1
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Müller M, Abetz V. Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment. Chem Rev 2021; 121:14189-14231. [PMID: 34032399 DOI: 10.1021/acs.chemrev.1c00029] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.
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Affiliation(s)
- Marcus Müller
- Georg-August Universität, Institut für Theoretische Physik, 37073 Göttingen, Germany
| | - Volker Abetz
- Helmholtz-Zentrum Hereon, Institut für Membranforschung, 21502 Geesthacht, Germany.,Universität Hamburg, Institut für Physikalische Chemie, 20146 Hamburg, Germany
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2
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Ma M, Fu Y. Electromechanical response of lamellar forming ionic diblock copolymer thin films. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138817] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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3
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Müller M. Process-directed self-assembly of copolymers: Results of and challenges for simulation studies. Prog Polym Sci 2020. [DOI: 10.1016/j.progpolymsci.2019.101198] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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4
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Zheng B, Man X, Ou-Yang ZC, Schick M, Andelman D. Orienting Thin Films of Lamellar Block Copolymer: The Combined Effect of Mobile Ions and Electric Field. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01506] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bin Zheng
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xingkun Man
- Center of Soft Matter Physics and Its Applications, and School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
| | - Zhong-Can Ou-Yang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - M. Schick
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
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5
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Martin JM, Li W, Delaney KT, Fredrickson GH. SCFT Study of Diblock Copolymer Melts in Electric Fields: Selective Stabilization of Orthorhombic Fddd Network Phase. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00394] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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6
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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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7
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Welling U, Müller M. Ordering block copolymers with structured electrodes. SOFT MATTER 2017; 13:486-495. [PMID: 27973625 DOI: 10.1039/c6sm01911k] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the kinetics of alignment and registration of block copolymers in an inhomogeneous electric field by computer simulations of a soft, coarse-grained model. The two blocks of the symmetric diblock copolymers are characterized by different dielectric constants. First, we demonstrate that a combination of graphoepitaxy and a homogeneous electric field extends the maximal distance between the topographical guiding patterns that result in defect-free ordering compared to graphoepitaxy alone. In a second study, the electric field in the thin block copolymer film is fabricated by spatially structured electrodes on an isolating substrate arranged in a one-dimensional periodic array; no additional topographical guiding patterns are applied. The dielectrophoretic effect induces long-range orientational order of the lamellae and, additionally, registers the lamellar structure with the electrodes due to the field inhomogeneities at the edges of the structured electrodes. Thus, orientational and translational order is established by the inhomogeneous electric field. The simulations identify a process protocol of time-dependent electric potentials that suppresses defect formation by initially forming a sandwich-like structure and subsequently reorienting these lying into standing lamellae that are registered with the structure of the electrodes. This process-directed self-assembly results in large defect-free arrays of aligned and registered lamellae using electrodes with a saw-tooth period of 4 lamellar periodicities, L0, and a spacing of 10L0.
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Affiliation(s)
- Ulrich Welling
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany.
| | - Marcus Müller
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany.
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8
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Martin JM, Li W, Delaney KT, Fredrickson GH. Statistical field theory description of inhomogeneous polarizable soft matter. J Chem Phys 2016; 145:154104. [DOI: 10.1063/1.4964680] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan M. Martin
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Wei Li
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Kris T. Delaney
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
- Department of Materials, University of California, Santa Barbara, California 93106, USA
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9
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Orzechowski K, Adamczyk M, Wolny A, Tsori Y. Shift of the critical mixing temperature in strong electric fields. Theory and experiment. J Phys Chem B 2014; 118:7187-94. [PMID: 24886337 DOI: 10.1021/jp503654e] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We study the shift in the critical temperature T(c) in binary mixtures in strong electric fields. In experiments we measure the nonlinear dielectric effect (NDE) in a mixture of nitrobenze and n-octane and calculate Piekara's factor. We find that the critical anomaly of Piekara's factor is a function of an electric field strength. We propose to explain this observation as a result of a downward shift of T(c), and this allows us to calculate (∂T(c)/∂E(2)) = (-22 ± 10) × 10(-16) (K m(2))/V(2). In the theoretical part we amend Landau and Lifshitz's formula and show that the downward shift of Tc can be estimated from a simple mean-field theory taking into account the linear and quadratic terms in an expansion of the constitutive relation ε(x) between the electric constant ε and mixture composition x.
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Sakaue T, Shitara K, Ohta T. Dynamics and electrorheology of sheared immiscible fluid mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052301. [PMID: 25353794 DOI: 10.1103/physreve.89.052301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2014] [Indexed: 06/04/2023]
Abstract
We analyze the electrorheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electrorheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through comparison with recent experiments, we point out a unique dynamical stress response inherent in situations where the cross-coupling between different fields is essential.
