Feng "Bill" Shi, University of North Carolina at Chapel Hill


Network Analysis for Electrical Properties of Sheared Nanorod Dispersions

Abstract: The first goal of this paper is to build a tight connection between two previously disjoint subjects: on one hand, complex networks, their graph representations, and graph analysis, and on the other hand, electrical properties of composite materials consisting of conducting rods or fibers dispersed in a poorly conducting matrix with at least one percolating path in the particle phase. This connection yields a new network analysis tool for experimental or numerical databases of a 3D rod or fiber dispersion. The novel application is for flow generated nano-rod and nano-fiber composites where particle number density overwhelms existing software and non-equilibrium, anisotropic distributions violate assumptions based on percolation threshold scaling behavior. When the rod phase is non-percolating, alternative and efficient tools already exist: homogenization theory yields the effective conductivity of the matrix, whereas more detailed information can be gleaned from graph theoretic methods. The second goal of this paper is to apply this network analysis tool to the dimensional percolation phase diagram of sheared nano-rod dispersions [Zheng et al.]. The result is a statistical description of electrical properties appropriate to and consistent with statistical mechanics of nano-rod ensembles. The network analysis yields averaged conductance as well as local current and voltage distributions within the rod phase per realization.

Collaborators: M. Gregory Forest, Peter Mucha, Simi Wang, Xiaoyu Zheng, Ruhai Zhou.