Percolation in suspensions of hard nanoparticles: From spheres to needles

Abstract

We investigate geometric percolation and scaling relations in suspensions of\nnanorods, covering the entire range of aspect ratios from spheres to extremely\nslender needles. A new version of connectedness percolation theory is\nintroduced and tested against specialized Monte Carlo simulations. The theory\naccurately predicts percolation thresholds for aspect ratios as low as 10. The\npercolation threshold for rod-like particles of aspect ratios below 1000\ndeviates significantly from the inverse aspect ratio scaling prediction,\nthought to be valid in the limit of infinitely slender rods and often used as a\nrule of thumb for nano-fibers in composite materials. Hence, most fibers that\nare currently used as fillers in composite materials cannot be regarded as\npractically infinitely slender for the purposes of percolation theory.\nComparing percolation thresholds of hard rods and new benchmark results for\nideal rods, we find that (i) for large aspect ratios, they differ by a factor\nthat is inversely proportional to the connectivity distance between the hard\ncores, and (ii) they approach the slender rod limit differently.\n