Simplified Calculation of the Electrical Conductivity of Composites with Carbon Nanotubes

The electrical conductivity of two groups of polymer nanocomposites filled with the same NC7000 carbon nanotubes (CNTs) beyond the percolation threshold is described with the help of simple formulas. Different manufacturing process of the nanocomposites led to different CNT network structures, and, as a consequence, their electrical conductivity, at the same CNT volume, differed by two orders of magnitude. The relation between the electrical conductivity and the volume content of CNTs of the first group of composites (with a higher electrical conductivity) is described assuming that the CNT network structure is close to a statistically homogeneous one. The formula for this case, derived on the basis of a self-consistent model, includes only two parameters: the effective longitudinal electrical conductivity of CNT and the percolation threshold (the critical value of CNT volume content). These parameters were determined from two experimental points of electrical conductivity as a function of the volume fraction of CNTs. The second group of nanocomposites had a pronounced agglomerative structure, which was confirmed by microscopy data. To describe the low electrical conductivity of this group of nanocomposites, a formula based on known models of micromechanics is proposed. Two parameters of this formula were determined from experimental data of the first group, but the other two — of the second group of nanocomposites. A comparison of calculation and experimental relations confirmed the practical expediency of using the approach described.