1/f or flicker noise in cellular percolation systems

Flicker or 1/f noise is studied in a series of four composite discs, which consists of carbon black (ground and unground), graphite, and graphite/boron nitride, as the conducting components coating, and a common insulating matrix of talc wax. The measurements were done on the conducting side (π > π_c) of the critical volume fraction (π_c), within a frequency range of 1.2-1001.2 Hz. The results are analyzed in terms of Hooge's empirical formula with frequency and voltage exponents y and m, respectively. Values of γ obtained are in the range 0.97-1.2. Samples with larger (π - π_c) have m ≈ 2, while those with smaller (π - π_c) have m significantly lower than 2. The normalized noise at 10 Hz (S_v10Hz/V^m) obey the well-established relationships S_v(f)/V^m∞(π - π_c)^-k and S_v(f)/V^m∞R^w, where Vis the voltage across the sample with resistance R, while m, k, and w are exponents. However, a change in the value of the exponent k and w was observed in the measured systems, with k taking the values k₁ ∼ 0.75-5.23 close to π_c and k₂ ∼ 2.23-5.54 further into the conducting region. Values of w₁ range from 0.36-1.37, while w₂ ∼ 0.99-1.59. The k₁(w₁) are observed when m < 2. The nonuniversality of the k₁ and k2 regimes are interpreted as due to the superposition of the behavior that results from the geometry (a random voidlike structure) and the behavior resulting from the presence of non-Ohmic, intergranular contacts between the conducting grains. These exponents are tested for consistency using w =k/t, and compared with predictions from recent theoretical models.