Electrically Conductive Polymer Nanocomposites with High Thermal Conductivity

  • Prabhakar R. Bandaru
  • B.-W. Kim
  • S. Pfeifer
  • R. S. Kapadia
  • S.-H. Park


The utility of one-dimensional nanostructures, such as linear and nonlinear carbon nanotubes (CNTs), as fillers in polymer matrices and their influence in modulating the electrical, electromagnetic, and thermal properties of the resulting composites. This chapter will first consider the rationale for the use of structures with a large aspect ratio, based on percolation theory. At the very outset, a large length-to-diameter ratio enables matrix spanning at lower volume fractions, with the implication of observing novel phenomena at relatively dilute filler content. Subsequent geometric effects on significantly affecting DC and AC electrical conductivity, with respect to nonlinearity in the structure will also be considered. A significant new result is the observation of a power–law relation for the thermal conductivity, indicative of percolation, which contradicts earlier assertions and indicates that synthesis methodologies may be adapted to facilitate such behavior. Modeling of the experimentally determined electrical and thermal conductivity anisotropy, in addition to the incorporation of interfacial resistance, provides a better understanding of the underlying mechanisms and variations.


Polymer composites Carbon nanotubes Helical nanostructures Percolation Anisotropy Thermal conductivity Electrical conductivity Shielding efficiency 


  1. 1.
    Breuer O, Sundararaj U (2004) Big returns from small fibers: a review of polymer/carbon nanotube composites. Polym Compos 25:630–645CrossRefGoogle Scholar
  2. 2.
    Ajayan P, Schadler LS, Giannaris C, Rubio A (2000) Single-walled carbon nanotube-polymer composites: strength and weakness. Adv Mater 12:750–753CrossRefGoogle Scholar
  3. 3.
    Rashid ESA, Ariffin K, Akil HM, Kooi CC (2008) Mechanical and thermal properties of polymer composites for electronic packaging application. J Reinf Plast Compos 27:1573–1584CrossRefGoogle Scholar
  4. 4.
    Thomas S, Joseph K, Malhotra SK, Goda K, Sreekala MS (2013) Polymer composites. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  5. 5.
    Chung DDL (2001) Electromagnetic interference shielding effectiveness of carbon materials. Carbon N Y 39:279–285CrossRefGoogle Scholar
  6. 6.
    Ci L, Suhr J, Pushparaj V, Zhang X, Ajayan PM (2008) Continuous carbon nanotube reinforced composites. Nanoletters 8:2762–2766CrossRefGoogle Scholar
  7. 7.
    Li N, Huang Y, Du F, He X, Lin X, Gao H, Ma Y, Li F, Chen Y, Eklund PC (2006) Electromagnetic interference (EMI) shielding of single-walled carbon nanotube epoxy composites. Nanoletters 6:1141–1145CrossRefGoogle Scholar
  8. 8.
    Bigg DM, Stutz DE (1983) Plastic composites for electromagnetic interference shielding applications. Polym Compos 4:40–46CrossRefGoogle Scholar
  9. 9.
    Liu Z, Bai G, Huang Y, Ma Y, Du F, Li F, Guo T, Chen Y (2007) Reflection and absorption contributions to the electromagnetic interference shielding of single-walled carbon nanotube/polyurethane composites. Carbon N Y 45:821–827CrossRefGoogle Scholar
  10. 10.
    Liu Z, Bai G, Huang Y, Li F, Ma Y, Guo T, He X, Lin X, Gao H, Chen Y (2007) Microwave absorption of single-walled carbon nanotubes/soluble cross-linked polyurethane composites. J Phys Chem C 111:13696–13700CrossRefGoogle Scholar
  11. 11.
    Hoefer M, Bandaru PR (2009) Determination and enhancement of the capacitance contributions in carbon nanotube based electrode systems. Appl Phys Lett 95:183108CrossRefGoogle Scholar
  12. 12.
    Hughes M, Schwarz JA, Contescu CI, Putyera K (2004) Carbon nanotube-conducting polymer composites in supercapacitors. In: Dekker encyclopedia of nanoscience and nanotechnology. Taylor & Francis, London, pp 447–459Google Scholar
  13. 13.
    Halpin JC, Kardos JL (1976) The Halpin-Tsai equations: a review. Polym Eng Sci 16:344–352CrossRefGoogle Scholar
  14. 14.
    Bandaru PR (2007) Electrical properties and applications of carbon nanotube structures. J Nanosci Nanotechnol 7:1239–1267CrossRefGoogle Scholar
  15. 15.
