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Hybrid Time-Dependent Ginzburg–Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy. Polymers (Basel) 2022; 14:polym14091910. [PMID: 35567080 PMCID: PMC9103753 DOI: 10.3390/polym14091910] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 04/27/2022] [Accepted: 05/02/2022] [Indexed: 11/16/2022] Open
Abstract
Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.
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2
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Bao C, Che S, Han L. Discovery of single gyroid structure in self-assembly of block copolymer with inorganic precursors. JOURNAL OF HAZARDOUS MATERIALS 2021; 402:123538. [PMID: 33254739 DOI: 10.1016/j.jhazmat.2020.123538] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Revised: 07/16/2020] [Accepted: 07/20/2020] [Indexed: 06/12/2023]
Abstract
Triply periodic hyperbolic surfaces have attracted great attention due to their unique geometries and physical properties. Among them, the single gyroid (SG) is of significant interest due to its inherent chirality as well as the potential applications in energy and environmental science. However, the formation of the thermodynamically unstable structure is still unclear. In this work, we show the formation of SG structure in the structural transformation from the cylindrical to shifted double diamond (SDD) scaffold in a self-assembly system of diblock copolymer and silica precursors in solution. It has been found that the cylindrical tubes with zero Gaussian curvature were split and curved into hyperbolic surfaces and extruded to form SG structures and further evolved into the SDD networks. This growth or extrusion process suggests the SG structure is an intermediate phase of the cylindrical and SDD, and this transformation is found similar to the formation of butterfly wing scales (Thecla opisena), which has not been observed in neither the theoretical calculation nor the experimental self-assembly of amphiphilic molecules. We hope the structural relationship may bring new insights in understanding the formation of single networks in the biological system and the creation of new functional materials.
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Affiliation(s)
- Chao Bao
- School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Key Laboratory for Molecular Engineering of Chiral Drugs, Shanghai Jiao Tong University 800 Dongchuan Road, Shanghai, 200240, PR China
| | - Shunai Che
- School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Key Laboratory for Molecular Engineering of Chiral Drugs, Shanghai Jiao Tong University 800 Dongchuan Road, Shanghai, 200240, PR China; School of Chemical Science and Engineering, Tongji University 1239 Siping Road, Shanghai, 200092, PR China
| | - Lu Han
- School of Chemical Science and Engineering, Tongji University 1239 Siping Road, Shanghai, 200092, PR China.
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3
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Guliyeva A, Vayer M, Warmont F, Takano A, Matsushita Y, Sinturel C. Transition Pathway between Gyroid and Cylindrical Morphology in Linear Triblock Terpolymer Thin Films. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01263] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Aynur Guliyeva
- Interfaces, Confinement, Matériaux et Nanostructures (ICMN), UMR 7374, CNRS-Université d’Orléans, CS 40059, F-45071 Orléans, France
| | - Marylène Vayer
- Interfaces, Confinement, Matériaux et Nanostructures (ICMN), UMR 7374, CNRS-Université d’Orléans, CS 40059, F-45071 Orléans, France
| | - Fabienne Warmont
- Interfaces, Confinement, Matériaux et Nanostructures (ICMN), UMR 7374, CNRS-Université d’Orléans, CS 40059, F-45071 Orléans, France
| | - Atsushi Takano
- Department of Molecular & Macromolecular Chemistry, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, 464-8603 Nagoya, Japan
| | - Yushu Matsushita
- Department of Molecular & Macromolecular Chemistry, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, 464-8603 Nagoya, Japan
| | - Christophe Sinturel
- Interfaces, Confinement, Matériaux et Nanostructures (ICMN), UMR 7374, CNRS-Université d’Orléans, CS 40059, F-45071 Orléans, France
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4
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Wen T, Wang HF, Georgopanos P, Avgeropoulos A, Ho RM. Three-dimensional visualization of phase transition in polystyrene-block-polydimethylsiloxane thin film. POLYMER 2019. [DOI: 10.1016/j.polymer.2019.01.047] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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5
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Wu J, Huang Z, Lang W, Wang X, Li S. Surface-Induced Nanostructures and Phase Diagrams of ABC Linear Triblock Copolymers under Spherical Confinement: A Self-Consistent Field Theory Simulation. Polymers (Basel) 2018; 10:E1276. [PMID: 30961201 PMCID: PMC6401785 DOI: 10.3390/polym10111276] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 11/08/2018] [Accepted: 11/14/2018] [Indexed: 11/23/2022] Open
Abstract
We investigate the nanostructures and phase diagrams of ABC linear triblock copolymers confined in spherical cavities by using real-space self-consistent field theory. Various 3D morphologies, such as spherical concentric lamellae, dumbbell-like cylinder, and rotational structures, are identified in the phase diagrams, which are constructed on the basis of the diameters of spherical cavities and the interaction between the polymers and preferential surfaces. We designate specific monomer-monomer interactions and block compositions, with which the polymers spontaneously form a cylindrical morphology in bulk, and firstly study morphology transformation with a neutral surface when a confining radius progressively increases. We then focus on phase morphologies under the preferential surfaces and consolidate them into phase diagrams. The spherical radius and the degree of preferential interactions can obviously induce the formation of a cylindrical morphology. Theoretical results correspond to an amount of recent experimental observations to a high degree and contribute to synthesising functional materials.
