Percolation in metal-insulator composites of randomly packed spherocylindrical nanoparticles

While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite system of disordered spherocylinders, to identify the relation between structural (percolation) and functional properties of nanocomposites. Experimentally, we determine the percolation threshold $p_c$ and the conductivity critical exponent $t$ for composites of conducting (CrO$_2$) and insulating (Cr$_2$O$_3$) rodlike nanoparticles that are nominally geometrically identical, yielding $p_c=0.305 \pm 0.026$ and $t=2.52 \pm 0.03$ respectively. Simulations and modeling are implemented through a combination of the mechanical contraction method and a variant of random walk (de Gennes ant) approach, in which charge diffusion is correlated with the system conductivity via the Nernst-Einstein relation. The percolation threshold and critical exponents identified through finite size scaling are in good agreement with the experimental values. Curiously, the calculated percolation threshold for spherocylinders with an aspect ratio of 6.5, $p_c=0.312 \pm 0.002$, is very close (within numerical errors) to the one found previously in two other distinct systems of disordered jammed spheres and simple cubic lattice, an intriguing and surprising result.