Frequency and temperature scaling of the conductivity in percolating fractal networks of carbon-black/polymer composites

We have measured the frequency ω/2π dependence of the complex conductivity (σ′ and σ′ʹ) of conducting composites of carbon-black particles in a non-conducting polymer matrix up to 0.6 THz. The concentration p ranges from just above the percolation threshold pc up to 33pc. Temperatures T were varied between 4.2 K and 300 K. When scaled to σDC, σ′(T, ω) shows a unique dependence on ω, independent of T. We show how this relation follows from the hopping mechanism and relate the data to the microscopic hopping parameters.