51
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Gin P, Jiang N, Liang C, Taniguchi T, Akgun B, Satija SK, Endoh MK, Koga T. Revealed architectures of adsorbed polymer chains at solid-polymer melt interfaces. PHYSICAL REVIEW LETTERS 2012; 109:265501. [PMID: 23368578 DOI: 10.1103/physrevlett.109.265501] [Citation(s) in RCA: 171] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2012] [Revised: 10/22/2012] [Indexed: 05/26/2023]
Abstract
We report the chain conformations of polymer molecules accommodated at the solid-polymer melt interfaces in equilibrium. Polystyrene "Guiselin" brushes (adsorbed layers) with different molecular weights were prepared on Si substrates and characterized by using x-ray and neutron reflectivity. The results are intriguing to show that the adsorbed layers are composed of the two different nanoarchitectures: flattened chains that constitute the inner higher density region of the adsorbed layers and loosely adsorbed polymer chains that form the outer bulklike density region. In addition, we found that the lone flattened chains, which are uncovered by the additional prolonged solvent leaching (∼120 days), are reversibly densified with increasing temperature up to 150 °C. By generalizing the chain conformations of bulks, we postulate that the change in probabilities of the local chain conformations (i.e., trans and gauche states) of polymer molecules is the origin of this densification process.
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Affiliation(s)
- Peter Gin
- Department of Materials Science and Engineering, Stony Brook University, Stony Brook, New York 11794-2275, USA
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52
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Chong Lua A, Shen Y. Influence of inorganic fillers on the structural and transport properties of mixed matrix membranes. J Appl Polym Sci 2012. [DOI: 10.1002/app.38614] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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53
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54
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Yang S, Choi J, Cho M. Elastic stiffness and filler size effect of covalently grafted nanosilica polyimide composites: molecular dynamics study. ACS APPLIED MATERIALS & INTERFACES 2012; 4:4792-4799. [PMID: 22931169 DOI: 10.1021/am301144z] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The filler size-dependent elastic stiffness of nanosilica (α-quartz)-reinforced polyimide(s-BPDA/1,3,4-APB) composites under the same volume fraction and grafting ratio conditions was investigated via molecular dynamics(MD) simulations. To enhance the interfacial load transfer efficiency, we treated the surface oxygen atoms of the silica nanoparticle with additional silicon atoms attached by a propyl group to which the aromatic hydrocarbon in the polyimide is directly grafted. As the radius of the embedded nanoparticle increases, the Young's and shear moduli gradually decrease, showing a prominent filler size effect. At the same time, the moduli of the nanocomposites increase as the grafting ratio increases. The contribution of different nanoparticles to the filler size dependency in elastic stiffness of the nanocomposites can be elucidated by comparing the normalized adhesive interaction energy between the particle and matrix which exhibits prominent filler size dependency. Because of the immobilization of the matrix polymer in the vicinity of the nanoparticles, which was confirmed by the self-diffusion coefficient, the highly grafted interface is found to bring about a greater reinforcing effect than the ungrafted interface.
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Affiliation(s)
- Seunghwa Yang
- Division of WCU Multiscale Mechanical Design, School of Mechanical and Aerospace Engineering, Seoul National University 599, Kwanak-Ro, Kwanak-Ku, Seoul151-744, Korea
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55
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Liu J, Zhang L, Cao D, Shen J, Gao Y. COMPUTATIONAL SIMULATION OF ELASTOMER NANOCOMPOSITES: CURRENT PROGRESS AND FUTURE CHALLENGES. RUBBER CHEMISTRY AND TECHNOLOGY 2012. [DOI: 10.5254/rct.12.87966] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
ABSTRACT
In the field of elastomer nanocomposites (ENCs), computational simulation technique is becoming more and more essential, as a result of its ability to provide important and clear information at the molecular level, which is always difficult to obtain or not accessible through experimental investigations. We focus on summarizing the progress achieved in the simulation research of three critical topics of ENCs, namely, (i) the dispersion mechanism (particularly polymer-mediated interparticle interaction, the “many-body” effect at high filler loading), (ii) the characterization of the nanoscale/microscale structure and dynamics [the modified chain configuration in the presence of nanoparticles (NPs), the interfacial binding strength determining the efficiency of the stress transfer, the possibly altered interfacial chain structure, interfacial segmental dynamics leading to the shift of the glass transition temperature Tg, the formation of the filler network and its structure, the chemical cross-linking process], and (iii) the macroscopic viscoelasticity (the Payne effect), mechanical reinforcement, and physical property (thermal conductivity). Since recently only limited simulation work has been carried out pertaining to ENCs, we discuss these three topics in light of the simulation and theoretical achievements of polymer nanocomposites (mainly polymer melts filled with NPs). Meanwhile, some relevant experimental studies are also included for better illustration. Furthermore, for each topic, three typically different reinforcing fillers, such as three-dimensional spherical, two-dimensional sheet, and one-dimensional rod NPs, separately corresponding to carbon black or silica, clay sheets, and carbon nanotubes intensively used in the practical applications of ENCs, are illustrated in order. In order to realize a comprehensive understanding of the structure–property relation and in the meantime to provide more practical guidelines for the engineering applications of ENCs, we investigate future simulation opportunities and difficulties.
