Simplification and development of McLachlan model for electrical conductivity of polymer carbon nanotubes nanocomposites assuming the networking of interphase regions

This paper simplifies and develops the conventional model suggested by McLachlan for electrical conductivity of polymer CNT nanocomposites. The original model expresses the conductivity as a function of filler concentration, filler conductivity, filler percolation threshold and an exponent. However, this model is developed by considering the roles of interfacial tension between polymer matrix and nanoparticles, tunneling distance between adjacent nanotubes, interphase regions around nanoparticles and waviness of CNT. The experimental results of conductivity for some samples and the analysis of the effects of various parameters on the conductivity evaluate the developed model. The predictions demonstrate fine agreement with the experimental results and the parameters show acceptable roles in the conductivity of nanocomposites. A large tunneling distance significantly decreases the conductivity to zero. Likewise, the higher and slighter surface energies of the polymer matrix and filler, respectively cause an improved conductivity. A thin interphase produces very low conductivity, while a thick interphase and a low waviness improve the conductivity.