The percolation staircase model and its manifestation in composite materials

We studied the tunneling percolation conductivity dependence on the site or bond occupation probability in the square lattice. The model predicts that in both, lattice and continuum systems in which there is a hierarchy of the local conductances, the dependence of the global conductivity on the site or volume occupation probability will yield a conductivity staircase. In particular we evaluate the implications of the staircase on the critical behavior of the conductivity. We then show experimental evidence for the predicted percolation-tunneling staircase in a Ag-Al2O3 granular metal system and in a carbon black-polymer composite. Following that, we propose that for carbon nanotube (CNT) polymer composites the data in the literature give ample support to a percolation-dispersion staircase behavior. The implication of the present findings on the percolation-hopping problem in composite materials is also discussed.