1
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Zhong Z, Xu L, Jiang J. A Neural-Network-Based Mapping and Optimization Framework for High-Precision Coarse-Grained Simulation. J Chem Theory Comput 2025; 21:859-870. [PMID: 39782000 DOI: 10.1021/acs.jctc.4c01466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2025]
Abstract
The accuracy and efficiency of a coarse-grained (CG) force field are pivotal for high-precision molecular simulations of large systems with complex molecules. We present an automated mapping and optimization framework for molecular simulation (AMOFMS), which is designed to streamline and improve the force field optimization process. It features a neural-network-based mapping function, DSGPM-TP (deep supervised graph partitioning model with type prediction). This model can accurately and efficiently convert atomistic structures to CG mappings, reducing the need for manual intervention. By integrating bottom-up and top-down methodologies, AMOFMS allows users to freely combine these approaches or use them independently as optimization targets. Moreover, users can select and combine different optimizers to meet their specific mission. With its parallel optimizer, AMOFMS significantly accelerates the optimization process, reducing the time required to achieve optimal results. Successful applications of AMOFMS include parameter optimizations for systems such as POPC and PEO, demonstrating its robustness and effectiveness. Overall, AMOFMS provides a general and flexible framework for the automated development of high-precision CG force fields.
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Affiliation(s)
- Zhixuan Zhong
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Lifeng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Jian Jiang
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
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2
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Grest GS, Ge T, Plimpton SJ, Rubinstein M, O’Connor TC. Entropic Mixing of Ring/Linear Polymer Blends. ACS POLYMERS AU 2022; 3:209-216. [PMID: 37065717 PMCID: PMC10103188 DOI: 10.1021/acspolymersau.2c00050] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Revised: 11/03/2022] [Accepted: 11/03/2022] [Indexed: 11/29/2022]
Abstract
The topological constraints of nonconcatenated ring polymers force them to form compact loopy globular conformations with much lower entropy than unconstrained ideal rings. The closed-loop structure of ring polymers also enables them to be threaded by linear polymers in ring/linear blends, resulting in less compact ring conformations with higher entropy. This conformational entropy increase promotes mixing rings with linear polymers. Here, using molecular dynamics simulations for bead-spring chains, ring/linear blends are shown to be significantly more miscible than linear/linear blends and that there is an entropic mixing, negative χ, for ring/linear blends compared to linear/linear and ring/ring blends. In analogy with small angle neutron scattering, the static structure function S(q) is measured, and the resulting data are fit to the random phase approximation model to determine χ. In the limit that the two components are the same, χ = 0 for the linear/linear and ring/ring blends as expected, while χ < 0 for the ring/linear blends. With increasing chain stiffness, χ for the ring/linear blends becomes more negative, varying reciprocally with the number of monomers between entanglements. Ring/linear blends are also shown to be more miscible than either ring/ring or linear/linear blends and stay in single phase for a wider range of increasing repulsion between the two components.
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Affiliation(s)
- Gary S. Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Ting Ge
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Steven J. Plimpton
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Michael Rubinstein
- Thomas Lord Department of Mechanical Engineering and Materials Science, Biomedical Engineering, Chemistry, and Physics Departments, Duke University, Durham, North Carolina 27708, United States
| | - Thomas C. O’Connor
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburg, Pennsylvania 15213, United States
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3
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Yang J, Chen L, Zhu M, Ishaq MW, Chen S, Li L. Investigation of the Multimer Cyclization Effect during Click Step-Growth Polymerization of AB-Type Macromonomers. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01087] [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)
- Jinxian Yang
- College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
| | - Lunliang Chen
- College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
| | - Mo Zhu
- College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
| | - Muhammad Waqas Ishaq
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Shengqi Chen
- Anhui University of Chinese Medicine, Hefei, Anhui 230038, China
| | - Lianwei Li
- College of Chemistry and Environmental Engineering, Shenzhen University, Shenzhen 518060, China
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4
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Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering-A Review. Polymers (Basel) 2020; 12:polym12091884. [PMID: 32825628 PMCID: PMC7563567 DOI: 10.3390/polym12091884] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 08/14/2020] [Accepted: 08/17/2020] [Indexed: 11/24/2022] Open
Abstract
The physical properties of polymers depend on a range of both structural and chemical parameters, and in particular, on molecular topology. Apparently simple changes such as joining chains at a point to form stars or simply joining the two ends to form a ring can profoundly alter molecular conformation and dynamics, and hence properties. Cyclic polymers, as they do not have free ends, represent the simplest model system where reptation is completely suppressed. As a consequence, there exists a considerable literature and several reviews focused on high molecular weight cyclics where long range dynamics described by the reptation model comes into play. However, this is only one area of interest. Consideration of the conformation and dynamics of rings and chains, and of their mixtures, over molecular weights ranging from tens of repeat units up to and beyond the onset of entanglements and in both solution and melts has provided a rich literature for theory and simulation. Experimental work, particularly neutron scattering, has been limited by the difficulty of synthesizing well-characterized ring samples, and deuterated analogues. Here in the context of the broader literature we review investigations of local conformation and dynamics of linear and cyclic polymers, concentrating on poly(dimethyl siloxane) (PDMS) and covering a wide range of generally less high molar masses. Experimental data from small angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), including Neutron Spin Echo (NSE), are compared to theory and computational predictions.
