Conductivity of a mixture of conducting and insulating grains: Dimensionality effects

The percolation behavior of films of thickness d composed of a compact mixture of conducting (concentration p) and insulating (concentration 1-p) beads is studied by measuring their conductivity σ(d, p). A theoretical model based on a renormalization operation to the thickness of the film leads to predictions on the threshold pc(d), the crossover values between two- and three-dimensional behavior p_±(d), and the amplitude of the conductivity above threshold. The experiments are analyzed in terms of the model and lead to the determination of several critical exponents.