Network-Based Assessments of Percolation-Induced Current Distributions in Sheared Rod Macromolecular Dispersions

Conducting high-aspect-ratio rods with 1--10 nm-scale diameters dispersed in poorly conducting matrices at extremely low, $O(1\%)$, volume fractions induce dramatic gains in bulk conductivity at rod percolation threshold. Experimentally [Nan, Shen, and Ma, Annu. Rev. Mater. Res., 40 (2010), pp. 131--151], bulk conductivity abandons the prepercolation, linear scaling with volume fraction that follows from homogenization theory [Zheng et al., Adv. Funct. Mater., 15 (2005), pp. 627--638], and then postpercolation jumps orders of magnitude to approach that of the pure rod macromolecular phase as predicted by classical percolation theory [Stauffer and Aharony, Introduction to Percolation Theory, CRC Press, Boca Raton, FL, 1994]. Our aim here is to use the orientational probability distribution functions from kinetic Brownian rod dispersion flow codes [Forest, Wang, and Zhou, Rheol. Acta, 44 (2004), pp. 80--93] to generate physical three-dimensional (3D) nanorod dispersions, followed by graph-theoretic algorith...