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Affiliation(s)
- Ji Wu
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Zhihong Huang
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Wenchang Lang
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Xianghong Wang
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China.
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China.
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6
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Chu CY, Pei RY, Chen HL. Order–Order Transition from Ordered Bicontinuous Double Diamond to Hexagonally Packed Cylinders in Stereoregular Diblock Copolymer/Homopolymer Blends. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01570] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Che-Yi Chu
- Department of Chemical Engineering, National Chung Hsing University, Taichung 402, Taiwan
| | - Rou-Yuan Pei
- Department of Chemical Engineering, National Tsing Hua University, Hsin-Chu 30013, Taiwan
| | - Hsin-Lung Chen
- Department of Chemical Engineering, National Tsing Hua University, Hsin-Chu 30013, Taiwan
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7
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Chen Y, Xu Q, Jin Y, Qian X, Ma R, Liu J, Yang D. Shear-induced parallel and transverse alignments of cylinders in thin films of diblock copolymers. SOFT MATTER 2018; 14:6635-6647. [PMID: 29999081 DOI: 10.1039/c8sm00833g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Coarse-grained Langevin dynamics simulations were performed to investigate the alignment behavior of monolayer films of cylinder-forming diblock copolymers under steady shear, a structure of significant importance for many technical applications such as nanopatterning. The influences of shear conditions, the interactions involved in the films, and the initial morphology of the cylinder-forming phase were examined. Our results showed that above a critical shear rate, the cylinders can align either along the shearing direction or transverse (log-rolling) to the shearing direction depending on the relative strength between the interchain attraction in the cylinders (εAA) and the surface attraction of the confining walls with the film (εBW). To understand the underlying mechanism, the microscopic properties of the films under shear were systematically investigated. It was found that at low εAA/εBW, the majority blocks of the diblock polymer that are adsorbed on the confining walls prefer to move synchronously with the walls, inducing the cylinder-forming blocks to align along the flow direction. When εAA/εBW is above a threshold value, a strong attraction between the cylinder-forming blocks restrains their movement during shear, leading to the log-rolling motions of the cylinders. To predict the threshold εAA/εBW, we developed an approach based on equilibrium thermodynamics data and found good agreement with our shear simulations.
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Affiliation(s)
- Yulong Chen
- College of Materials Science and Engineering, Zhejiang University of Technology, Hangzhou 310014, China.
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8
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Stopper D, Roth R. Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory. Phys Rev E 2018; 97:062602. [PMID: 30011532 DOI: 10.1103/physreve.97.062602] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Indexed: 06/08/2023]
Abstract
By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex three-dimensional periodically ordered cluster phases such as lamellae, two-dimensional hexagonally packed cylinders, gyroid structures, or spherical micelles. While the bulk phase behavior has been studied extensively in earlier work, in this paper we focus on such structures confined between planar repulsive walls under shear flow. For sufficiently high shear rates, we observe that microphase separation can become fully suppressed. For lower shear rates, however, we find that, e.g., the gyroid structure undergoes a kinetic phase transition to a hexagonally packed cylindrical phase, which is found experimentally and theoretically in amphiphilic block copolymer systems. As such, besides the known similarities between the latter and colloidal systems regarding the equilibrium phase behavior, our work reveals further intriguing nonequilibrium relations between copolymer melts and colloidal fluids with competing interactions.
