In this paper, we examined the effect of electron tunneling upon the electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. A CNT percolating network model was developed to account for the random distribution of the CNT network using Monte Carlo simulations, where the tunneling resistance between CNTs was established based on the electron transport theory. Our work shows several novel features that result from this tunneling resistance: (i) direct contact resistance is the result of one-dimensional electron ballistic tunneling between two adjacent CNTs, (ii) the nanoscale CNT-CNT contact resistance should be represented by the Landauer-Büttiker (L-B) formula, which accounts for both tunneling and direct contact resistances, and (iii) the difference in contact resistance between single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) can be modeled by the channel number in the L-B model. The model predictions reveal that the contact resistance due to electron tunneling effects in nanocomposites with dispersed SWCNTs plays a more dominant role than those with MWCNTs. These results compare favorably with existing experimental data and demonstrate that the proposed model can properly estimate the electrical conductivity of nanocomposites containing homogeneously dispersed percolating CNT network.

We have developed an improved three-dimensional (3D) percolation model to investigate the effect of the alignment of carbon nanotubes (CNTs) on the electrical conductivity of nanocomposites. In this model, both intrinsic and contact resistances are considered, and a new method of resistor network recognition that employs periodically connective paths is developed. This method leads to a reduction in the size effect of the representative cuboid in our Monte Carlo simulations. With this new technique, we were able to effectively analyze the effects of the CNT alignment upon the electrical conductivity of nanocomposites. Our model predicted that the peak value of the conductivity occurs for partially aligned rather than perfectly aligned CNTs. It has also identified the value of the peak and the corresponding alignment for different volume fractions of CNTs. Our model works well for both multi-wall CNTs (MWCNTs) and single-wall CNTs (SWCNTs), and the numerical results show a quantitative agreement with existing experimental observations.