A Micromechanics Model for the Electrical Conductivity of Nanotube-Polymer Nanocomposites

The introduction of carbon nanotubes (CNTs) into nonconducting polymers has been observed to yield orders of magnitude increases in conductivity at very low concentrations of CNTs. These low percolation concentrations have been attributed to both the formation of conductive networks of CNTs within the polymer and to a nanoscale effect associated with the ability of electrons to transfer from one CNT to another known as electron hopping. In the present work, a micromechanics model is developed to assess the impact of the effects of electron hopping and the formation of conductive networks on the electrical conductivity of CNT-polymer nanocomposites. The micromechanics model uses the composite cylinders model as a nanoscale representative volume element where the effects of electron hopping are introduced in the form of a continuum interphase layer, resulting in a distinct percolation concentration associated with electron hopping. Changes in the aspect ratio of the nanoscale representative volume element are used to reflect the changes in nanocomposite conductivity associated with the formation of conductive networks due to the formation of nanotube bundles. The model results are compared with experimental data in the literature for both single- and multi-walled CNT nanocomposites where it is observed that the model developed is able to qualitatively explain the relative impact of electron hopping and nanotube bundling on the nanocomposite conductivity and percolation concentrations.

[1]  Hatta Hiroshi,et al.  Equivalent inclusion method for steady state heat conduction in composites , 1986 .

[2]  Hui-Ming Cheng,et al.  Mechanical and electrical properties of a MWNT/epoxy composite , 2002 .

[3]  Linda S. Schadler,et al.  LOAD TRANSFER IN CARBON NANOTUBE EPOXY COMPOSITES , 1998 .

[4]  Thermal Conductivity of Single-Walled Carbon Nanotube/PMMA Nanocomposites , 2007 .

[5]  Daniel C. Hammerand,et al.  Computational Micromechanics of Clustering and Interphase Effects in Carbon Nanotube Composites , 2007 .

[6]  C. Friedrich,et al.  Mechanical properties and electrical conductivity of carbon-nanotube filled polyamide-6 and its blends with acrylonitrile/butadiene/styrene , 2004 .

[7]  D. Lagoudas,et al.  A Micromechanics Model for the Thermal Conductivity of Nanotube-Polymer Nanocomposites , 2008 .

[8]  T. Miloh,et al.  On the effective thermal conductivity of coated short‐fiber composites , 1991 .

[9]  H. Lezec,et al.  Electrical conductivity of individual carbon nanotubes , 1996, Nature.

[10]  G. Seidel.  Micromechanics modeling of the multifunctional nature of carbon nanotube-polymer nanocomposites , 2007 .

[11]  J. Coleman,et al.  Charge transport effects in field emission from carbon nanotube-polymer composites , 2005 .

[12]  Guangjun Hu,et al.  Low percolation thresholds of electrical conductivity and rheology in poly(ethylene terephthalate) through the networks of multi-walled carbon nanotubes , 2006 .

[13]  J. Fischer,et al.  Effect of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites , 2005 .

[14]  Elizabeth C. Dickey,et al.  Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites , 2000 .

[15]  Petra Pötschke,et al.  Carbon nanotube-filled polycarbonate composites produced by melt mixing and their use in blends with polyethylene , 2004 .

[16]  G. Odegard,et al.  Effect of Nanotube Functionalization on the Elastic Properties of Polyethylene Nanotube Composites , 2005 .

[17]  A. Zettl,et al.  Thermal conductivity of single-walled carbon nanotubes , 1998 .

[18]  Zvi Hashin,et al.  Thermoelastic properties and conductivity of carbon/carbon fiber composites , 1990 .

[19]  Karen Lozano,et al.  Reinforcing Epoxy Polymer Composites Through Covalent Integration of Functionalized Nanotubes , 2004 .

[20]  D. Carroll,et al.  Dynamic electrical properties of polymer-carbon nanotube composites: Enhancement through covalent bonding , 2006 .

[21]  Jiang Zhu,et al.  Improving the Dispersion and Integration of Single-Walled Carbon Nanotubes in Epoxy Composites through Functionalization , 2003 .

[22]  Yunsheng Xu,et al.  Thermal behavior of single-walled carbon nanotube polymer–matrix composites , 2006 .

[23]  Zvi Hashin,et al.  Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites , 1968 .

[24]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[25]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[26]  Martin L. Dunn,et al.  Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites , 1993 .

[27]  Riichiro Saito,et al.  Electronic structure of chiral graphene tubules , 1992 .

[28]  Christian A. Martin,et al.  Formation of percolating networks in multi-wall carbon-nanotube–epoxy composites , 2004 .

[29]  Dimitris C. Lagoudas,et al.  Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites , 2006 .

[30]  Takashi Kashiwagi,et al.  An infiltration method for preparing single-wall nanotube/epoxy composites with improved thermal conductivity , 2006 .

[31]  Wei Zhou,et al.  Nanotube Networks in Polymer Nanocomposites: Rheology and Electrical Conductivity , 2004 .

[32]  Y. M. Wang,et al.  Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes , 2006, Microscopy and Microanalysis.

[33]  C. Nan.  Effective‐medium theory of piezoelectric composites , 1994 .

[34]  Yang Wang,et al.  Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes , 2002, Microscopy and Microanalysis.

[35]  P. T. Lillehei,et al.  AC and DC percolative conductivity of single wall carbon nanotube polymer composites , 2005 .

[36]  Dimitris C. Lagoudas,et al.  Modeling porous shape memory alloys using micromechanical averaging techniques , 2002 .

[37]  I. Kinloch,et al.  Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites , 2003 .

[38]  E. Siochi,et al.  Electrical properties of single wall carbon nanotube reinforced polyimide composites , 2003 .

[39]  H. Garmestani,et al.  Enhancement of thermal and electrical properties of carbon nanotube polymer composites by magnetic field processing , 2003 .

[40]  C. Nan,et al.  Effective thermal conductivity of particulate composites with interfacial thermal resistance , 1997 .

[41]  Minoru Taya,et al.  Effective thermal conductivity of a misoriented short fiber composite , 1985 .

[42]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[43]  V. Sobolev,et al.  Theoretical and computational studies of carbon nanotube composites and suspensions : Electrical and thermal conductivity , 2005 .

[44]  P. Avouris,et al.  Mechanical Properties of Carbon Nanotubes , 2001 .

[45]  Darren J. Martin,et al.  Polyethylene multiwalled carbon nanotube composites , 2005 .

[46]  Gregory M. Odegard,et al.  Constitutive Modeling of Nanotube-Reinforced Polymer Composites , 2002 .

[47]  N. Marzari,et al.  Textural and Micromorphological Effects on the Overall Elastic Response of Macroscopically Anisotropic Composites , 1992 .

[48]  Bodo Fiedler,et al.  Evaluation and identification of electrical and thermal conduction mechanisms in carbon nanotube/epoxy composites , 2006 .

[49]  Milo S. P. Shaffer,et al.  Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties , 1999 .