    Peigney A, Laurent C, Flahaut E, Basca RR, Rousset A (2001) Specific surface area of carbon nanotubes and bundles of carbon nanotubes. Carbon N Y 39:507–514CrossRefGoogle Scholar
  16. 16.
    Ni C, Chattopadhyay J, Billups WE, Bandaru PR (2008) Modification of the electrical characteristics of single wall carbon nanotubes through selective functionalization. Appl Phys Lett 93:243113CrossRefGoogle Scholar
  17. 17.
    Berber S, Kwon Y-K, Tomanek D (2000) Unusually high thermal conductivity of carbon nanotubes. Phys Rev Lett 84:4613–4616CrossRefGoogle Scholar
  18. 18.
    Balberg I, Anderson CH, Alexander S, Wagner N (1984) Excluded volume and its relation to the onset of percolation. Phys Rev B 30:3933–3943CrossRefGoogle Scholar
  19. 19.
    Balberg I (1985) ‘Universal’ percolation-threshold limits in the continuum. Phys Rev B 31:4053–4055CrossRefGoogle Scholar
  20. 20.
    Pfeifer S, Park SH, Bandaru PR (2010) Analysis of electrical percolation thresholds in carbon nanotube networks using the Weibull probability distribution. J Appl Phys 108:24305CrossRefGoogle Scholar
  21. 21.
    Tasis D, Tagmatarchis N, Bianco A, Prato M (2006) Chemistry of carbon nanotubes. Chem Rev 106:1105–1136CrossRefGoogle Scholar
  22. 22.
    Antoniotti S, Antonczak S, Golebiowski J (2004) Acid-catalyzed oxidative ring-opening of epoxide by DMSO. Theoretical investigation of the effect of acid catalysts and substituents. Theor Chem Acc 112:290–297CrossRefGoogle Scholar
  23. 23.
    Park S-H, Theilmann P, Asbeck P, Bandaru PR (2010) Enhanced electromagnetic interference shielding through the use of functionalized carbon nanotube-reactive polymer composites. IEEE Trans Nanotechnol 9:464–469CrossRefGoogle Scholar
  24. 24.
    Bekyarova E, Thostenson ET, Yu A, Itkis ME, Fakhrutdinov D, Chou T-W, Haddon RC (2007) Functionalized single-walled carbon nanotubes for carbon fiber-epoxy composites. J Phys Chem C 111:17865–17871CrossRefGoogle Scholar
  25. 25.
    Nichols J, Deck CP, Saito H, Bandaru PR (2007) Artificial introduction of defects into vertically aligned multiwalled carbon nanotube ensembles: application to electrochemical sensors. J Appl Phys 102:64306CrossRefGoogle Scholar
  26. 26.
    Lin Y, Meziani MJ, Sun Y-P (2007) Functionalized carbon nanotubes for polymeric nanocomposites. J Mater Chem 17:1143–1148CrossRefGoogle Scholar
  27. 27.
    Haggenmueller R, Fischer JE, Winey KI (2006) Single wall carbon nanotube/polyethylene nanocomposites: nucleating and templating polyethylene crystallites. Macromolecules 39:2964–2971CrossRefGoogle Scholar
  28. 28.
    Bryning MB, Islam MF, Kikkawa JM, Yodh AG (2005) Very low conductivity threshold in bulk isotropic single-walled carbon nanotube-epoxy composites. Adv Mater 17:1186–1191CrossRefGoogle Scholar
  29. 29.
    Park S-H, Thielemann P, Asbeck P, Bandaru PR (2009) Enhanced dielectric constants and shielding effectiveness of, uniformly dispersed, functionalized carbon nanotube composites. Appl Phys Lett 94:243111CrossRefGoogle Scholar
  30. 30.
    Pfeifer S, Bandaru PR (2014) A methodology for quantitatively characterizing the dispersion of nanostructures in polymers and composites. Mater Res Lett, 2(3):166–175Google Scholar
  31. 31.
    Pozar DM (1998) Microwave engineering, 2nd edn. Wiley, New YorkGoogle Scholar
  32. 32.
    Engen GF, Hoer CA (1979) ‘Thru-reflect-line’: an improved technique for calibrating the dual six-port automatic network analyzer. IEEE Trans Microwave Theory Tech MTT-27:987–993CrossRefGoogle Scholar
  33. 33.
    Kim HM, Kim K, Lee CY, Joo J, Cho SJ, Yoon HS, Pejakovic DA, Yoo JW, Epstein AJ (2004) Electrical conductivity and electromagnetic interference shielding of multiwalled carbon nanotube composites containing Fe catalyst. Appl Phys Lett 84:589–591CrossRefGoogle Scholar
  34. 34.
