A physics-based hierarchical modeling approach considering tunneling resistance through polymer is proposed to predict the percolation threshold and resistivity of carbon nanotube (CNT)/graphene nanoplatelet (GNP)-reinforced polymer hybrid nanocomposites. At first, a method is developed to calculate the resistivity of CNT-polymer nanocomposites. Then, percolation theory model is employed to calculate the percolation threshold of CNT-reinforced nanocomposites. At the end, an analytical model is presented for estimating the resistivity of CNT/GNP hybrid nanocomposites. The effects of barrier height, nanofiller aspect ratio and tunneling distance on the percolation threshold and resistivity of hybrid nanocomposites are extensively investigated. The results show that the percolation threshold depends on many factors such as aspect ratio, electrical conductivity and volume fraction of nanofillers. It is clearly shown that the smaller GNP aspect ratio leads to an increase in percolation threshold and electrical resistivity. The results also indicate the dominant role of nanofiller volume fraction at low tunneling distance. The model results are compared with experimental data in the literature for GNP/CNT hybrid nanocomposites where it is demonstrated that the represented model is able to explain the impact of electrical tunneling on the resistivity of polymer nanocomposites.

提出了一种考虑通过聚合物的隧道电阻的基于物理的分层建模方法，以预测碳纳米管 (CNT)/石墨烯纳米片 (GNP) 增强的聚合物混合纳米复合材料的渗透阈值和电阻率。首先，开发了一种计算CNT-聚合物纳米复合材料电阻率的方法。然后，采用渗流理论模型计算碳纳米管增强纳米复合材料的渗流阈值。最后，提出了一个分析模型，用于估计 CNT/GNP 混合纳米复合材料的电阻率。广泛研究了势垒高度、纳米填料纵横比和隧道距离对混合纳米复合材料的渗透阈值和电阻率的影响。结果表明，渗透阈值取决于纵横比、纳米填料的电导率和体积分数。清楚地表明，较小的 GNP 纵横比导致渗透阈值和电阻率的增加。结果还表明纳米填料体积分数在低隧穿距离下的主导作用。将模型结果与 GNP/CNT 混合纳米复合材料的文献中的实验数据进行比较，其中证明所代表的模型能够解释电隧道效应对聚合物纳米复合材料电阻率的影响。