Evaluation of the structural state of carbon nanotubes in the polymer matrix of nanocomposites

Abstract

By virtue of high degree of anisotropy and small transverse stiffness, carbon nanotubes are known to form ring-shaped annular structures (fractal objects) in the polymer matrix of nanocomposites. We used the fractal dimension for quantitative and physically strict characterization of the nanofiller structure (carbon nanotubes) in the polymer matrix of nanocomposites. Two methods of calculation based on the models of irreversible aggregation and fractal analysis are proposed. The results obtained using both approaches match each other within 6%. It has been shown that formation of the annular structures occurs according to the cluster-cluster mechanism (i.e., by combining small formations into larger ones, rather than individual nanotubes). Moreover, the method of fractal analysis takes into account the effect of the polymer matrix on the structure of ring-shaped formations and, hence, on the properties of polymer nanocomposites. The correctness of the methods thus used was proved using the percolation model, which showed good agreement between the theory and experiment when using fractal dimensions determined by both methods. This means that for a fixed nanofiller content, the properties of nanocomposites are determined only by the nanofiller structure. In other words, a significant change in the properties (for the degree of reinforcement more than by an order of magnitude) is possible even at a low content of a nanofiller, which is realized only through change in the nanofiller structure using various methods of nanofiller treatment (ultrasound, functionalization, construction of special types of nanofiller frame, etc.).