A theoretical model for double percolation in hybrid polymer nanocomposites reinforced with carbon nanotubes and aramid nanofibers

Abstract

A theoretical model of double percolation in hybrid polymer nanocomposites reinforced with carbon nanotubes (CNTs) and aramid nanofibers (ANFs) is proposed. The model is based on the excluded-volume concept and a mean-field description of network connectivity. An analytical expression describing the effective connectivity of the hybrid system was derived by considering CNT–CNT, ANF–ANF, and CNT–ANF interactions. The proposed approach demonstrates that the formation of a continuous transport network is governed not only by the individual percolation behavior of each filler type, but also by hybrid interactions between dissimilar nanostructures. The model predicts that ANFs can promote network formation at reduced CNT concentrations through the development of hybrid CNT–ANF contacts. Theoretical concentration maps, scaling dependences, and parametric analyses were constructed to investigate the influence of filler composition and hybrid interaction probability on network connectivity. The obtained results provide a theoretical framework for describing double-percolation phenomena and transport network formation in hybrid polymer nanocomposites.