Modeling the dynamic percolation of carbon nanotubes and revisiting critical exponents

Abstract

In this paper, dynamic percolation of carbon nanotubes in silicone oil was probed by means of electrical measurements. Carbon nanotubes were first dispersed in silicone oils with ultrasounds. The obtained suspension was then slowly diluted. After each dilution, the changes in electrical properties was monitored over time. This procedure enabled to collect a large number volume fraction and define both the percolation threshold and the critical exponents with unmatched accuracy. The percolation threshold was found to decrease with time as a consequence of the already described aggregation of conductive nanoparticles. More surprisingly, the critical exponent also largely varied over time. This changes were correlated to the quality of the dispersion of carbon nanotubes within the host matrix. Finally, statistic percolation model was adapted into one that take into account for conductivity changes as a function of time and filler content.