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Interaction models for effective thermal and electric conductivities of carbon nanotube composites

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Abstract

The present article provides supplementary information of previous works of analytic models for predicting conductivity enhancements of carbon nanotube composites. The models, though fairly simple, are able to take account of the effects of conductivity anisotropy, nonstraightness, and aspect ratio of the CNT additives on the conductivity enhancement of the composite and to give predictions agreeing well with existing experimental data. The omitted detailed derivation of this model is demonstrated in the present article with a more systematical analysis, which may help with further development in this direction. Furthermore, the effects of various orientation distributions of CNTs are reported here for the first time. The information may be useful in design or fabrication technology of CNT composites for better or specified conductivities.

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References

  1. Deng, F., Zheng, Q.S., Wang, L.F. and Nan, C.W., Effects of anisotropy, aspect ratio, and nonstraightness of carbon nanotubes on thermal conductivity of carbon nanotube composites. Applied Physics Letters, 2007, 90: 021914.

    Article  Google Scholar 

  2. Deng, F. and Zheng, Q.S., An analytical model of effective electrical conductivity of carbon nanotube composites. Applied Physics Letters, 2008, 92: 071902.

    Article  Google Scholar 

  3. Zheng, Q.S. and Du, D.X., An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution. Journal of the Mechanics and Physics of Solids, 2001, 49: 2765–2788.

    Article  Google Scholar 

  4. Kim, P., Shi, L., Majumdar, A. and McEuen, P.L., Thermal transport measurements of individual multiwalled nanotubes. Physical Review Letters, 2001, 87: 215502.

    Article  Google Scholar 

  5. Pop, E., Mann, D., Wang, Q. Goodson, K. and Dai, H., Thermal conductance of an individual single-wall carbon nanotube above room temperature. Nano Letters, 2006, 6(1): 96–100.

    Article  Google Scholar 

  6. Yu, C., Shi, L., Yao, Z., Li, D. and Majumdar, A., Thermal conductance and thermopower of an individual single-wall carbon nanotube. Nano Letters, 2005, 5(9): 1842–1846.

    Article  Google Scholar 

  7. Dai, H.J., Wong, E.W. and Lieber, C.M., Probing electrical transport in nanomaterials: conductivity of individual carbon nanotubes. Science, 1996, 272: 523–526.

    Article  Google Scholar 

  8. Ebbsen, T.W., Lezec, H.J., Hiura, H.J., Bennett, W., Ghaemi, H.F. and Thio, T., Electrical conductivity of individual carbon nanotubes. Nature, 1996, 382: 54–56.

    Article  Google Scholar 

  9. Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E. and Grulke, E.A., Anomalous thermal conductivity enhancement in nanotube suspensions. Applied Physics Letters, 2001, 79: 2252–2254.

    Article  Google Scholar 

  10. Nan, C.W., Shi, Z. and Lin, Y., A simple model for thermal conductivity of carbon nanotube-based composites. Chemical Physics Letters, 2003, 375: 666–669.

    Article  Google Scholar 

  11. Nan, C.W., Liu, G., Lin, Y. and Li, M., Interface effect on thermal conductivity of carbon nanotube composites. Applied Physics Letters, 2004, 85: 3549–3551.

    Article  Google Scholar 

  12. Huxtable, S., Cahill, D.G., Shenogin, S., Xue, L., Ozisik, R., Barone, P., Usrey, M., Strano, M.S., Siddons, G., Shim, M. and Keblinski, P., Interfacial heat flow in carbon nanotube suspensions. Nature Materials, 2003, 2: 731–734.

    Article  Google Scholar 

  13. Chen, T.Y., Wen, G. and Liu, W.C., Effect of Kapitza contact and consideration of tube-end transport on the effective conductivity in nanotube-based composites. Journal of Applied Physics, 2005, 97: 104312.

    Article  Google Scholar 

  14. Milton, G.W., The Theory Of Composites, New York: Cambridge University Press, 2002.

    Book  Google Scholar 

  15. Ramasubramaniam, R. and Chen, J., Homogeneous carbon nanotube/polymer composites for electrical applications. Applied Physics Letters, 2003, 83: 2928–2930.

    Article  Google Scholar 

  16. Grunlan, J.C., Mehrabi, A.R., Bannon, M.V. and Bahr, J.L., Water-based single-walled-nanotube-filled polymer composite with an exceptionally low percolation threshold. Advanced Materials, 2004, 16(2): 150–153.

    Article  Google Scholar 

  17. Ahmad, K., Pan, W. and Shi, S.L., Electrical conductivity and dielectric properties of multiwalled carbon nanotube and alumina composites. Applied Physics Letters, 2006, 89: 133122.

    Article  Google Scholar 

  18. Du, F.M., Fischer, J.E. and Winey, K.I., Effect of nanotube alignment on percolation conductivity in carbon nanotubepolymer composites. Physical Review B, 2005, 72: 121404.

    Article  Google Scholar 

  19. Ounaies, Z., Park, C., Wise, K.E., Siochi, E.J. and Harrison, J.S., Electrical properties of single wall carbon nanotube reinforced polyimide composites. Composites Science and Technology, 2003, 63: 1637–1646.

    Article  Google Scholar 

  20. Bryning, M.B., Islam, M.F., Kikkawa, J.M. and Yodh, A.G., Very low conductivity threshold in bulk isotropic single-walled carbon nanotube-epoxy composites. Advanced Materials, 2005, 17: 1186–1191.

    Article  Google Scholar 

  21. Geoffrey, G., Percolation, 2nd ed. New York: Springer, 1999.

    MATH  Google Scholar 

  22. Kirkpatrick, S., Percolation and Conduction. Review of Modern Physics, 1973, 45(4): 574–588.

    Article  Google Scholar 

  23. Du, D.X. and Zheng, Q.S., A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of muhiphase composites taking into account inclusion distribution. Acta Mechanica, 2002, 157: 61–81.

