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

Abstract

The percolation behavior of films of thickness $d$ composed of a compact mixture of conducting (concentration $p$) and insulating (concentration $1\ensuremath{-}p$) beads is studied by measuring their conductivity $\ensuremath{\sigma}(d, p)$. A theoretical model based on a renormalization operation to the thickness of the film leads to predictions on the threshold ${p}_{c}(d)$, the crossover values between two- and three-dimensional behavior ${p}_{\ifmmode\pm\else\textpm\fi{}}(d)$, 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.