Conductivity of a suspension of nanowires in a weakly conducting medium

TL;DR

This paper investigates how the electrical or thermal conductivity of a composite with nanowires in a poorly conducting medium varies across different regimes, revealing scaling laws and practical applications to DNA-protein diffusion.

Contribution

It introduces new scaling regimes for conductivity in nanowire suspensions, considering various ratios of conductivities, wire lengths, and volume fractions, expanding understanding of composite material behavior.

Findings

Macroscopic conductivity scales with the square root of wire and medium conductivities.

Multiple regimes identified depending on conductivity ratios and wire parameters.

Results applicable to diffusion of DNA-binding proteins in semidilute DNA solutions.

Abstract

We study macroscopic electrical or thermal conductivity of a composite made of straight or coiled nanowires suspended in poorly conducting medium. We assume that volume fraction of the wires is so large that spaces occupied by them overlap, but there is still enough room to distribute wires isotropically. We found a wealth of scaling regimes at different ratios of conductivities of the wire, $\sigma_1$ and of the medium, $\sigma_2$, length of wires, their persistent length and volume fraction. There are large ranges of parameters where macroscopic conductivity is proportional to $(\sigma_{1}\sigma_{2})^{1/2}$. These results are directly applicable to the calculation of the macroscopic diffusion constant of the nonspecific DNA-binding proteins in semidilute DNA solution.