Predicting effective electrical resistivity and conductivity of carbon nanotube/carbon black-filled polymer matrix hybrid nanocomposites

A two-step analytical model based on a percolation network model and electron tunneling theory has been developed to predict the electrical resistivity and percolation threshold of a hybrid nanocomposite system comprising carbon black (CB) and carbon nanotube (CNT). The nanostructure of a tunneling network consisting of CNT and CB agglomerates has been generated to study the effects of various parameters on electrical conductivity. Electron tunneling is the primary mechanism for electrical percolation, which is incorporated into the model by considering the effective tunneling distance of CNTs. Later, a percolation network model is introduced to evaluate the electrical properties of the hybrid nanocomposite. Our results indicate that a high level of alignment leads to a significant decrease of the percolation threshold with an increase in conductivity, while a low CB volume fraction with low intrinsic electrical conductivity degrades the percolation and overall conductivity. Our results also reveal that the addition of CB as a second filler in a hybrid nanocomposite leads to improvements in conductance and percolation threshold. Analytical results show that the current model agrees well with existing experimental data, which reveals that tunneling and percolation are the dominant mechanisms for transition behavior in electrical conductivity. • The electrical resistivity behavior of a hybrid nanocomposite has been modeled. • A greater improvement in conductance is achieved by the incorporation of hybrid CB/CNT filler. • Aspect ratio, maximum orientation angle, and agglomerate size are effective factors. • Large CB agglomerate surface area facilitates the establishment of percolation paths. • Model predictions agree well with experimental data.