    Cahill DG (1990) Thermal conductivity measurement from 30 to 750K: the 3w method. Rev Sci Instrum 61:802–808CrossRefGoogle Scholar
  35. 35.
    Kapadia RS, Louie BM, Bandaru PR (2013) The influence of carbon nanotube aspect ratio on thermal conductivity enhancement in nanotube–polymer composites. J Heat Transf 136(1):011303CrossRefGoogle Scholar
  36. 36.
    Carslaw HS, Jaeger JC (1986) Conduction of heat in solids, 2nd edn. Oxford University Press, New YorkGoogle Scholar
  37. 37.
    Borca-Tasciuc T, Kumar AR, Chen G (2001) Data reduction in 3w method for thin-film thermal conductivity determination. Rev Sci Instrum 72:2139–2147CrossRefGoogle Scholar
  38. 38.
    Kim B-W, Park S-H, Kapadia RS, Bandaru PR (2013) Evidence of percolation related power law behavior in the thermal conductivity of nanotube/polymer composites. Appl Phys Lett 102(24):243105CrossRefGoogle Scholar
  39. 39.
    Kirkpatrick S (1973) Percolation and conduction. Rev Mod Phys 45:574–588CrossRefGoogle Scholar
  40. 40.
    Celzard A, McRae E, Deleuze C, Dufort M, Furdin G, Mareche JF (1996) Critical concentration in percolating systems containing a high-aspect ratio filler. Phys Rev B 53:6209–6214CrossRefGoogle Scholar
  41. 41.
    Stauffer D, Aharony A (2003) Introduction to percolation theory, 2nd edn. Taylor and Francis, LondonGoogle Scholar
  42. 42.
    White SL, DiDonna BA, Mu M, Lubensky TC, Winey KL (2009) Simulations and electrical conductivity of percolated networks of finite rods with various degrees of axial alignment. Phys Rev B 79:24301CrossRefGoogle Scholar
  43. 43.
    Du F, Fischer JE, Winey KL (2005) Effects of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites. Phys Rev B 72:121404(R)CrossRefGoogle Scholar
  44. 44.
    Foygel M, Morris RD, Anez D, French S, Sobolev V (2005) Theoretical and computational studies of carbon nanotube composites and suspensions: electrical and thermal conductivity. Phys Rev B 71:104201CrossRefGoogle Scholar
  45. 45.
    Shklovskii BI, Efros AL (1984) Percolation theory. In: Electronic properties of doped semiconductors. Springer, New YorkGoogle Scholar
  46. 46.
    Straley JP (1977) Critical exponents for the conductivity of random resistor lattices. Phys Rev B 15:5733–5737CrossRefGoogle Scholar
  47. 47.
    Shenogina N, Shenogin S, Xue L, Keblinski P (2005) On the lack of thermal percolation in carbon nanotube composites. Appl Phys Lett 87:133106CrossRefGoogle Scholar
  48. 48.
    Landauer R (1978) Electrical conductivity in inhomogeneous media. AIP Conf Proc 40:2–45CrossRefGoogle Scholar
  49. 49.
    Huxtable ST, Cahill DG, Shenogin S, Xue L, Ozisik R, Barone P, Usrey M, Strano MS, Siddons G, Shim M, Keblinski P (2003) Interfacial heat flow in carbon nanotube suspensions. Nat Mater 2:731–734CrossRefGoogle Scholar
  50. 50.
    Biercuk MJ, Llaguno MC, Radosavljevic M, Hyun JK, Johnson AT, Fischer JE (2002) Carbon nanotube composites for thermal management. Appl Phys Lett 80:2767–2769CrossRefGoogle Scholar
  51. 51.
    Bonnet P, Sireude D, Garnier B, Chauvet O (2007) Thermal properties and percolation in carbon nanotube-polymer composites. Appl Phys Lett 91:201910CrossRefGoogle Scholar
  52. 52.
    Deng F, Zheng Q-S, Wang L-F, Nan C-W (2007) Effects of anisotropy, aspect ratio, and nonstraightness of carbon nanotubes on thermal conductivity of carbon nanotube composites. Appl Phys Lett 90:021914CrossRefGoogle Scholar
  53. 53.
    Swartz ET, Pohl RO (1989) Thermal boundary resistance. Rev Mod Phys 61:605–668CrossRefGoogle Scholar
  54. 54.
