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Oda K, Yasuda S. Effect of shear flow on the transverse thermal conductivity of polymer melts. Phys Rev E 2024; 109:064501. [PMID: 39021017 DOI: 10.1103/physreve.109.064501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 05/08/2024] [Indexed: 07/20/2024]
Abstract
The effect of shear flows on the thermal conductivity of polymer melts is investigated using a reversed nonequilibrium molecular-dynamics (RNEMD) method. We extended the original RNEMD method to simultaneously produce spatial gradients of temperature and flow velocity in a single direction. This method enables accurate measurement of the thermal conductivity in the direction transverse to shear flow. The Weissenberg number defined with the shear rate and the relaxation time of the polymer conformation can uniformly differentiate the occurrence of shear rate dependence of the thermal conductivity across different chain lengths. The stress-thermal rule (STR) (i.e., the linear relationship between anisotropic parts of the stress tensor and the thermal conductivity tensor) holds for entangled polymer melts even under shear flows but not for unentangled polymer melts. Furthermore, once entanglements form in polymer chains, the stress-thermal coefficient in the STR remains independent of the polymer chain length. These observations align with the theoretical foundation of the STR, which focuses on energy transmission along the network structure of entangled polymer chains [B. van den Brule, Rheol. Acta 28, 257 (1989)0035-451110.1007/BF01329335]. However, under driven shear flows, the stress-thermal coefficient is notably smaller than that measured in the literature for a quasiquiescent state without external forces. Although the mechanism of the STR in shear flows has yet to be fully elucidated, our study confirmed the validity of the STR in shear flows. This allows us to use the STR as a constitutive equation for computational thermofluid dynamics of polymer melts, thus having broad engineering applications.
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2
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Zheng Y, Tsige M, Wang SQ. Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening. Macromol Rapid Commun 2023; 44:e2200159. [PMID: 35881534 DOI: 10.1002/marc.202200159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 06/20/2022] [Indexed: 01/11/2023]
Abstract
In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (WiR >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as WiR > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.
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Affiliation(s)
- Yexin Zheng
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Mesfin Tsige
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
| | - Shi-Qing Wang
- School of Polymer Science and Polymer Engineering, University of Akron, Akron, OH, 44325, USA
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3
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Shen Z, Carrillo JMY, Sumpter BG, Wang Y. Fingerprinting Brownian Motions of Polymers under Flow. PHYSICAL REVIEW LETTERS 2022; 129:057801. [PMID: 35960564 DOI: 10.1103/physrevlett.129.057801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
We present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.
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Affiliation(s)
- Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Shen Z, Carrillo JMY, Sumpter BG, Wang Y. Decoding polymer self-dynamics using a two-step approach. Phys Rev E 2022; 106:014502. [PMID: 35974619 DOI: 10.1103/physreve.106.014502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.
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Affiliation(s)
- Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Ma J, Carrillo JMY, Do C, Chen WR, Falus P, Shen Z, Hong K, Sumpter BG, Wang Y. Spatial correlations of entangled polymer dynamics. Phys Rev E 2021; 104:024503. [PMID: 34525580 DOI: 10.1103/physreve.104.024503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 08/03/2021] [Indexed: 11/07/2022]
Abstract
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
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Affiliation(s)
- Jihong Ma
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jan-Michael Y Carrillo
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Changwoo Do
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Wei-Ren Chen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Péter Falus
- Institut Laue-Langevin, B.P. 156, F-38042 Grenoble CEDEX 9, France
| | - Zhiqiang Shen
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kunlun Hong
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Bobby G Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yangyang Wang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Synchronized Molecular-Dynamics Simulation of the Thermal Lubrication of an Entangled Polymeric Liquid. Polymers (Basel) 2019; 11:polym11010131. [PMID: 30960115 PMCID: PMC6401902 DOI: 10.3390/polym11010131] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Revised: 01/04/2019] [Accepted: 01/09/2019] [Indexed: 11/16/2022] Open
Abstract
The thermal lubrication of an entangled polymeric liquid in wall-driven shear flows between parallel plates is investigated by using a multiscale hybrid method, coupling molecular dynamics and hydrodynamics (i.e., the synchronized molecular dynamics method). The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value, and the rheological properties drastically change at around the critical drive force. In the weak viscous-heating regime, the conformation of polymer chains is dominated by the flow field so that the polymers are more elongated as the drive force increases. However, in the large viscous-heating regime, the conformation dynamics is dominated by the thermal agitation of polymer chains so that the conformation of polymers recovers more uniform and random structures as the drive force increases, even though the local shear flows are further enhanced. Remarkably, this counter-intuitive transitional behavior gives an interesting re-entrant transition in the stress–optical relation, where the linear stress–optical relation approximately holds even though each of the macroscopic quantities behaves nonlinearly. Furthermore, the shear thickening behavior is also observed in the large viscous-heating regime—this was not observed in a series of previous studies on an unentangled polymer fluid. This qualitative difference of the thermo-rheological property between the entangled and unentangled polymer fluids gives completely different velocity profiles in the thermal lubrication system.
