https://doi.org/10.1140/epjb/e2003-00042-6
Dielectric resonances in disordered media
Laboratoire Matériaux et Microélectronique de
Provence (UMR CNRS 6137) , Université Aix-Marseille I,
bâtiment IRPHE, Technopole de Château-Gombert, 49 rue Joliot Curie,
BP 146, 13384 Marseille Cedex 13, France
Corresponding authors: a laurent.raymond@l2mp.fr - b steffen.schaefer@l2mp.fr
Received:
16
August
2002
Published online:
14
February
2003
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 of the complex
conductances,
and
, of the two components,
and their relative abundances p (or, respectively,
). 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.
PACS: 66.10.Ed – Ionic conduction / 66.30.Dn – Theory of diffusion and ionic conduction in solids / 61.43.Gt – Powders, porous materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003