The percolation staircase model and its manifestation in composite materials

• Published in: The European physical journal. B, Condensed matter physics Vol. 86; no. 10
• Main Authors: Balberg, I., Azulay, D., Goldstein, Y., Jedrzejewski, J., Ravid, G., Savir, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013; EDP Sciences; Springer
• Subjects: Analysis; Complex Systems; Composite materials; Composite materials industry; Condensed Matter Physics; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Conductivity of specific materials; Electronic transport in condensed matter; Exact sciences and technology; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Solid State and Materials; Aluminium oxide; Electrical conductivity; Carbon black; Volume fraction; Tunnel effect; Carbon nanotubes; Percolation theory; Critical phenomena; Granular structure; Continuum; Silver; Composite materials; Crystallographic site; Carbon fiber reinforced plastics; Square lattices
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2013-40200-7

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-Al 2 O 3 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.