Effective Medium Theory of Dielectric Constant of Granular Materials in the Presence of Skin Effect
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EFFECTIVE MEDIUM THEORY OF DIELECTRIC CONSTANT OF GRANULAR MATERIALS IN THE PRESENCE OF SKIN EFFECT L.V.PANINA,
A.N.
LAGAR'KOV, A.k SARYCHEV, Y.R. SMYCHKOVICH AND A.P. VINOGRADOV Institute for High Temperature, USSR Academy of Science, Moscow 127412, USSR
I INTRODUCTION We consider the behavior of the dielectric constant of percolation composite systems. An example of such systems is a composite material consisting of a disordered mixture of metallic and insulating particles. A reduction in concentration P of the metallic (conducting) component reduces the static conductivity of the composite, so that it vanishes at some critical concentration PC known as the percolation threshold. The electrophysical characteristics of a composite exhibit a number of special features near PC. For example, the effective dielectric constant 8eff diverges at the percolation threshold 8ofe edl%-q, q = 0.75 [1,2J where Ed is the dielectric constant of the insulator and T =(P-P)/PC The main subject of the work is the investigation of dielectric constant %,, of the composite as a function of P and frequency W of external electric field. Up to day as we know the results of such investigation obtained in the framework of so-called quasi static approximation (see[3,4] and reference there). We consider in this paper the effects arising due to internal inductance and skin effect. It is clear that arising of internal inductance will change the frequency spectrum of 6eff substantially. To realize this fact one may imagine percolation system not only as system of disordered R and C elements, but including inductances too. In the second section the results of MC simulation presented. It is shown that internal inductance is largely determined by the properties of a single conductive inclusion. The analytical consideration of Eeff behavior is presented in section III.
II
INTERNAL INDUCTION OF COMPOSITE MATERIALS
The distinctive features in the electrical properties of composite materials with metal concentration near PC stem from inhomogeneity of the current distribution over the material; specifically, the current flows exclusively along percolation channels, which form an infinite cluster. For samples with a scale dimension A much larger than correlation length,the inductance L of the composite sample can be written [5]
Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
276
where J(A) is the current density at point A, I is the current flowing through the system, the angle brackets mean an average over the total volume, and V is the total volume of the system. We are interested in LL ,the component of the inductance due exclusively to the channels. To find it,
internal structure of the percolation we subtract from L the component (Iýoo)
of the inductance due to a homogeneous system shape. The component IL can be expressed in term
rG
internal inductance I,
=
r.,r ( - 41E) = lef rHo
W--6 P 8
=-i
r , B4(M)
(9)
-
(-0)
= < E(r) B(i)> = E0.f( - 4%) = S.,,o [rHj0 (r+)]I dir,
P JimL
= iW
(11) (12)
where a
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