    Article  Google Scholar 

  24. Mura, T., Micromechanics of Defects in Solids. Martinus Nijhoff: Dordrecht, 1987.

    Book  Google Scholar 

  25. Kelly, B.T., Physics of Graphite. London: Applied Science, 1981.

    Google Scholar 

  26. Hooker, C.N., Ubbelohde, A.R. and Young, D.A., Anisotropy of thermal conductance in near-ideal graphite. Proceedings of the Royal Society of London Series A, 1965, 284: 17–31.

    Article  Google Scholar 

  27. Che, J.W. Çagin, T. and Goddard III, W.A., Thermal conductivity of carbon nanotubes. Nanotechnology, 2000, 11: 65–69.

    Article  Google Scholar 

  28. Zhou, W., Islam, M.F., Wang, H., Ho, D.L., Yodh, A.G., Winey, K.I. and Fischer, J.E., Small angle neutron scattering from single-wall carbon nanotube suspensions, evidence for isolated rigid rods and rod networks. Chemical Physics Letters, 2004, 384: 185–189.

    Article  Google Scholar 

  29. Jang, H.S., Lee, H.R. and Kim, D.H., Field emission properties of carbon nanotubes with different morphologies. Thin Solid films, 2006, 500: 124–128.

    Article  Google Scholar 

  30. Song, P.C., Liu, C.H. and Fan, S.S., Improving the thermal conductivity of nanocomposites by increasing the length efficiency of loading carbon nanotubes. Applied Physics Letters, 2006, 88: 153111.

    Article  Google Scholar 

  31. Duggal, R. and Pasquali, M., Dynamics of individual single-walled carbon nanotubes in water by real-time visualization. Physical Review Letters, 2006, 96: 246104.

    Article  Google Scholar 

  32. Lee, H.S., Yun, C.H., Kim, H.M. and Lee, C.J., Persistence length of multiwalled carbon nanotubes with static bending. Journal of Physical Chemistry C, 2007, 111: 18882–18887.

    Article  Google Scholar 

  33. Ahir, S.V. and Terentjev, E.M., Thermal fluctuations, stress relaxation, and actuation in carbon nanotube networks. Physical Review B, 2007, 76: 165437.

    Article  Google Scholar 

  34. Geblinger, N., Ismach, A. and Joselevich, E., Self-organized nanotube serpentines. Nature nanotechnology, 2008, 3: 195–200.

    Article  Google Scholar 

  35. Shenogina, N., Shenogin, S., Xue, L. and Keblinski, P., On the lack of thermal percolation in carbon nanotube composites. Applied Physics Letters, 2005, 87: 133106.

    Article  Google Scholar 

  36. Frank, S., Poncharal, P., Wang, Z.L. and W.A. de Heer, Carbon nanotube quantum resistors. Science, 1998, 280: 1744–1746.

    Article  Google Scholar 

  37. Liang, W.J., Bockrath, M., Bozovic, D., Hafner, J.H., Tinkham, M. and Park, H., Perot interference in a nanotube electron waveguide. Nature, 2001, 411: 665.

    Article  Google Scholar 

  38. Brandrup, J. and Immergut, E.H., Polymer Handbook, 3rd ed. New York: Wiley Interscience, 1989.

    Google Scholar 

  39. Rouby, D., Gobin, F. and Bonjour, E., Anelastic relaxation peaks in graphites after neutron irradiation at low temperature. Philosophical Magazine, 1974, 29: 983–999.

    Article  Google Scholar 

  40. Bonjour, E., Le Diouron, R., Fiorese, G., Rouby, D. and Gob, P.F., Young’s modulus and internal friction of graphite irradiated at low temperature. Radiation Effects and Defects in Solids, 1971, 11: 155–165.

    Article  Google Scholar 

  41. Mitchell, E.J.W. and Taylor, M. R., Mechanism of stored-energy release at 200°C in electron-irradiated graphite. Nature, 1965, 208: 638–641.

    Article  Google Scholar 

  42. Foygel, M., Morris, R.D., Anez, D., French, S. and Sobolev, V.L., Theoretical and computational studies of carbon nanotube composites and suspensions, Electrical and thermal conductivity. Physical Review B, 2005, 71: 104201.

    Article  Google Scholar 

  43. Balberg, I., Anderson, C.H., Alexander, S. and Wagner, N., Excluded volume and its relation to the onset of percolation. Physical Review B, 1984, 30: 3933–3943.

    Article  Google Scholar 

  44. Bug, A.L.R., Safran, S.A. and Webman, I., Continuum percolation of rods. Physical Review Letters, 1985, 54: 1412–1415.

    Article  Google Scholar 

  45. Gao, L. and Li, Z.Y., Effective medium approximation for two-component nonlinear composites with shape distribution. Journal of Physics: Condensed Matter, 2003, 15: 4397.

    Google Scholar 

  46. Bergman, D.J. Composite Media and Homogenization Theory. Boston: Birkhauser, 1991.

    Google Scholar 

  47. Landau, L.D. and Lifshitz, E.M., Electrodynamics of Continuous Media, 2nd ed. Oxford: Pergamon, 1984.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Fei Deng & Quanshui Zheng

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  1. Fei Deng
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  2. Quanshui Zheng
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Correspondence to Quanshui Zheng.

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Deng, F., Zheng, Q. Interaction models for effective thermal and electric conductivities of carbon nanotube composites. Acta Mech. Solida Sin. 22, 1–17 (2009). https://doi.org/10.1016/S0894-9166(09)60085-9

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  • DOI: https://doi.org/10.1016/S0894-9166(09)60085-9

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