Percolation in suspensions of hard nanoparticules: From Spheres to needles

We investigate geometric percolation and scaling relations in suspensions of nanorods, covering the entire range of aspect ratios from spheres to extremely slender needles. A new version of connectedness percolation theory is introduced and tested against specialised Monte Carlo simulations. The theory accurately predicts percolation threshold for aspect ratios of length to width as low as 10. The percolation threshold for rod-like particules of aspect ratios below 1000 deviates significantly from the inverse aspect ratio scaling prediction, thought to be valid in the limit of infinitely slender rods and often used as a rule of thumb for nanofibres in composites materials. Hence, most fibres that are currently used as fillers in composite materials cannot be regarded as pratically infinitely slender for the purposes of percolation theory. Comparing percolation thresholds of hard rods and new benchmark results for ideal rods, we find that i) for large aspect ratios, they differ by a factor that is inversely proportional to the connectivity distance between the hard cores, and ii) they approach the slender rod limit differently.