    Bandaru PR, Rao AM (2007) Electrical Applications for Novel Carbon Nanotube Morphologies: Does function follow shape? J Mater (Special Issue Nanomater Electron Appl) 7:33–38Google Scholar
  55. 55.
    Wang W, Yang K, Gaillard J, Bandaru PR, Rao AM (2008) Rational synthesis of helically coiled carbon nanowires and nanotubes through the use of tin and indium catalysts. Adv Mater 20(1):179–182CrossRefGoogle Scholar
  56. 56.
    Bandaru PR, Daraio C, Yang K, Rao AM (2007) A plausible mechanism for the evolution of helical forms in nanostructure growth. J Appl Phys 101:094307Google Scholar
  57. 57.
    Faraby HM, Rao AM, Bandaru PR (2013) Modeling high energy density electrical inductors operating at THz frequencies based on coiled carbon nanotubes. IEEE Electron Device Lett 34(6):807–809CrossRefGoogle Scholar
  58. 58.
    Daraio C, Nesterenko V, Jin S, Wang W, Rao AM (2006) Impact response by a foam like forest of coiled carbon nanotubes. J Appl Phys 100:64309CrossRefGoogle Scholar
  59. 59.
    Castrucci P, Scarselli M, De Crescenzi M, El Khakani MA, Rosei F, Braidy N, Yi J-H (2004) Effect of coiling on the electronic properties along single-wall carbon nanotubes. Appl Phys Lett 85:3857–3859CrossRefGoogle Scholar
  60. 60.
    Newnham RE (2005) Properties of materials. Oxford University Press, Oxford, UKGoogle Scholar
  61. 61.
    Landau L, Lifshitz EM, Pitaevskii LP (1995) Electrodynamics of continuous media, 2nd edn. Butterworth-Heinemann Ltd., BostoGoogle Scholar
  62. 62.
    Park SH, Theilmann P, Yang K, Rao AM, Bandaru PR (2010) The influence of coiled nanostructure on the enhancement of dielectric constants and electromagnetic shielding efficiency in polymer composites. Appl Phys Lett 96:43115CrossRefGoogle Scholar
  63. 63.
    Dumitrică T, Landis CM, Yakobson BI (2002) Curvature-induced polarization in carbon nanoshells. Chem Phys Lett 360:182–188CrossRefGoogle Scholar
  64. 64.
    Liu K, Roth S, Düsberg G, Kim GT, Popa D, Mukhopadhyay K, Doome R, Nagy JB (2000) Antilocalization in multiwalled carbon nanotubes. Phys Rev B 61:2375–2379CrossRefGoogle Scholar
  65. 65.
    Li Z, Mutlu M, Ozbay E (2013) Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission. J Opt 15(2):023001CrossRefGoogle Scholar
  66. 66.
    Lindell IV, Sihvola AH, Kurkijarvi J (1992) Karl F. Lindman: the last Hertzian, and a harbinger of electromagnetic chirality. IEEE Antennas Propag Mag 34(3):24–30CrossRefGoogle Scholar
  67. 67.
    Li Z, Alici KB, Colak E, Ozbay E (2011) Complementary chiral metamaterials with giant optical activity and negative refractive index. Appl Phys Lett 98(16):161907CrossRefGoogle Scholar
  68. 68.
    Bush V (1945) Science, the endless frontier. US Government Printing Office, Washington, DCGoogle Scholar
  69. 69.
    Torquato S (2006) Random heterogeneous materials. Springer Science, New YorkGoogle Scholar
  70. 70.
    Pendry JB, Holden AJ, Robbins DJ, Stewart WJ (1999) Magnetism from conductors, and enhanced non-linear phenomena. IEEE Trans Microwave Theory Tech 47:2075CrossRefGoogle Scholar
  71. 71.
    Vemuri KP, Bandaru PR (2013) Geometric considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials. Appl Phys Lett 103:133111CrossRefGoogle Scholar
  72. 72.
    Vemuri KP, Canbazoglu FM, Bandaru PR (2014) Guiding conductive heat flux through thermal metamaterials. Appl Phys Lett 105(19):193904CrossRefGoogle Scholar
  73. 73.
    Morrison RT, Boyd RN (1983) Organic chemistry. Allyn & Bacon, BostonGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Prabhakar R. Bandaru
    • 1
  • B.-W. Kim
    • 1
  • S. Pfeifer
    • 1
  • R. S. Kapadia
    • 1
  • S.-H. Park
    • 1
  1. 1.Program in Materials Science, Department of Mechanical and Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

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