Theoretical and computational studies of carbon nanotube composites and suspensions: Electrical and thermal conductivity

TLDR

Monte Carlo simulations of randomly oriented, high‑aspect‑ratio capped nanotubes treated as conductive cylinders were used to determine the critical fractional volume for percolation and to calculate percolation critical indices such as the conductivity exponent t. The simulations show that the critical fractional volume scales inversely with aspect ratio, enabling percolation at loadings as low as 0.01 %, that the conductivity exponent t decreases with increasing aspect ratio, and that the predicted thermal and electrical conductivities match experimental data.

Abstract

Monte Carlo simulations have been performed, aimed at finding a critical fractional volume (CFV) associated with the onset of percolation for randomly oriented nanotubes (or, indeed, any conductive particles with large aspect ratios) that are randomly dispersed in a low thermo- or electroconductive medium. The nanotubes were treated as capped interpenetrating conductive cylinders (``sticks'') with high (up to 2000) aspect ratio $a$. It has been found that for these aspect ratios the CFV is inversely proportional to $a$ resulting in surprisingly low filler volume loadings, of the order of 0.01%, required to achieve percolation in such systems. By studying fluctuations of the CFV and the density of the percolation clusters, various critical indices of the percolation theory have been calculated including the critical index of conductivity, $t$. For three-dimensional systems it has been found that $t$ decreases substantially with an increase in the aspect ratio. The calculated thermal and electrical conductivity of the nanotube suspensions and composites as functions of the nanotube loading is in good agreement with recent experimental data.