The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models

1990/06/01 by J.P. Clerc, J. P. Clerc, G. Giraud +3 · 693 citations
Materials Science · Mathematics · Physics and Astronomy · #Binary number #Condensed matter physics #Conductivity #Dielectric #Directed percolation #Electrical resistivity and conductivity #Fractal #Geometry #Material Dynamics and Properties #Materials science #Mathematical analysis #Mathematics #NMR spectroscopy and applications #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Scaling #Statistical physics #Theoretical and Computational Physics

paper · doi:10.1080/00018739000101501

published in Advances In Physics 39(3), 191-309 (Taylor & Francis)

openalex publication_date 1990/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We review theoretical and experimental studies of the AC dielectric response of inhomogeneous materials, modelled as bond percolation networks, with a binary (conductor-dielectric) distribution of bond conductances. We first summarize the key results of percolation theory, concerning mostly geometrical and static (DC) transport properties, with emphasis on the scaling properties of the critical region around the percolation threshold. The frequency-dependent (AC) response of a general binary model is then studied by means of various approaches, including the effective-medium approximation, a scaling theory of the critical region, numerical computations using the transfer-matrix algorithm, and several exactly solvable deterministic fractal models. Transient regimes, related to singularities in the complex-frequency plane, are also investigated. Theoretical predictions are made more explicit in two specific cases, namely R-C and RL-C networks, and compared with a broad variety of experimental results, concerning, for example, granular composites, thin films, powders, microemulsions, cermets, porous ceramics and the viscoelastic properties of gels.

Citations

• The energy spectrum of disordered systems
• The Fractal Geometry of Nature
• Diffusion in disordered media

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