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5
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Aboudzadeh MA, Dolz M, Monnier X, González de San Román E, Cangialosi D, Grzelczak M, Barroso-Bujans F. Synthesis of macrocyclic poly(ethylene oxide)s containing a protected thiol group: a strategy for decorating gold surfaces with ring polymers. Polym Chem 2019. [DOI: 10.1039/c9py01394f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Macrocyclic poly(ethylene oxide)s containing a protected thiol group are able to attach to gold substrates without thiol deprotection enabling surface modification.
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Affiliation(s)
- M. Ali Aboudzadeh
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
| | - Mikel Dolz
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
| | - Xavier Monnier
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
| | | | - Daniele Cangialosi
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
| | - Marek Grzelczak
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
| | - Fabienne Barroso-Bujans
- Centro de Física de Materiales
- CSIC-UPV/EHU
- 20018 Donostia-San Sebastián
- Spain
- Donostia International Physics Center (DIPC)
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6
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Huang H, Wu L, Xiong H, Sun H. A Transferrable Coarse-Grained Force Field for Simulations of Polyethers and Polyether Blends. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01802] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Hao Huang
- School of Chemistry and Chemical Engineering, Materials Genome Initiative Center, and Key Laboratory of Scientific and Engineering Computing of Ministry of Education, Shanghai Jiao Tong University, Shanghai, China 200240
| | - Liang Wu
- School of Chemistry and Chemical Engineering, Materials Genome Initiative Center, and Key Laboratory of Scientific and Engineering Computing of Ministry of Education, Shanghai Jiao Tong University, Shanghai, China 200240
| | - Huiming Xiong
- School of Chemistry and Chemical Engineering, Materials Genome Initiative Center, and Key Laboratory of Scientific and Engineering Computing of Ministry of Education, Shanghai Jiao Tong University, Shanghai, China 200240
| | - Huai Sun
- School of Chemistry and Chemical Engineering, Materials Genome Initiative Center, and Key Laboratory of Scientific and Engineering Computing of Ministry of Education, Shanghai Jiao Tong University, Shanghai, China 200240
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Honda S, Tanaka N, Toyota T. Synthesis of star-shaped poly(n
-butyl acrylate) oligomers with coumarin end groups and their networks for a UV-tunable viscoelastic material. ACTA ACUST UNITED AC 2017. [DOI: 10.1002/pola.28777] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Satoshi Honda
- Department of Basic Science, Graduate School of Arts and Sciences; The University of Tokyo, 3-8-1 Komaba; Meguro Tokyo 153-8902 Japan
| | - Nobuaki Tanaka
- Department of Basic Science, Graduate School of Arts and Sciences; The University of Tokyo, 3-8-1 Komaba; Meguro Tokyo 153-8902 Japan
| | - Taro Toyota
- Department of Basic Science, Graduate School of Arts and Sciences; The University of Tokyo, 3-8-1 Komaba; Meguro Tokyo 153-8902 Japan
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8
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Regan K, Ricketts S, Robertson-Anderson RM. DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics. Polymers (Basel) 2016; 8:E336. [PMID: 30974610 PMCID: PMC6432451 DOI: 10.3390/polym8090336] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Revised: 08/25/2016] [Accepted: 08/25/2016] [Indexed: 02/04/2023] Open
Abstract
Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.
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Affiliation(s)
- Kathryn Regan
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92110, USA.
| | - Shea Ricketts
- Department of Physics and Biophysics, University of San Diego, San Diego, CA 92110, USA.
