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Rational Design of Nanocomposites for Barrier Applications

2001; Volume: 13; Issue: 21 Linguagem: Inglês

10.1002/1521-4095(200111)13

1521-4095

А. А. Гусев, Hans Rudolf Lusti,

Composite Material Mechanics

Advanced MaterialsVolume 13, Issue 21 p. 1641-1643 Communication Rational Design of Nanocomposites for Barrier Applications A. A. Gusev, A. A. Gusev [email protected] Department of Materials, Institute of Polymers, ETH, CH-8092 Zürich (Switzerland)Search for more papers by this authorH. R. Lusti, H. R. Lusti Department of Materials, Institute of Polymers, ETH, CH-8092 Zürich (Switzerland)Search for more papers by this author A. A. Gusev, A. A. Gusev [email protected] Department of Materials, Institute of Polymers, ETH, CH-8092 Zürich (Switzerland)Search for more papers by this authorH. R. Lusti, H. R. Lusti Department of Materials, Institute of Polymers, ETH, CH-8092 Zürich (Switzerland)Search for more papers by this author First published: 25 October 2001 https://doi.org/10.1002/1521-4095(200111)13:21 3.0.CO;2-PCitations: 266AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Barrier properties of a nanocomposite comprised of perfectly aligned randomly dispersed platelets are described in this communication. The finite-element based methodology employed is generic and can readily be used to identify the role of various morphological imperfections typical of nanocomposites. The Figure shows a sketch of a periodic multi-inclusion computer model comprised of 25 identical parallel non-overlapping identical platelets of aspect ratio 50. References 1 E. P. Giannelis, Adv. Mater. 1996, 8, 29. 2 P. C. LeBaron, Z. Wang, T. J. Pinnavaia, Appl. Clay Sci. 1999, 15, 11. 3 J. M. Garces, D. J. Moll, J. Bicerano, R. Fibiger, D. G. McLeod, Adv. Mater. 2000, 12, 1835. 4 T. Lan, P. D. Kaviratna, T. J. Pinnavaia, Chem. Mater. 1994, 6, 573. 5 K. Yano, A. Usuki, A. Okada, J. Polym. Sci. A: Polym. Chem. 1997, 35, 2289. 6 R. J. Xu, E. Manias, A. J. Snyder, J. Runt, Macromolecules 2001, 34, 337. 7 A. A. Gusev, Macromolecules 2001, 34, 3081. 8 Rigorously speaking, gas permeability through a material is described by a 3 - 3 symmetric permeability tensor. Here we consider isotropic matrices so the local permeability tensor can be written as P(r)δik, where P(r) is the local permeability coefficient, δik the Kronecker tensor with indices i and k varying from 1 to 3. 9 L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, Volume 5: Statistical Physics, Part 1, 3 ed., Pergamon Press, Oxford, UK 1988. 10 An in-house iterative conjugate-gradient solver with a diagonal preconditioner was used in calculations [7,11]. The stopping criterion was that the first residual norm be reduced by a factor of 105 relative to its initial value. Calculations were carried out on a DEC AXP 8400 5/300 workstation. On a single processor, a single permeability calculation typically took 510 CPUh. 11 J. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston 1996. 12 In this work, the aspect ratio of a platelet is defined as the ratio of the platelet diameter to its thickness, thus leading to an aspect ratio of 1 for spheres. 13 Equation 2 does not reduce to the Maxwell equation for spheres whereas direct numerical predictions accurately follow this equation. 14 L. E. Nielsen, J. Macromol. Sci. (Chem) 1967, A 1, 929. 15 R. Aris, Arch. Ration. Mech. Anal. 1986, 95, 83. 16 E. L. Cussler, S. E. Hugnes, W. J. Ward III, R. Aris, J. Membr. Sci. 1988, 38, 161. 17 G. H. Fredrickson, J. Bicerano, J. Chem. Phys. 1999, 110, 2181. 18 W. J. Drugan, J. R. Willis, J. Mech. Phys. Solids 1996, 44, 497. 19 A. A. Gusev, J. Mech. Phys. Solids 1997, 45, 1449. 20 A. A. Gusev, J. J. M. Slot, Adv. Eng. Mater. 2001, 6, 427. 21 V. V. Ginzburg, A. C. Balazs, Adv. Mater. 2000, 12, 1805. 22 O. C. Zienkiewicz, R. L. Taylor, The Finite Element Method, Volume 1: The Basis, 5 ed., Butterworth-Heinemann, Oxford, UK 2000. 23 S. H. Anastasiadis, K. Karatasos, G. Vlachos, E. Manias, E. P. Giannelis, Phys. Rev. Lett. 2000, 84, 915. Citing Literature Volume13, Issue21November, 2001Pages 1641-1643 ReferencesRelatedInformation