Modelling the Effects of Carbon Nanotube Length Non-Uniformity and Waviness on the Electrical Behavior of Polymer Composites

Carbon nanotube (CNT) length non-uniformity and waviness exist inevitably in practical CNT/polymer composites (CPCs) and are two major factors that have significant influences on the composite electrical behavior. However, these two factors have been rarely considered simultaneously in previous modellings. In this study, a numerical model is presented to predict the electrical behavior of CPCs by simultaneously taking into account the two factors besides other ones considered in existing modellings. The length non-uniformity of CNTs is represented by the Weibull distribution and each wavy CNT is modeled by a piecewise sequence of several line segments. Besides, the tunneling distance is reasonably defined to calculate the tunneling resistance between adjacent CNTs. The prediction results reveal that both the CNT length non-uniformity and waviness have significant effects on the electrical behavior of CPCs. It is shown that the percolation threshold evidently decreases with either increasing the CNT length non-uniformity or decreasing the CNT waviness degree. Furthermore, the predictions agree well with existing experimental data, indicating the validity of the present numerical model in predicting the electrical conductivity of CPCs. In particular, it should be emphasized that compared with the previous models without simultaneously considering the effects of these two factors, the present model provides better predictions of the electrical behavior of CPCs.