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Affiliation(s)
- Jun Liu
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials,Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
| | - Liqun Zhang
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials,Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
- Division of Molecular and Materials Simulation, State Key Laboratory of Organic–Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
| | - Dapeng Cao
- Division of Molecular and Materials Simulation, State Key Laboratory of Organic–Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
| | - Jianxiang Shen
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials,Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
| | - Yangyang Gao
- Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials,Beijing University of Chemical Technology, Beijing 100029, People's Republic of China
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56
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Riccardi E, Böhm MC, Müller-Plathe F. Molecular dynamics method to locally resolve Poisson's ratio: Mechanical description of the solid-soft-matter interphase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036704. [PMID: 23031050 DOI: 10.1103/physreve.86.036704] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2012] [Indexed: 06/01/2023]
Abstract
A method based on "small-deformation mechanical response" has been developed to locally resolve the Poisson's ratio via molecular dynamics simulations. The approach can be used for simple and composite materials to characterize systems with two or more continuous phases in the framework of periodic boundary conditions. The proposed technique represents a simple method to obtain a local mechanical description of complex systems. A polystyrene bulk, a silica bulk, and a polystyrene-silica heterogeneous composite material have been characterized under imposed strain. The results show the effects of local material inhomogeneities which are present in the glassy material and in the composite system. The Poisson's ratio spatial profiles for silica, the polystyrene bulk, and in the interphase region between the soft polymer bulk and the hard surface have also been calculated. The obtained local mechanical description can be employed in micromechanical models developed to predict the overall mechanical properties of multicomponent materials.
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Affiliation(s)
- Enrico Riccardi
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany.
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57
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Rahimi M, Iriarte-Carretero I, Ghanbari A, Böhm MC, Müller-Plathe F. Mechanical behavior and interphase structure in a silica-polystyrene nanocomposite under uniaxial deformation. NANOTECHNOLOGY 2012; 23:305702. [PMID: 22751262 DOI: 10.1088/0957-4484/23/30/305702] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The mechanical behavior of polystyrene and a silica-polystyrene nanocomposite under uniaxial elongation has been studied using a coarse-grained molecular dynamics technique. The Young's modulus, the Poisson ratio and the stress-strain curve of polystyrene have been computed for a range of temperatures, below and above the glass transition temperature. The predicted temperature dependence of the Young's modulus of polystyrene is compared to experimental data and predictions from atomistic simulations. The observed mechanical behavior of the nanocomposite is related to the local structure of the polymer matrix around the nanoparticles. Local segmental orientational and structural parameters of the deforming matrix have been calculated as a function of distance from nanoparticle's surface. A thorough analysis of these parameters reveals that the segments close to the silica nanoparticle's surface are stiffer than those in the bulk. The thickness of the nanoparticle-matrix interphase layer is estimated. The Young's modulus of the nanocomposite has been obtained for several nanoparticle volume fractions. The addition of nanoparticles results in an enhanced Young's modulus. A linear relation describes adequately the dependence of Young's modulus on the nanoparticle volume fraction.
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Affiliation(s)
- Mohammad Rahimi
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Centre of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 22, D-64287 Darmstadt, Germany.
