DC and AC Conductivity of Carbon Nanotubes−Polyepoxy Composites

TLDR

The study aims to explain how the critical frequency ωc scales with conductive weight fraction p and its proportionality to dc conductivity σdc using a biased random walk in three dimensions. The authors measured dc and ac conductivities of carbon nanotube–polyepoxy composites across 20–110 °C and 10⁻²–10⁶ Hz for CNT loadings of 0.04–2.5 wt %, examined universality via master curves, and applied a biased random walk model to interpret the results. Conductivity follows the universal dynamic response with a dc plateau and ω^s (s≈0.6–1) power law above a critical frequency, while dc conductivity obeys a percolation scaling law σdc∝(p−pc)^t with pc≈0.3 wt % and t≈1.4–1.8, reaching 10⁻⁴ S cm⁻¹ at 2.5 wt % CNTs and rising with temperature.

Abstract

The dc and ac conductivities of carbon nanotubes−polyepoxy composites have been investigated from 20 to 110 °C in the frequency range 10-2−106 Hz as a function of the conductive weight fraction p ranging from 0.04 to 2.5 wt %. The frequency dependence of the measured conductivity obeys the universal dynamic response (UDR): a dc plateau followed, above a critical frequency ωc, by the ωs power law with exponent s ∼ 0.6−1. The dc conductivity follows a percolation scaling law: σdc ∝ (p − pc)t with pc = 0.3 wt % and t = 1.4−1.8, according to the temperature. σdc reached 10-4 S/cm for 2.5 wt % CNTs content and increases with increasing temperature. Considering a biased random walk in three dimensions approach, we may explain the scaling law of ωc with p and its proportionality to σdc. The universality of ac conduction in carbon nanotubes−polymer composites is examined by the construction of master curves.