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 (φ>φ_c) of the critical volume fraction (φ_c), within a frequency range of 1.2–1001.2Hz. The results are analyzed in terms of Hooge’s empirical formula with frequency and voltage exponents γ and m, respectively. Values of γ obtained are in the range 0.97–1.2. Samples with larger (φ-φ_c) have m≈2, while those with smaller (φ-φ_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∝(φ-φ_c)^-k and S_v(f)/V^m∝R^w, where V is 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 φ_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.