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9
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Sun D, Cho J. Ring gradient copolymers as amphiphiles in their ternary blends with two linear homopolymers. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.04.023] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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10
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Wang S, Zhang K, Chen Y, Xi F. Isomeric Dicyclic Polymers via Atom Transfer Radical Polymerization and Atom Transfer Radical Coupling Cyclization. Macromolecules 2014. [DOI: 10.1021/ma402335f] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Shuangshuang Wang
- Laboratory of Polymer Physics and Chemistry,
Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China
| | - Ke Zhang
- Laboratory of Polymer Physics and Chemistry,
Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China
| | - Yongming Chen
- Laboratory of Polymer Physics and Chemistry,
Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China
- Key Laboratory for
Polymeric Composite and Functional Materials of Ministry of Education,
School of Chemistry and Chemical Engineering, Sun Yat-Sen University, No. 135, Xingang Xi Road, Guangzhou 510275, China
| | - Fu Xi
- Laboratory of Polymer Physics and Chemistry,
Institute of Chemistry, The Chinese Academy of Sciences, Beijing 100190, China
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11
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Hatakeyama F, Yamamoto T, Tezuka Y. Systematic Synthesis of Block Copolymers Consisting of Topological Amphiphilic Segment Pairs from kyklo- and kentro-Telechelic PEO and Poly(THF). ACS Macro Lett 2013; 2:427-431. [PMID: 35581851 DOI: 10.1021/mz400150m] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A set of four types of block copolymers consisting of topological amphiphilic segment pairs was effectively synthesized via kyklo- (functionalized cyclic) and kentro- (center-functionalized linear) telechelic poly(ethylene oxide) (PEO) and poly(tetrahydrofuran) (poly(THF)). Accordingly, kyklo- and kentro-telechelic PEO with an ethynyl group was newly prepared from relevant linear PEO precursors with quinuclidinium end groups and an ethynyl-functionalized dicarboxylate counteranion by the electrostatic self-assembly and covalent fixation (ESA-CF) process. Similarly, kyklo- and kentro-telechelic poly(THF) with an azido group was obtained. The PEO and poly(THF) telechelics were subjected to click chemistry to systematically produce amphiphilic block copolymers with two symmetric topological forms, that is, an "8" shape (IC·IIC) and a four-armed star shape (IL·IIL), and two asymmetric topological forms, that is, twin-tailed tadpole shapes (IL·IIC and IC·IIL) with respect to the hydrophilic-hydrophobic plane.
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Affiliation(s)
- Fumiya Hatakeyama
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama,
Meguro-ku, Tokyo 152−8552, Japan
| | - Takuya Yamamoto
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama,
Meguro-ku, Tokyo 152−8552, Japan
| | - Yasuyuki Tezuka
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama,
Meguro-ku, Tokyo 152−8552, Japan
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12
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Li L, Yang J, Zhou J. Linear-, Cyclic-, and Multiblock Amphiphilic Polyelectrolytes as Surfactants in Emulsion Polymerization: Role of Topological Structure. Macromolecules 2013. [DOI: 10.1021/ma3022025] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lianwei Li
- Hefei National
Laboratory for
Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei,
China 230026
| | - Jinxian Yang
- Hefei National
Laboratory for
Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei,
China 230026
| | - Jianfeng Zhou
- Research Center
for Analysis
and Measurement, Donghua University, Shanghai,
China 201620
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13
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Wang G, Fan X, Hu B, Zhang Y, Huang J. Synthesis of Eight-shaped Poly(ethylene oxide) by the Combination of Glaser Coupling with Ring-opening Polymerization. Macromol Rapid Commun 2011; 32:1658-63. [DOI: 10.1002/marc.201100390] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2011] [Revised: 07/09/2011] [Indexed: 11/09/2022]
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14
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Yamamoto T, Tezuka Y. Topological polymer chemistry: a cyclic approach toward novel polymer properties and functions. Polym Chem 2011. [DOI: 10.1039/c1py00088h] [Citation(s) in RCA: 238] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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15
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YAMAMOTO T, TEZUKA Y. Topological Polymer Chemistry: New Synthesis of Cyclic and Multicyclic Polymers and Topology Effects Thereby. KOBUNSHI RONBUNSHU 2011. [DOI: 10.1295/koron.68.782] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Takuya YAMAMOTO
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology
| | - Yasuyuki TEZUKA
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology
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16
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Ishikawa K, Yamamoto T, Harada H, Tezuka Y. Synthesis and Topological Conversion of an 8-shaped Poly(THF) Having a Metathesis-Cleavable Unit at the Focal Position. Macromolecules 2010. [DOI: 10.1021/ma1012094] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kazuyuki Ishikawa
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Takuya Yamamoto
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Hiroyuki Harada
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Yasuyuki Tezuka
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
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17
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Sugai N, Heguri H, Ohta K, Meng Q, Yamamoto T, Tezuka Y. Effective Click Construction of Bridged- and Spiro-Multicyclic Polymer Topologies with Tailored Cyclic Prepolymers (kyklo-Telechelics). J Am Chem Soc 2010; 132:14790-802. [DOI: 10.1021/ja103402c] [Citation(s) in RCA: 123] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Naoto Sugai
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Hiroyuki Heguri
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Kengo Ohta
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Qingyuan Meng
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Takuya Yamamoto
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
| | - Yasuyuki Tezuka
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
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18
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Nam S, Leisen J, Breedveld V, Beckham HW. Melt Dynamics of Blended Poly(oxyethylene) Chains and Rings. Macromolecules 2009. [DOI: 10.1021/ma802294j] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sunghyun Nam
- Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0295, and Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
| | - Johannes Leisen
- Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0295, and Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
| | - Victor Breedveld
- Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0295, and Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
| | - Haskell W. Beckham
- Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0295, and Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
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