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Affiliation(s)
- Daniel Stopper
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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9
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Park S, Kim Y, Lee W, Hur SM, Ryu DY. Gyroid Structures in Solvent Annealed PS-b-PMMA Films: Controlled Orientation by Substrate Interactions. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00898] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Sungmin Park
- Department
of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Yeongsik Kim
- Department
of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Wooseop Lee
- Department
of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
| | - Su-Mi Hur
- Department
of Polymer Science and Engineering, Chonnam National University, Gwangju 61186, Korea
| | - Du Yeol Ryu
- Department
of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea
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10
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Katsir Y, Tsori Y. Recent advances in liquid mixtures in electric fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:063002. [PMID: 27991433 DOI: 10.1088/1361-648x/29/6/063002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
When immiscible liquids are subject to electric fields interfacial forces arise due to a difference in the permittivity or the conductance of the liquids, and these forces lead to shape change in droplets or to interfacial instabilities. In this topical review we discuss recent advances in the theory and experiments of liquids in electric fields with an emphasis on liquids which are initially miscible and demix under the influence of an external field. In purely dielectric liquids demixing occurs if the electrode geometry leads to sufficiently large field gradients. In polar liquids field gradients are prevalent due to screening by dissociated ions irrespective of the electrode geometry. We examine the conditions for these 'electro prewetting' transitions and highlight few possible systems where they might be important, such as in stabilization of colloids and in gating of pores in membranes.
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Affiliation(s)
- Yael Katsir
- Department of Chemical Engineering and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel
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11
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12
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Shagolsem LS, Kreer T, Galuschko A, Sommer JU. Diblock-copolymer thin films under shear. J Chem Phys 2016; 145:164908. [PMID: 27802665 DOI: 10.1063/1.4966151] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The behavior of lamellae forming diblock-copolymer melts confined by two non-selective substrates under shear is studied by means of molecular dynamics simulations. Since the substrate/copolymer preferential interaction is absent, the vertically oriented lamellae (L⊥) are formed. The response of L⊥ phase under transverse and perpendicular modes of shear is studied for a wide range of shear rates, γ̇. In particular, shear deformation and reorientation transition, flow behavior, and difference in the macroscopic response under the two modes of shear are discussed. We show that an inclined lamellae state observed for transverse shear below a critical shear rate γ̇* is stabilized by a cyclic motion of chains close to the substrates. The value of γ̇*, at which lamellae dissolve and reorient along the flow field during transverse shear, coincides with the onset of shear-thinning. For γ̇<γ̇*, the shear viscosity for transverse shear is much larger compared to that observed in perpendicular shear, while there is no difference for γ̇>γ̇*.
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Affiliation(s)
- Lenin S Shagolsem
- Department of Physics, National Institute of Technology, Manipur, Imphal 795004, India
| | - Torsten Kreer
- Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Andre Galuschko
- Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany
| | - Jens-Uwe Sommer
- Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany
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13
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Mukherjee A, Ankit K, Reiter A, Selzer M, Nestler B. Electric-field-induced lamellar to hexagonally perforated lamellar transition in diblock copolymer thin films: kinetic pathways. Phys Chem Chem Phys 2016; 18:25609-25620. [PMID: 27722519 DOI: 10.1039/c6cp04903f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Symmetric block-copolymers, hitherto, are well known to evolve into parallel, perpendicular and mixed lamellar morphologies under the concomitant influence of an electric field and substrate affinity. In the present work, we show that an additional imposed confinement can effectuate a novel parallel lamellar to hexagonally perforated lamellar (HPL) transition in monolayer and bilayer films. Three dimensional numerical studies are performed using the Ohta-Kawasaki functional, complemented with an exact solution of Maxwell's equation. HPL is shown to stabilize at large substrate affinity in a narrow region of the phase diagram between parallel and perpendicular lamellar transitions in ultra-thin films. Additionally, we also identify perforated lamellae as intermediate structures during parallel-to-perpendicular lamellar transition. A systematic analysis using Minkowski functionals yields deeper insights into the associated kinetic pathways.
