  The electrical conductivity of the polyimide R-BAPB polymer filled with
single-wall carbon nanotubes (CNT) with chirality (5,5) is modeled using a
multi-scale approach. The modeling starts with molecular dynamics simulations
of time-dependent fluctuating 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 Green's function based quantum transport
technique. And finally, those contact resistances are supplied as an input to a
statistical calculation of a CNTs ensemble conductivity using a Monte Carlo
percolation model. The results of the first-principles calculations show a very
strong dependence of the polymer filled CNTs junctions contact resistance on
the geometry of CNTs junctions, including an angle $\varphi$ between nanotubes
axes and the positions of polymer atoms around CNTs. Incorporating into the
percolation model this strong dependence as well as CNTs agglomeration, pushed
the calculated values of electrical conductivity 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.
