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.

蒙特卡罗（MC）方法通常用于计算具有直线碳纳米管（CNT）的纳米复合材料的直流电导率，但很少使用弯曲碳纳米管计算与频率相关的交流电导率和介电特性。难点在于弯曲 CNT 的几何建模以及确定数千个 CNT 和每个 CNT 周围涂层表面上数千个随机点的电势。在本文中，基于随机三阶贝塞尔曲线建立了三维弯曲的碳纳米管网络。通过剔除方法计算曲线之间的距离，开发了MC方法来计算AC场下的复电导率。弯曲的碳纳米管根据最大曲率分为三组，并与直线碳纳米管进行比较。结果表明，随着贝塞尔曲线弯曲程度的增加，电导率和介电常数均显着降低，与直线形碳纳米管相比，渗流阈值可提高约20%。还评估了复合电导率的频率效应，发现还取决于 CNT 的直径、势垒高度和聚合物基体的复合电导率。还强调了该理论的其他几个新特征。