In this paper, an analytical model is developed for electrical conductivity of nanocomposites, particularly polymer/carbon nanotubes nanocomposites. This model considers the effects of aspect ratio, concentration, waviness, conductivity and percolation threshold of nanoparticles, interphase thickness, wettability between polymer and filler, tunneling distance between nanoparticles and network fraction on the conductivity. The developed model is confirmed by experimental results and parametric studies. The calculations show good agreement with the experimental data of different samples. The concentration and aspect ratio of nanoparticles directly control the conductivity. Moreover, a smaller distance between nanoparticles increases the conductivity based on the tunneling mechanism. A thick interphase also causes an increased conductivity, because the interphase regions participate in the networks and enhance the effectiveness of nanoparticles.

Cross model correlates the dynamic complex viscosity of polymer systems to zero complex viscosity, relaxation time and power-law index. However, this model disregards the growth of complex viscosity in nanocomposites containing filler networks, especially at low frequencies. The current paper develops the Cross model for complex viscosity of nanocomposites by yield stress as a function of the strength and density of networks. The predictions of the developed model are compared to the experimental results of fabricated samples containing poly(lactic acid), poly(ethylene oxide) and carbon nanotubes. The model’s parameters are calculated for the prepared samples, and their variations are explained. Additionally, the significances of all parameters on the complex viscosity are justified to approve the developed model. The developed model successfully estimates the complex viscosity, and the model’s parameters reasonably change for the samples. The stress at transition region between Newtonian and power-law behavior and the power-law index directly affects the complex viscosity. Moreover, the strength and density of networks positively control the yield stress and the complex viscosity of nanocomposites. The developed model can help to optimize the parameters controlling the complex viscosity in polymer nanocomposites.