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Affiliation(s)
- Arnab Mukherjee
- Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestr. 30, 76133, Karlsruhe, Germany. and Institute of Applied Materials - Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu str. 7, 76131, Karlsruhe, Germany
| | - Kumar Ankit
- Institute of Applied Materials - Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu str. 7, 76131, Karlsruhe, Germany
| | - Andreas Reiter
- Institute of Applied Materials - Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu str. 7, 76131, Karlsruhe, Germany
| | - Michael Selzer
- Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestr. 30, 76133, Karlsruhe, Germany. and Institute of Applied Materials - Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu str. 7, 76131, Karlsruhe, Germany
| | - Britta Nestler
- Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestr. 30, 76133, Karlsruhe, Germany. and Institute of Applied Materials - Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu str. 7, 76131, Karlsruhe, Germany
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14
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Zhang Q, Xu R, Kan D, He X. Molecular dynamics simulation of electric-field-induced self-assembly of diblock copolymers. J Chem Phys 2016; 144:234901. [DOI: 10.1063/1.4953689] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qiuzhi Zhang
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, China
| | - Rui Xu
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, China
| | - Di Kan
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, China
| | - Xuehao He
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, China
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15
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Kathrein CC, Bai W, Nunns A, Gwyther J, Manners I, Böker A, Tsarkova L, Ross CA. Electric field manipulated nanopatterns in thin films of metalorganic 3-miktoarm star terpolymers. SOFT MATTER 2016; 12:4866-4874. [PMID: 27136891 DOI: 10.1039/c6sm00451b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We report the effect of electric field on the morphological transitions and ordering behavior of polyferrocenylethylmethylsilane block (PFEMS)-containing copolymers. By analyzing structures in solvent-annealed films of metalorganic sphere- and cylinder-forming diblock copolymers, as well as of 3-miktoarm polyisoprene-arm-polystyrene-arm-PFEMS (3μ-ISF) terpolymers, we decouple two types of responses to the electric field: morphological transformations as a result of an increase in the volume fraction of the PFEMS block by oxidation of the ferrocenyl groups, and the orientation of the dielectric interfaces of microdomains parallel to the electric field vector. In the case of 3μ-ISF, the former effect dominates at high electric field strengths which results in an unexpected cylinder-to-sphere transition, leading to a well-ordered hexagonal dot pattern. Our results demonstrate multiple tunability of ordered microdomain morphologies, suggesting future applications in nanofabrication and surface patterning.
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Affiliation(s)
- Christine C Kathrein
- DWI - Leibniz Institut für Interaktive Materialien, Institut für Physikalische Chemie, RWTH Aachen University, Forckenbeckstraße 50, D-52056 Aachen, Germany
| | - Wubin Bai
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
| | - Adam Nunns
- School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
| | - Jessica Gwyther
- School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
| | - Ian Manners
- School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
| | - Alexander Böker
- Lehrstuhl für Polymermaterialien und Polymertechnologien, Fraunhofer-Institut für Angewandte Polymerforschung - IAP, University of Potsdam, D-14476 Potsdam-Golm, Germany
| | - Larisa Tsarkova
- DWI - Leibniz Institut für Interaktive Materialien, Institut für Physikalische Chemie, RWTH Aachen University, Forckenbeckstraße 50, D-52056 Aachen, Germany
| | - Caroline A Ross
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
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16
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Kan D, He X. Tuning phase structures of a symmetrical diblock copolymer with a patterned electric field. SOFT MATTER 2016; 12:4449-4456. [PMID: 27102422 DOI: 10.1039/c5sm03154k] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Electric fields can induce the orientation of the phase interfaces of block copolymers and provide a potential method to tune polymer phase structures for nanomaterial manufacture. In this work, we applied self-consistent field theory to study the self-assembly of a diblock copolymer confined between two parallel neutral substrates on which a set of electrodes was imposed to form a patterned electric field. The results showed that an alternatively distributed electric field can induce the formation of a parallel lamellar phase structure, which exists stably only in the system with selective substrates. The phase structure was proved to be sensitive to the characteristics of the electric field distribution, such as the strength of the electric field, the size and position of the electrodes, and the corresponding phase diagram was calculated in detail. The transition pathway of the phase structure from the perpendicular layered phase to the parallel layered phase was further analysed using the minimum energy path method. It is shown that the path and the active energy barrier of the phase transition depend on the electric field strength. Compound electric field patterns that can be designed to control the formation of novel and complex microphase structures were also examined.
