A Monte Carlo model with equipotential approximation and tunneling resistance for the electrical conductivity of carbon nanotube polymer composites

Abstract

A Monte Carlo model with equipotential approximation and tunneling resistance is developed to predict the percolation threshold and electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. We first establish a random CNT network, and then calculate their intrinsic and contact conductance. To provide a pathway for the current to flow from CNT to polymer, a thin coated surface (CS) is introduced. The CNTs, CS, and the two electrodes then constitute the three major components of the conduction process. To solve this problem, we develop the method of equipotential approximation to determine the electrical potentials of CNTs and CS, and further determine their coefficient matrix by the walk-on-spheres method. In this way the electrical properties of CNT nanocomposites, both before and after percolation, are predicted. It is demonstrated that the developed theory compares well with three sets of experimental data for the electrical conductivity and several sets of data for the percolation threshold. The effects of barrier heights, polymer conductivity, aspect ratio, diameter (and chirality) of CNTs are also investigated. This equipotential approximation possesses the distinct features that it can break through the limits of ellipsoidal fillers and properly estimate the electrical conductivity with any shape, orientation and distribution of fillers.