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...
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Published in | The European physical journal. B, Condensed matter physics Vol. 86; no. 10 |
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Main Authors | , , , , , |
Format | Journal Article |
Language | English |
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Springer Berlin Heidelberg
01.10.2013
EDP Sciences Springer |
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Abstract | 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. |
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AbstractList | 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.sub.2][O.sub.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. 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. |
ArticleNumber | 428 |
Audience | Academic |
Author | Ravid, G. Jedrzejewski, J. Azulay, D. Goldstein, Y. Balberg, I. Savir, E. |
Author_xml | – sequence: 1 givenname: I. surname: Balberg fullname: Balberg, I. email: balberg@mail.huji.ac.il organization: The Racah Institute of Physics, The Hebrew University – sequence: 2 givenname: D. surname: Azulay fullname: Azulay, D. organization: The Racah Institute of Physics, The Hebrew University – sequence: 3 givenname: Y. surname: Goldstein fullname: Goldstein, Y. organization: The Racah Institute of Physics, The Hebrew University – sequence: 4 givenname: J. surname: Jedrzejewski fullname: Jedrzejewski, J. organization: The Racah Institute of Physics, The Hebrew University – sequence: 5 givenname: G. surname: Ravid fullname: Ravid, G. organization: The Racah Institute of Physics, The Hebrew University – sequence: 6 givenname: E. surname: Savir fullname: Savir, E. organization: The Racah Institute of Physics, The Hebrew University |
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CitedBy_id | crossref_primary_10_1063_1_4900777 crossref_primary_10_1063_1_4917234 crossref_primary_10_1103_PhysRevB_103_134110 crossref_primary_10_1002_app_47409 crossref_primary_10_1088_1757_899X_64_1_012002 crossref_primary_10_1016_j_heliyon_2019_e02961 crossref_primary_10_1063_1_4885498 crossref_primary_10_1103_PhysRevB_89_214201 crossref_primary_10_1021_acs_jpcc_8b00122 crossref_primary_10_1088_1361_648X_ac5706 crossref_primary_10_1002_app_46650 crossref_primary_10_3390_ma7042501 crossref_primary_10_1590_0104_1428_08220 |
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Keywords | 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 |
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SubjectTerms | 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 |
Title | The percolation staircase model and its manifestation in composite materials |
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