Advanced predicting of conductivity for carbon nanofiber polymer systems: Incorporating of nanofiber, interphase, and tunneling impacts

In the current paper, important factors and simple equations are used to simplify and develop the Jang-Yin model for the conductivity prediction in polymeric samples consisting of carbon nanofiber (CNF) named as PCNFs. R_eff as the effective resistance of filler and the tunneling zone in the original model, is developed and formulated by considering the resistances of CNF, interphase, and tunnel. Additionally, the percolation onset and network percentage are formulated by the dimensions of both CNF and interphase. The developed model's predictions are evaluated by the measured conductivity of various examples. Besides, the factors’ impacts on the PCNF conductivity are described to validate the developed methodology. It is revealed that the resistances of the tunnel and interphase are much higher than the CNF resistance. Therefore, R_eff only considers the interphase and tunnel resistances. The calculations of the proposed model display good harmony with the measured data of many examples. The lowest values of CNF amount, network percentage, interphase depth, and contact diameter cannot increase the system conductivity. Nevertheless, the supreme conductivity of 3.38 S/m is reached at the lowest tunneling resistivity of 50 Ω·m and the highest contact diameter of 40 nm.