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.

In this study, a multiscale method for solving a thermoelasticity problem for interphase in the polymeric nanocomposites is developed. Molecular dynamics simulation and finite element analysis were numerically combined to describe the geometrical boundaries and the local mechanical response of the interfacial region where the polymer networks were highly interacted with the nanoparticle surface. Also, the micrmechanical thermoelasticity equations were applied to the obtained equivalent continuum unit to compute the growth of interphase thickness according to the size of nanoparticles, as well as the thermal phase transition behavior at a wide range of temperatures. Accordingly, the equivalent continuum model obtained from the multiscale analysis provides a meaningful description of the thermoelastic behavior of interphase as well as its nanoparticle size effect on thermoelasticity at both below and above the glass transition temperature.