Statistical continuum theory for the effective conductivity of carbon nanotubes filled polymer composites

The effective thermal conductivity of polymer nanocomposites filled with carbon nanotubes (CNTs) is studied using statistical continuum theory. A three-dimensional isotropic nanocomposite samples with randomly oriented CNTs are computer generated and used to calculate the effective thermal conductivity. The CNTs orientation, shape and spatial distribution are taken into account through two-point and three-point probability functions. The effect of filler content is studied by considering samples with filler contents vary form 1 to 10 wt%. The predicted effective conductivity is compared to our experiment, where the polymer matrix is taken to be poly(methyl methacrylate) (PMMA) filled with multiwalled carbon nanotubes (MWCNTs). Relative to the pure poly(methyl methacrylate) both the modeling and the experiment show an increase of the thermal conductivity as function of the MWCNTs volume fraction. However, the predicted results overestimate the experimental data, which might due the CNTs agglomerations. Therefore, the predicted effective conductivities have been compared to experimental results in order to estimate the volume fraction of CNT agglomeration.