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58
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Hong B, Chremos A, Panagiotopoulos AZ. Dynamics in coarse-grained models for oligomer-grafted silica nanoparticles. J Chem Phys 2012; 136:204904. [DOI: 10.1063/1.4719957] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
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59
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Abstract
It is well recognized that nanocomposites formed by adding nanoparticles to polymers can have significantly enhanced properties relative to the native polymer. This review focuses on three aspects that are central to the outstanding problem of realizing these promised property improvements. First, we ask if there exist general strategies to control nanoparticle spatial distribution. This is an important question because it is commonly accepted that the nanoparticle dispersion state crucially affects property improvements. Because ideas on macroscale composites suggest that optimizing different properties requires different dispersion states, we next ask if we can predict a priori the particle dispersion and organization state that can optimize one (or more) properties of the resulting nanocomposite. Finally, we examine the role that particle shape plays in affecting dispersion and hence property control. This review focuses on recent advances concerning these underpinning points and how they affect measurable properties relevant to engineering applications.
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Affiliation(s)
- Sanat K Kumar
- Department of Chemical Engineering, Columbia University, New York, NY 10027, USA.
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60
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Wang X, Qi G, Zhang X, Gao J, Li B, Song Z, Qiao J. The abnormal behavior of polymers glass transition temperature increase and its mechanism. Sci China Chem 2012. [DOI: 10.1007/s11426-012-4521-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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61
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Pandey YN, Doxastakis M. Detailed atomistic Monte Carlo simulations of a polymer melt on a solid surface and around a nanoparticle. J Chem Phys 2012; 136:094901. [DOI: 10.1063/1.3689316] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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62
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Hong B, Panagiotopoulos AZ. Molecular Dynamics Simulations of Silica Nanoparticles Grafted with Poly(ethylene oxide) Oligomer Chains. J Phys Chem B 2012; 116:2385-95. [DOI: 10.1021/jp2112582] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bingbing Hong
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544,
United States
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63
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Ghanbari A, Ndoro TVM, Leroy F, Rahimi M, Böhm MC, Müller-Plathe F. Interphase Structure in Silica–Polystyrene Nanocomposites: A Coarse-Grained Molecular Dynamics Study. Macromolecules 2011. [DOI: 10.1021/ma202044e] [Citation(s) in RCA: 146] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Azadeh Ghanbari
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Tinashe V. M. Ndoro
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Frédéric Leroy
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Mohammad Rahimi
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Michael C. Böhm
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische
Chemie and Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
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64
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Karatrantos A, Composto RJ, Winey KI, Clarke N. Structure and Conformations of Polymer/SWCNT Nanocomposites. Macromolecules 2011. [DOI: 10.1021/ma201359s] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Argyrios Karatrantos
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - Russell J. Composto
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Karen I. Winey
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Nigel Clarke
- Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
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65
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Nusser K, Schneider GJ, Pyckhout-Hintzen W, Richter D. Viscosity Decrease and Reinforcement in Polymer–Silsesquioxane Composites. Macromolecules 2011. [DOI: 10.1021/ma201585v] [Citation(s) in RCA: 106] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Klaus Nusser
- Jülich Centre for Neutron Science and Institute for Complex Solids, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Gerald J. Schneider
- Jülich Centre for Neutron Science and Institute for Complex Solids, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Wim Pyckhout-Hintzen
- Jülich Centre for Neutron Science and Institute for Complex Solids, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Dieter Richter
- Jülich Centre for Neutron Science and Institute for Complex Solids, Forschungszentrum Jülich GmbH, Jülich, Germany
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66
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Ershad-Langroudi A, Razavi-Nouri M, Oromiehie A. Prediction of viscoelastic behavior of interphase in polypropylene-chopped rice husk composites for β-relaxation domain. J Appl Polym Sci 2011. [DOI: 10.1002/app.33281] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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67