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Matsumiya Y, Watanabe H. Nonlinear Stress Relaxation of Miscible Polyisoprene/Poly( p- tert-butylstyrene) Blends in Pseudomonodisperse State. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00910] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yumi Matsumiya
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Hiroshi Watanabe
- Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
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Lu Y, An L, Wang SQ, Wang ZG. Molecular Mechanisms for Conformational and Rheological Responses of Entangled Polymer Melts to Startup Shear. Macromolecules 2015. [DOI: 10.1021/ma502236m] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Yuyuan Lu
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Shi-Qing Wang
- Department
of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States
| | - Zhen-Gang Wang
- State
Key Laboratory of Polymer Physics and Chemistry, Changchun Institute
of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
- Division
of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Abstract
To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.
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Affiliation(s)
- Yuichi Masubuchi
- Institute for Chemical Research, Kyoto University, Gokasho Uji-City, Japan 611-0011
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Affiliation(s)
- Alexei E. Likhtman
- School
of Mathematical and
Physical Sciences, University of Reading, Reading RG6 6AX, U.K
| | - M. Ponmurugan
- School
of Mathematical and
Physical Sciences, University of Reading, Reading RG6 6AX, U.K
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11
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De S. Computational study of the propagation of the longitudinal velocity in a polymer melt contained within a cylinder using a scale-bridging method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052311. [PMID: 24329268 DOI: 10.1103/physreve.88.052311] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Revised: 05/21/2013] [Indexed: 06/03/2023]
Abstract
The "constitutive equation"-free scale-bridging method connecting nonequilibrium molecular dynamics and continuum fluid mechanics, that had hitherto been applied only to a parallel-plates geometry, is extended to study the flow of a polymer melt in a cylindrical pipe subject to a velocity in the direction parallel to the cylinder's axis. The system, initially at rest, is given a velocity at the cylinder's surface, and the evolution of the velocity profile within the fluid is studied, along with the time taken for the velocity to propagate toward the cylinder's axis. The said time of propagation is found to increase with the boundary velocity-a fact in contrast with the case of a Newtonian fluid for which the time of propagation is expected to be independent of the boundary velocity. For a fixed value of the boundary velocity, the propagation time is found to increase with the cylinder radius according to a power law with an exponent that is smaller than the corresponding exponent for a Newtonian fluid. For the lower values of the boundary velocity and the lower values of the radius studied, a velocity overshoot is observed at the cylinder's axis-a manifestation of elastic behavior of the fluid.
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Affiliation(s)
- Subhranil De
- Department of Physics, Indiana University Southeast, New Albany, Indiana 47150, USA
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Anogiannakis SD, Tzoumanekas C, Theodorou DN. Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes. Macromolecules 2012. [DOI: 10.1021/ma300912z] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Stefanos D. Anogiannakis
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
| | - Christos Tzoumanekas
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
| | - Doros N. Theodorou
- School of Chemical Engineering, Zografou Campus, National Technical University of Athens, GR-15780 Athens,
Greece
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven,
The Netherlands
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13
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Uneyama T, Masubuchi Y. Multi-chain slip-spring model for entangled polymer dynamics. J Chem Phys 2012; 137:154902. [DOI: 10.1063/1.4758320] [Citation(s) in RCA: 90] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Puscasu RM, Todd BD, Daivis PJ, Hansen JS. Nonlocal viscosity of polymer melts approaching their glassy state. J Chem Phys 2010; 133:144907. [DOI: 10.1063/1.3499745] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Todd BD, Daivis PJ. Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications. MOLECULAR SIMULATION 2007. [DOI: 10.1080/08927020601026629] [Citation(s) in RCA: 81] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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16
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Jeszka JK, Pakula T. Monte Carlo simulation of linear polymer melts in shear flow. Effect of shear stress and confined space on chain dynamics. POLYMER 2006. [DOI: 10.1016/j.polymer.2006.04.071] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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Bruzzone S, Malvaldi M. Dynamics of relaxation of entangled polymers in shear flow. J Chem Phys 2006; 125:64909. [PMID: 16942314 DOI: 10.1063/1.2244552] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The application of shear flow to entangled polymer melts can strongly modify its rheological and physicochemical behaviors, giving rise to an acceleration of several chemical processes such as diffusion-controlled reactions. In the present work, we investigate the modification of conformational and diffusive properties of an entangled polymer in shear flow by numerical methods. The flow affects both the conformational and diffusive properties of the system, giving rise to a quasinematic ordering of the macromolecules which take prolate spheroid shape with the main axis aligned to the shear direction. The shear flow is found to accelerate the overall diffusion of the chains in all directions at times longer than the polymer relaxation time. The polymer chains display a quite peculiar displacement behavior in direction parallel to the flow. At the same conditions, the linear relation between the diffusion constant in direction perpendicular to the flow and the inverse of the relaxation time, usually adopted in equilibrium regimes, is shown to hold even in the presence of flow.
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Affiliation(s)
- Samantha Bruzzone
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56100 Pisa, Italy
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18
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Tzoumanekas C, Theodorou DN. Topological Analysis of Linear Polymer Melts: A Statistical Approach. Macromolecules 2006. [DOI: 10.1021/ma0607057] [Citation(s) in RCA: 245] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christos Tzoumanekas
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, and Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Doros N. Theodorou
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece, and Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
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