Monte Carlo method with Bézier curves for the complex conductivity of curved CNT-polymer nanocomposites

Abstract

Monte Carlo (MC) method is often adopted to calculate the DC conductivity of nanocomposites with straight-line carbon nanotubes (CNT), but calculations for the frequency-dependent AC conductivity and dielectric properties with curved CNTs are rare. The difficulties lie in the geometrical modeling of curved CNTs and the determination of electric potentials for thousands of CNTs and thousands of random points on the coated surface around each CNT. In this paper, a three-dimensional curved CNT network is established based on random third-order Bézier curves. By calculating the distance between the curves through a culling approach, the MC method is developed to calculate the complex conductivity under an AC field. Curved CNTs were divided into three groups according to the maximum curvature and compared with straight-line CNTs. The results show that both conductivity and dielectric constant can notably decrease with the bending degree of Bézier curves, and the percolation threshold can increase by about 20% as compared to that with straight-line CNTs. The frequency effects of complex conductivity are also assessed, and found to depend on the diameter of CNTs, barrier height, and the complex conductivity of polymer matrix as well. Several other new features of the theory are also highlighted.