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Affiliation(s)
- Di Kan
- Department of Chemistry, School of Science, Tianjin University, 300072 Tianjin, China.
| | - Xuehao He
- Department of Chemistry, School of Science, Tianjin University, 300072 Tianjin, China.
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17
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Orizaga S, Glasner K. Instability and reorientation of block copolymer microstructure by imposed electric fields. Phys Rev E 2016; 93:052504. [PMID: 27300942 DOI: 10.1103/physreve.93.052504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Indexed: 06/06/2023]
Abstract
The influence of electric fields on lamellar block copolymer microstructure is studied in the context of a density functional model and its sharp interface limit. A free boundary problem for domain interfaces of strongly segregated polymers is derived, which includes coupling of interface and electric field orientation. The linearized dynamics of lamellar configurations is computed in this context, leading to quantitative criteria for instability as a function of pattern wavelength, field magnitude, and orientation. Numerical simulations of the full model in two and three dimensions are used to study the nonlinear development of instabilities. In three dimensions, sufficiently large electric field magnitude always leads to instability. In two dimensions, the field has either stabilizing or destabilizing effects depending on the misorientation of the field and pattern. Even when linear instabilities are present, the dynamics can lead to stable corrugated domain interfaces which do not align with the electric field. Sufficiently high field strengths, on the other hand, produce topological rearrangement which may lead to alignment.
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Affiliation(s)
- Saulo Orizaga
- Department of Mathematics, University of Arizona, 617 N. Santa Rita Tucson, Arizona 85721, USA
| | - Karl Glasner
- Department of Mathematics, University of Arizona, 617 N. Santa Rita Tucson, Arizona 85721, USA
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18
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Wu J, Wang X, Ji Y, He L, Li S. Phase diagrams of diblock copolymers in electric fields: a self-consistent field theory study. Phys Chem Chem Phys 2016; 18:10309-19. [PMID: 27020849 DOI: 10.1039/c5cp08030d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We investigated the phase diagrams of diblock copolymers in external electrostatic fields by using real-space self-consistent field theory. The lamella, cylinder, sphere, and ellipsoid structures were observed and analyzed by their segment distributions, which were arranged to two types of phase diagrams to examine the phase behavior in weak and strong electric fields. One type was constructed on the basis of Flory-Huggins interaction parameter and volume fraction. We identified an ellipsoid structure with a body-centered cuboid arrangement as a stable phase and discussed the shift of phase boundaries in the electric fields. The other type of phase diagrams was established on the basis of the dielectric constants of two blocks in the electric fields. We then determined the regions of ellipsoid phase in the phase diagrams to examine the influence of dielectric constants on the phase transition between ellipsoidal and hexagonally packed cylinder phases. A general agreement was obtained by comparing our results with those described in previous experimental and theoretical studies.
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Affiliation(s)
- Ji Wu
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China.
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19
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Mukherjee A, Mukherjee R, Ankit K, Bhattacharya A, Nestler B. Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films. Phys Rev E 2016; 93:032504. [PMID: 27078402 DOI: 10.1103/physreve.93.032504] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Indexed: 11/07/2022]
Abstract
In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.
