Multiscale modeling of electrical conductivity of R-BAPB polyimide plus carbon nanotubes nanocomposites

The electrical conductivity of the polyimide R-BAPB polymer filled with single-wall carbon nanotubes (CNT) is modeled using a multiscale approach. The modeling starts with molecular dynamics simulations of time-dependent atomic configurations of polymer-filled CNTs junctions. Then the atomic positions obtained in the first step are used to perform fully first-principles microscopic calculations of the CNTs junctions contact resistances using the quantum transport technique based on Green's functions. Finally, those contact resistances are supplied as an input to a statistical calculation of a CNTs ensemble conductivity using a Monte Carlo percolation model. We discuss the effects of various geometrical peculiarities of CNTs mutual orientation, including an angle φ between nanotubes axes, a CNTs overlap, a separation between CNTs, as well as CNTs sizes, chiralities, CNTs functionalization on the contact resistance of CNTs junctions. The results of the first-principles calculations show that of all the considered geometrical peculiarities the angle dependence of CNTs intersections has the most significant influence on contact resistance of polymer-filled CNTs junctions. A simple fitting model, describing the dependence of a junction conductance of that angle, is proposed. Incorporating into the percolation model this strong dependence as well as CNTs agglomeration pushed the calculated values of electrical conductivity of the composite just above the percolation threshold below 0.01 S/m, which is within the experimental range for composites with various base polymers. Possible mechanisms for further reduction of composites conductivity are discussed.