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Affiliation(s)
- Takahiro Sakaue
- Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan
| | - Kyohei Shitara
- Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan
| | - Takao Ohta
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
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11
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Welling U, Müller M, Shalev H, Tsori Y. Block Copolymer Ordering in Cylindrical Capacitors. Macromolecules 2014. [DOI: 10.1021/ma4021888] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- U. Welling
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - M. Müller
- Institut für Theoretische Physik, Georg-August-Universität, 37077 Göttingen, Germany
| | - H. Shalev
- Department of Chemical Engineering and The Ilse Katz Institute for
Nanoscale Science and Technology, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel
| | - Y. Tsori
- 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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12
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Sakaue T, Ohta T. Maxwell stress in fluid mixtures. PHYSICAL REVIEW LETTERS 2012; 108:078301. [PMID: 22401262 DOI: 10.1103/physrevlett.108.078301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2011] [Indexed: 05/31/2023]
Abstract
We examine the structure of Maxwell stress in binary fluid mixtures under an external electric field and discuss its consequence. In particular, we show that, in immiscible blends, it is intimately related to the statistics of domain structure. This leads to a compact formula, which may be useful in the investigation of electrorheological effects in such systems. The stress tensor calculated in a phase separated fluid under a steady electric field is in a good agreement with recent experiments.
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Affiliation(s)
- Takahiro Sakaue
- Department of Physics, Kyushu University 33, Fukuoka, Japan.
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13
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14
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Affiliation(s)
- Xingkun Man
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - Henri Orland
- Institut de Physique Théorique, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France
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15
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Wang CH, Chen P, Lu CYD. Phase separation of thin-film polymer mixtures under in-plane electric fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:061501. [PMID: 20866419 DOI: 10.1103/physreve.81.061501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2010] [Indexed: 05/29/2023]
Abstract
Phase-separation dynamics of polymer thin-film mixtures of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are observed while an in-plane electric field is applied, instead of the out-of-plane fields usually employed previously. The phase separation is accompanied by the formation of PS dewetting holes at zero or weak fields. The dewetting velocity at 0.25 μm/min is a few times slower than that seen in regular bilayer dewetting. With the increasing of the field strength, we observe the formation of PS droplets in PMMA matrix, a reversal from zero- or low-field conditions. The PS dewetting holes are also suppressed. At further increased fields, PS droplets quickly penetrate up to the top of the PMMA matrix, leading to smaller and more irregular final PS droplets. This is manifested in the dramatic decrease in the growth exponent of the droplet size L from L∼t1.5 to L∼t0.1. These morphology changes are explained by the electrostatic energy resulted from the PS and PMMA dielectric contrast.
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Affiliation(s)
- Chen-Hung Wang
- Department of Physics and Center for Complex Systems, National Central University, Chungli 320, Taiwan
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16
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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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17
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Samin S, Tsori Y. Stability of binary mixtures in electric field gradients. J Chem Phys 2010; 131:194102. [PMID: 19929041 DOI: 10.1063/1.3257688] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the influence of electric field gradients on the phase behavior of nonpolar binary mixtures. Small fields give rise to smooth composition profiles, whereas large enough fields lead to a phase-separation transition. The critical field for demixing as well as the equilibrium phase-separation interface are given as a function of the various system parameters. We show how the phase diagram in the temperature-composition plane is affected by electric fields, assuming a linear or nonlinear constitutive relations for the dielectric constant. Finally, we discuss the unusual case where the interface appears far from any bounding surface.
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Affiliation(s)
- Sela Samin
- Department of Chemical Engineering and The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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18
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Stepanow S, Thurn-Albrecht T. Statistical mechanical description of liquid systems in an electric field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041104. [PMID: 19518170 DOI: 10.1103/physreve.79.041104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Indexed: 05/27/2023]
Abstract
We formulate the statistical mechanical description of liquid systems for both polarizable and polar systems in an electric field in the E ensemble, which is the pendant to the thermodynamic description in terms of the free energy at constant potential. The contribution of the electric field to the configurational integral Q[over ]_{N}(E) in the E ensemble is given in an exact form as a factor in the integrand of Q[over ]_{N}(E) . We calculate the contribution of the electric field to the Ornstein-Zernike formula for the scattering function in the E ensemble. As an application, we determine the field-induced shift of the critical temperature for polarizable and polar liquids and show that the shift is upward for polarizable liquids and downward for polar liquids.