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Affiliation(s)
- Arnab Mukherjee
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Rajdip Mukherjee
- Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India
| | - Kumar Ankit
- Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Avisor Bhattacharya
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Britta Nestler
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
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20
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Gentile L, Coppola L, Balog S, Mortensen K, Ranieri GA, Olsson U. Phase Coexistence in a Dynamic Phase Diagram. Chemphyschem 2015; 16:2459-65. [DOI: 10.1002/cphc.201500237] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Indexed: 11/07/2022]
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21
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Jung J, Lee J, Park HW, Chang T, Sugimori H, Jinnai H. Epitaxial Phase Transition between Double Gyroid and Cylinder Phase in Diblock Copolymer Thin Film. Macromolecules 2014. [DOI: 10.1021/ma5020275] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jueun Jung
- Division
of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea
| | - Junyoung Lee
- Division
of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea
| | - Hae-Woong Park
- Division
of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea
| | - Taihyun Chang
- Division
of Advanced Materials Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea
| | - Hidekazu Sugimori
- Department
of Macromolecular Science and Engineering, Graduate School of Science
and Engineering, Kyoto Institute of Technology, Kyoto 606-8585, Japan
| | - Hiroshi Jinnai
- Department
of Macromolecular Science and Engineering, Graduate School of Science
and Engineering, Kyoto Institute of Technology, Kyoto 606-8585, Japan
- Institute
for Materials Chemistry and Engineering (IMCE), CE80, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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22
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Millett PC. Electric-field induced alignment of nanoparticle-coated channels in thin-film polymer membranes. J Chem Phys 2014; 140:144903. [DOI: 10.1063/1.4870471] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Mkhonta SK, Elder KR, Huang ZF, Grant M. Microphase separation in comblike liquid-crystalline diblock copolymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042602. [PMID: 24229201 DOI: 10.1103/physreve.88.042602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2013] [Revised: 07/30/2013] [Indexed: 06/02/2023]
Abstract
The interplay between liquid crystallinity and microphase separation in comblike liquid-crystalline diblock copolymers is examined via a Brazovskii-type phenomenological model using both analytical and numerical calculations. For symmetric diblock copolymers we determine a critical electric field that is required to tilt the orientation of the constituent liquid crystals of the polymer side chains in the microphase-separated lamellar state. Such electrically induced reorientation of the liquid-crystal molecules can lead to substantially large changes of lamellar periodicity. Our numerical results show that highly aligned polymer lamellar domains can self-assemble when the liquid-crystal ordering precedes microphase separation, and that weak electric fields can be used to direct the self-assembly process due to the dielectric anisotropy of the liquid-crystal side chains. We also find that phase separation of asymmetric diblock copolymers can coexist with a network of liquid-crystal nematic orientations, with domain morphology depending on the details of copolymer and liquid-crystal coupling.
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Affiliation(s)
- S K Mkhonta
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA and Department of Physics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland
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25
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Ly DQ, Pinna M, Honda T, Kawakatsu T, Zvelindovsky AVM. Kinetic pathways of sphere-to-cylinder transition in diblock copolymer melt under electric field. J Chem Phys 2013; 138:074904. [PMID: 23445032 DOI: 10.1063/1.4791639] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D Q Ly
- Computational Physics Group and Institute of Nanotechnology and Bioengineering, University of Central Lancashire, Preston PR1 2HE, United Kingdom
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26
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Dessí R, Pinna M, Zvelindovsky AV. Cell Dynamics Simulations of Cylinder-Forming Diblock Copolymers in Thin Films on Topographical and Chemically Patterned Substrates. Macromolecules 2013. [DOI: 10.1021/ma400124j] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Roberta Dessí
- Computational Physics
Group and Institute for Nanotechnology
and Bioengineering, University of Central Lancashire, Preston PR1 2HE, U.K
| | - Marco Pinna
- Computational Physics
Group and Institute for Nanotechnology
and Bioengineering, University of Central Lancashire, Preston PR1 2HE, U.K
| | - Andrei V. Zvelindovsky
- Computational Physics
Group and Institute for Nanotechnology
and Bioengineering, University of Central Lancashire, Preston PR1 2HE, U.K
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28
