This study provides a multi-step analytical model to investigate the synergistic effects of carbon black nanoparticles and micro-scale carbon fibers on the electrical conductivity of the polymer matrix multi-scale nanocomposites. In the first step, the homogenized electrical conductivity of the nanoparticle-polymer nanocomposites containing the nanoparticle agglomeration is calculated using the percolation like electrical network model. The second step presents the details of Mori-Tanaka micromechanical model to predict the effective electrical conductivity of the multi-scale nanocomposites composed of the micro-fibers embedded in the nanoparticle-enriched polymer as the matrix phase. The influences of different parameters such as the nanoparticle agglomerate diameter to tunneling distance ratio, fiber aspect ratio, intrinsic electrical conductivity, volume fraction, and polymer potential barrier height on the electrical resistivity of the multi-scale nanocomposites are investigated. Based on the comparative studies, the model predictions are in good agreement with the available experimental results. It is found that the electrical resistivity decreases with the addition of multi-scale fillers. The results also suggest that the tunneling distance between the agglomerates plays a dominant role in the electrical conductivity of the multi-scale nanocomposites.

这项研究提供了一个多步骤的分析模型，以研究炭黑纳米颗粒和微米级碳纤维对聚合物基质多级纳米复合材料电导率的协同作用。在第一步中，使用类似渗流的电网络模型计算包含纳米颗粒团聚的纳米颗粒-聚合物纳米复合材料的均质电导率。第二步介绍了Mori-Tanaka微力学模型的细节，以预测由嵌入纳米颗粒富集的聚合物中的微纤维作为基质相的多尺度纳米复合材料的有效电导率。不同参数的影响，例如纳米颗粒的团聚体直径与隧穿距离比，纤维长径比，研究了多尺度纳米复合材料的固有电导率，体积分数和聚合物势垒高度对电阻率的影响。根据比较研究，模型预测与可用的实验结果非常吻合。发现随着多尺度填料的加入，电阻率降低。结果还表明，附聚物之间的隧穿距离在多尺度纳米复合材料的电导率中起主要作用。发现随着多尺度填料的加入，电阻率降低。结果还表明，附聚物之间的隧穿距离在多尺度纳米复合材料的电导率中起主要作用。发现随着多尺度填料的加入，电阻率降低。结果还表明，附聚物之间的隧穿距离在多尺度纳米复合材料的电导率中起主要作用。