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Affiliation(s)
- Semjon Stepanow
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
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19
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Andelman D, Rosensweig RE. Modulated Phases: Review and Recent Results. J Phys Chem B 2008; 113:3785-98. [DOI: 10.1021/jp807770n] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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20
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Wang JY, Chen W, Russell TP. Influence of Interfacial Energy on Electric-Field-Induced Sphere-to-Cylinder Transition in Block Copolymer Thin Films. Macromolecules 2008. [DOI: 10.1021/ma800717v] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jia-Yu Wang
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
| | - Wei Chen
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas P. Russell
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
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21
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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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22
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23
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Gunkel I, Stepanow S, Thurn-Albrecht T, Trimper S. Fluctuation Effects in the Theory of Microphase Separation of Diblock Copolymers in the Presence of an Electric Field. Macromolecules 2007. [DOI: 10.1021/ma0623993] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- I. Gunkel
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
| | - S. Stepanow
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
| | - T. Thurn-Albrecht
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
| | - S. Trimper
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
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24
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Wang JY, Leiston-Belanger JM, Sievert JD, Russell TP. Grain Rotation in Ion-Complexed Symmetric Diblock Copolymer Thin Films under an Electric Field. Macromolecules 2006. [DOI: 10.1021/ma0614287] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jia-Yu Wang
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
| | - Julie M. Leiston-Belanger
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
| | - James D. Sievert
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas P. Russell
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003
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25
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Kyrylyuk AV, Fraaije JGEMH. Electric field versus surface alignment in confined films of a diblock copolymer melt. J Chem Phys 2006; 125:164716. [PMID: 17092129 DOI: 10.1063/1.2360947] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrode surfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.
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Affiliation(s)
- Andriy V Kyrylyuk
- Theoretical and Polymer Physics Group, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
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26
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Pinna M, Zvelindovsky AV, Todd S, Goldbeck-Wood G. Cubic phases of block copolymers under shear and electric fields by cell dynamics simulation. I. Spherical phase. J Chem Phys 2006; 125:154905. [PMID: 17059291 DOI: 10.1063/1.2356468] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Cell dynamics simulation is used to investigate pathways of sphere-to-cylinder transition in block copolymer melt under applied simple shear flow and electric field. Both fields can induce the transition when their strength is above some critical value. At weak fields the spherical phase is preserved, with spheres being deformed into ellipsoids. Weak shear flow is found to improve order in the spherical phase. Observed sliding of layers of spheres under shear is very similar to the experimental finding by Hamley et al. [J. Chem. Phys. 108, 6929 (1998)]. The kinetic pathways are sensitive to the degree of microphase separation in the system and hence affected by temperature. The details of the pathways are described by means of Minkowski functionals.
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Affiliation(s)
- Marco Pinna
- Centre for Materials Science, Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2HE, United Kingdom
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27
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Lin CY, Schick M. Self-consistent field study of the alignment by an electric field of a cylindrical phase of block copolymer. J Chem Phys 2006; 125:34902. [PMID: 16863380 DOI: 10.1063/1.2214718] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Self-consistent field theory is applied to a film of cylindrical-forming block copolymer subject to a surface field which tends to align the cylinders parallel to electrical plates, and to an external electric field tending to align them perpendicular to the plates. The Maxwell equations and self-consistent field equations are solved exactly, numerically, in real space. By comparing the free energies of different configurations, we show that for weak surface fields, the phase of cylinders parallel to the plates makes a direct transition to a phase in which the cylinders are aligned with the field throughout the sample. For stronger surface fields, there is an intermediate phase in which cylinders in the interior of the film, aligned with the field, terminate near the plates. For surface fields which favor the minority block, there is a boundary layer of hexagonal symmetry at the plates in which the monomers favored by the surface field occupy a larger area than they would if the cylinders extended to the surface.
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Affiliation(s)
- Chin-Yet Lin
- Department of Physics, University of Washington, Box 351560, Seattle, WA 98195-1560, USA.
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28
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Wang JY, Xu T, Leiston-Belanger JM, Gupta S, Russell TP. Ion complexation: a route to enhanced block copolymer alignment with electric fields. PHYSICAL REVIEW LETTERS 2006; 96:128301. [PMID: 16605963 DOI: 10.1103/physrevlett.96.128301] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2006] [Indexed: 05/08/2023]
Abstract
We investigate the enhanced alignment of lamellar microdomains under an electric field by addition of lithium chloride (LiCl) into polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) copolymers. A significant increase of dielectric contrast resulting from the formation of lithium-PMMA complexes markedly reduces the critical electric field strength required to overcome the preferential interactions of one block with the substrate, providing a route to achieve the complete alignment of microdomains in block copolymer thin films.
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Affiliation(s)
- Jia-Yu Wang
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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