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Chen CK, Hsueh HY, Chiang YW, Ho RM, Akasaka S, Hasegawa H. Single Helix to Double Gyroid in Chiral Block Copolymers. Macromolecules 2010. [DOI: 10.1021/ma1009885] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Chun-Ku Chen
- Department of Chemical Engineering, Nationsal Tsing-Hua University, Hsinchu 30013, Taiwan
| | - Han-Yu Hsueh
- Department of Chemical Engineering, Nationsal Tsing-Hua University, Hsinchu 30013, Taiwan
| | - Yeo-Wan Chiang
- Department of Chemical Engineering, Nationsal Tsing-Hua University, Hsinchu 30013, Taiwan
| | - Rong-Ming Ho
- Department of Chemical Engineering, Nationsal Tsing-Hua University, Hsinchu 30013, Taiwan
| | - Satoshi Akasaka
- Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto, 615-8510, Japan
| | - Hirokazu Hasegawa
- Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto, 615-8510, Japan
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29
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Pinna M, Hiltl S, Guo X, Böker A, Zvelindovsky AV. Block copolymer nanocontainers. ACS NANO 2010; 4:2845-2855. [PMID: 20496954 DOI: 10.1021/nn901853e] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Using cell dynamics computer simulation, we perform a systematic study of thin block copolymer films around a nanoparticle. Lamellar-, cylinder-, and sphere-forming block copolymers are investigated with respect to different film thicknesses, particle radii, and boundary conditions at the film interfaces. The obtained structures include standing lamellae and cylinders, "onions", cylinder "knitting balls", "golf ball", layered spherical, "virus"-like and mixed morphologies with T-junctions and U-type defects. The kinetics of the structure formation and difference with planar thin films are discussed. Our simulations suggest that novel porous nanocontainers can be formed by the coating of a sacrificial nanobead by a block copolymer layer with a well-controlled nanostructure. In addition, first scanning force microscopy experiments on a model system reveal surface structures similar to those predicted by our simulations.
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Affiliation(s)
- Marco Pinna
- Computational Physics Group, University of Central Lancashire, Preston PR1 2HE, United Kingdom.
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30
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Schmidt K, Pester CW, Schoberth HG, Zettl H, Schindler KA, Böker A. Electric Field Induced Gyroid-to-Cylinder Transitions in Concentrated Diblock Copolymer Solutions. Macromolecules 2010. [DOI: 10.1021/ma100278q] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kristin Schmidt
- Materials Research Laboratory, University of California, Santa Barbara, California 93106
| | - Christian W. Pester
- DWI an der RWTH Aachen e.V., Lehrstuhl für Makromolekulare Materialien und Oberflächen, RWTH Aachen University, D-52056 Aachen, Germany
| | - Heiko G. Schoberth
- Physikalische Chemie II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Heiko Zettl
- Physikalische Chemie II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | | | - Alexander Böker
- DWI an der RWTH Aachen e.V., Lehrstuhl für Makromolekulare Materialien und Oberflächen, RWTH Aachen University, D-52056 Aachen, Germany
- JARA-FIT, RWTH Aachen University, D-52056 Aachen, Germany
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31
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Pinna M, Guo X, Zvelindovsky AV. Diblock copolymers in a cylindrical pore. J Chem Phys 2009; 131:214902. [DOI: 10.1063/1.3264946] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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32
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Affiliation(s)
- Jun Hyuk Moon
- Department of Chemical and Biomolecular Engineering, Sogang University, 1 Shinsu-dong, Mapo-gu, Seoul 121-742, Korea, and Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut Street, Philadelphia, Pennsylvania 19104
| | - Shu Yang
- Department of Chemical and Biomolecular Engineering, Sogang University, 1 Shinsu-dong, Mapo-gu, Seoul 121-742, Korea, and Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut Street, Philadelphia, Pennsylvania 19104
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Ly DQ, Honda T, Kawakatsu T, Zvelindovsky AV. Hexagonally Perforated Lamella-to-Cylinder Transition in a Diblock Copolymer Thin Film under an Electric Field. Macromolecules 2008. [DOI: 10.1021/ma0708850] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Dung Q. Ly
- Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom; ZEON Corporation, 1-6-2, Marunouchi, Chioda-ku, Tokyo 100-8246, Japan; and Department of Physics, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
| | - Takashi Honda
- Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom; ZEON Corporation, 1-6-2, Marunouchi, Chioda-ku, Tokyo 100-8246, Japan; and Department of Physics, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
| | - Toshihiro Kawakatsu
- Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom; ZEON Corporation, 1-6-2, Marunouchi, Chioda-ku, Tokyo 100-8246, Japan; and Department of Physics, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
| | - Andrei V. Zvelindovsky
- Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom; ZEON Corporation, 1-6-2, Marunouchi, Chioda-ku, Tokyo 100-8246, Japan; and Department of Physics, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
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