Dielectric resonances in disordered media |
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Authors: | L Raymond J-M Laugier S Schäfer G Albinet |
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Institution: | (1) Laboratoire Matériaux et Microélectronique de Provence, Université Aix-Marseille I, batiment IRPHE, Technopole de Chateau-Gombert, 49 rue Joliot Curie, BP 146, 13384 Marseille Cedex 13, France, FR |
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Abstract: | Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator,
or conductor and super-conductor. They present very specific properties, in particular the second-order percolation phase
transition, with its fractal geometry and the multi-fractal properties of the current moments. These systems are naturally
modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities.
The two significant parameters are the ratio h = σ
1/σ of the complex conductances, σ and σ
1, of the two components, and their relative abundances p (or, respectively, 1 - p). In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method,
which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of
resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites constituted of resistive inductances and capacitors (LR-C systems),
representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very
intricate structures in the vicinity of the percolation threshold. In this paper, we analyse the LR-C behavior of compounds
formed by the inclusion of small conducting clusters (“n-legged animals”) in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp
lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each
animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties
in a given frequency domain.
Received 16 August 2002 Published online 14 February 2003
RID="a"
ID="a"e-mail: laurent.raymond@l2mp.fr
RID="b"
ID="b"e-mail: steffen.schaefer@l2mp.fr
RID="c"
ID="c"UMR CNRS 6137 |
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Keywords: | PACS 66 10 Ed Ionic conduction – 66 30 Dn Theory of diffusion and ionic conduction in solids – 61 43 Gt Powders porous materials |
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