliation(s)
- You-lee Hong
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
| | - Toshikazu Miyoshi
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325-3909, United States
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14
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Hong YL, Miyoshi T. Chain-Folding Structure of a Semicrystalline Polymer in Bulk Crystals Determined by 13C- 13C Double Quantum NMR. ACS Macro Lett 2013; 2:501-505. [PMID: 35581806 DOI: 10.1021/mz300630j] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A unique approach using 13C-13C double quantum (DQ) NMR combined with selective 13C isotope labeling is proposed to investigate the chain trajectory of the synthetic polymer in bulk crystals. Since the DQ buildup curve highly depends upon coupled spin number, topology, and internuclear distance, which originated from the chain trajectory of selectively 13C-labeled polymers, the adjacent re-entry site and fraction under finite chain-folding number can be determined.
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Affiliation(s)
- You-lee Hong
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
| | - Toshikazu Miyoshi
- Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States
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15
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