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Affiliation(s)
- Juan J. de Pablo
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706;
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68
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Vogiatzis GG, Voyiatzis E, Theodorou DN. Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system. Eur Polym J 2011. [DOI: 10.1016/j.eurpolymj.2010.09.017] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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69
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Ndoro TVM, Voyiatzis E, Ghanbari A, Theodorou DN, Böhm MC, Müller-Plathe F. Interface of Grafted and Ungrafted Silica Nanoparticles with a Polystyrene Matrix: Atomistic Molecular Dynamics Simulations. Macromolecules 2011. [DOI: 10.1021/ma102833u] [Citation(s) in RCA: 222] [Impact Index Per Article: 17.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tinashe V. M. Ndoro
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Evangelos Voyiatzis
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, GR-15780, Greece
| | - Azadeh Ghanbari
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Doros N. Theodorou
- School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, GR-15780, Greece
| | - Michael C. Böhm
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany
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70
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Liu J, Wu Y, Shen J, Gao Y, Zhang L, Cao D. Polymer–nanoparticle interfacial behavior revisited: A molecular dynamics study. Phys Chem Chem Phys 2011; 13:13058-69. [DOI: 10.1039/c0cp02952a] [Citation(s) in RCA: 86] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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71
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Schmidt RG, Gordon GV, Dreiss CA, Cosgrove T, Krukonis VJ, Williams K, Wetmore PM. A Critical Size Ratio for Viscosity Reduction in Poly(dimethylsiloxane)−Polysilicate Nanocomposites. Macromolecules 2010. [DOI: 10.1021/ma1004919] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Glenn V. Gordon
- Dow Corning Corporation, Midland, Michigan 48686-0994, United States
| | - Cécile A. Dreiss
- Pharmaceutical Science Division, King's College London, SE1 9NH London, U.K
| | - Terence Cosgrove
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol, BS8 1TS, U.K
| | - Val J. Krukonis
- Phasex Corporation, Lawrence, Massachusetts 01843, United States
| | - Kara Williams
- Phasex Corporation, Lawrence, Massachusetts 01843, United States
| | - Paula M. Wetmore
- Phasex Corporation, Lawrence, Massachusetts 01843, United States
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72
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Harton SE, Kumar SK, Yang H, Koga T, Hicks K, Lee H, Mijovic J, Liu M, Vallery RS, Gidley DW. Immobilized Polymer Layers on Spherical Nanoparticles. Macromolecules 2010. [DOI: 10.1021/ma902484d] [Citation(s) in RCA: 227] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shane E. Harton
- Department of Chemical Engineering, Columbia University, New York, New York
| | - Sanat K. Kumar
- Department of Chemical Engineering, Columbia University, New York, New York
| | - Hoichang Yang
- Rensselaer Nanotechnology Institute, Rensselaer Polytechnic University, Troy, New York
| | - Tadanori Koga
- Chemical and Molecular Engineering Program, Department of Materials Science and Engineering, Stony Brook University, Stony Brook, New York
| | - Kyle Hicks
- Othmer-Jacobs Department of Chemical and Biological Engineering, Polytechnic Institute of New York University, Brooklyn, New York
| | - HyungKi Lee
- Othmer-Jacobs Department of Chemical and Biological Engineering, Polytechnic Institute of New York University, Brooklyn, New York
| | - Jovan Mijovic
- Othmer-Jacobs Department of Chemical and Biological Engineering, Polytechnic Institute of New York University, Brooklyn, New York
| | - Ming Liu
- Department of Physics, University of Michigan, Ann Arbor, Michigan
| | | | - David W. Gidley
- Department of Physics, University of Michigan, Ann Arbor, Michigan
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73
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Luo YD, Chen JH, Huang CI, Chiu WY. Molecular dynamics study of TiO 2/poly(acrylic acid- co-methyl methacrylate) and Fe 3O 4/polystyrene composite latex particles prepared by heterocoagulation. J Appl Polym Sci 2010. [DOI: 10.1002/app.31652] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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74
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Goswami M, Sumpter BG. Effect of polymer-filler interaction strengths on the thermodynamic and dynamic properties of polymer nanocomposites. J Chem Phys 2009; 130:134910. [DOI: 10.1063/1.3105336] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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75
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76
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Liu J, Zhang L, Cao D, Wang W. Static, rheological and mechanical properties of polymer nanocomposites studied by computer modeling and simulation. Phys Chem Chem Phys 2009; 11:11365-84. [DOI: 10.1039/b913511a] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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