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Cited by 5,260Theoretical and Computational PhysicsStochastic processes and statistical mechanicsMagnetic and transport properties of perovskites and related materials

Percolation and Conduction

Kirkpatrick, Scott·1973·Reviews of Modern Physics
DOI 10.1103/revmodphys.45.574
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Abstract

Extensions of percolation theory to treat transport are described. Resistor networks, from which resistors are removed at random, provide the natural generalization of the lattice models for which percolation thresholds and percolation probabilities have previously been considered. The normalized conductance, $G$, of such networks proves to be a sharply defined quantity with a characteristic concentration dependence near threshold which appears sensitive only to dimensionality. Numerical results are presented for several families of $3D$ and $2D$ network models. Except close to threshold, the models based on bond percolation are accurately described by a simple effective medium theory, which can also treat continuous media or situations less drastic than the percolation models, for example, materials in which local conductivity has a continuous distribution of values. The present calculations provide the first quantitative test of this theory. A "Green's function" derivation of the effective medium theory, which makes contact with similar treatments of disordered alloys, is presented. Finally, a general expression for the conductance of a percolation model is obtained which relates $G$ to the spin-stiffness coefficient, $D$, of an appropriately defined model dilute ferromagnet. We use this relationship to argue that the "percolation channels" through which the current flows above threshold must be regarded as three dimensional.

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  • According to percolation theory, nanowires, nanotubes, or nanofibers are more effective in forming conductive pathways compared to nanoparticles.

    “According to the percolation theory, [10,11] nanowires, nanotubes, or nanofibers are more effective in forming conductive pathways compared to nanoparticles.”

    From Nanomaterial-Enabled Wearable Sensors for Healthcare (2018) · cites this paper as [11]

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Authors
Kirkpatrick, S.
Affiliations
IBM Research - Thomas J. Watson Research Center (US)
Corresponding author
Kirkpatrick, Scott
ORCID
Kirkpatrick, Scott
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
1973-10-01
Volume
45
Issue
4
Pages
574-588
ISSN
0034-6861 (ISSN-L)
DOI
10.1103/revmodphys.45.574
OpenAlex
W1996613237
Cited by
5,260
References
50
Citations by year
2026: 142 · 2025: 132 · 2024: 106 · 2023: 114 · 2022: 145 · 2021: 151 · 2020: 143 · 2019: 184 · 2018: 147 · 2017: 150 · 2016: 163 · 2015: 162 · 2014: 158 · 2013: 150 · 2012: 163
FWCI
25.83
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Reviews of Modern Physics (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
  • Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
  • Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Magnetic and transport properties of perovskites and related materials
Keywords
percolation theory, electrical transport, resistor networks, conductance, percolation threshold, bond percolation, effective medium theory, Green's function, dilute ferromagnets, percolation channels, disordered alloys, dimension dependence

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