A highly efficient numerical method to investigate the conductivity of CNT/polymer composite

Abstract

Compared to conventional electronic composites, polymer nanocomposites containing carbon nanotubes (CNT) have superior electrical properties. In the research, a highly efficient numerical method used to calculate the resistivity of the CNT/polymer composite is presented based on an integrated three-dimensional (3D) statistical resistor network model (RNM) which incorporates the tunneling effect between neighboring nanotubes. By this 3D RNM, the electrical properties of a composite brick in which a certain number of CNT are distributed randomly can be calculated. However, to guarantee the convergence of calculation, the number of CNTs must be larger than a threshold, and this may cause the calculation to be very time-consuming. In order to improve the computational efficiency, a modified calculation scheme using coarse-net model (CNM) is proposed. According to the scheme, a composite brick containing a large number of CNTs is divided into an array of cells, each of which has a limited volume and contains a small number of CNTs. These cells are assumed to be connected in a 3D network whereby each cell is considered as a resistor and its resistance can be calculated by the original integrated 3D model efficiently. Statistically, the effective resistance of such a resistor network that can be evaluated by Kirchhoff’s current law is the same as the resistance of the composite brick. The comparison between the conventional RNM and the CNM proves that the latter can improve the computational efficiency tremendously.