In this work, the depth of the interphase in graphene polymer systems is determined by the properties of graphene and interfacial parameters. Furthermore, the actual volume fraction and percolation onset of the nanosheets are characterized by the actual inverse aspect ratio, interphase depth, and tunneling distance. In addition, the dimensions of graphene, along with interfacial/interphase properties and tunneling characteristics, are utilized to develop the power-law equation for the conductivity of graphene-filled composites. Using the derived equations, the interphase depth, percolation onset, and nanocomposite conductivity are graphed against various ranges of the aforementioned factors. Moreover, numerous experimental data points for percolation onset and conductivity are presented to validate the equations. The optimal levels for interphase depth, percolation onset, and conductivity are achieved through high interfacial conductivity and large graphene nanosheets. In addition, increased nanocomposite conductivity can be attained with thinner nanosheets, a larger tunneling distance, and a thicker interphase. The calculations highlight the considerable impacts of interfacial/interphase factors and tunneling distance on the percolation onset. The highest nanocomposite conductivity of 0.008 S/m is acquired by the highest interfacial conduction of 900 S/m and graphene length (D) of 5 μm, while an insulated sample is observed at D < 1.2 μm. Therefore, higher interfacial conduction and larger nanosheets cause the higher nanocomposite conductivity, but the short nanosheets cannot promote the conductivity.

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.