Particle Interaction Model of Permittivity Enhancement in Metal-Insulator Composites
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PARTICLE INTERACTION MODEL OF PERMIT17IVITY ENHANCEMENT IN METAL-INSULATOR COMPOSITES
W. T. DOYLE* AND I. S. JACOBS** *Physics Department, Dartmouth College, Hanover, NH 03755 **GE Corporate Research and Development, P. 0. Box 8, Schenectady, NY 12301
ABSTRACT A simple effective spherical cluster model of generalized susceptibility enhancements in disordered monodisperse suspensions of conducting spheres is compared with experimental measurements of reduced permittivity and conductance. Good agreement with experiment is obtained by treating the suspension in the Clausius-Mossotti approximation as a mixture of isolated spheres and compact spherical metallized clusters. INTRODUCTION The average permittivity of an inhomogeneous medium composed of spheres of one substance embedded in a continuum of a different material (cermet topology) is, in general, a complicated function of the permittivities of the constituents, the volume filling factor, particle shape and size, and the details of the particle distribution function. Although the permittivities may be complex and depend upon frequency, we shall be concerned here only with perfectly conducting particles in the electrostatic limit. In the simplest case of a regular array of spheres of uniform size the permittivity may be computed exactly [1,2]. When one or the other of the various parameters has a non-zero variance, the problem becomes substantially more difficult. If all parameters exhibit wide variances the problem is essentially intractable. Fortunately, in practice it is possible to obtain nearly mono-disperse distributions of good spheres. However, even an array of uniform sized spheres presents difficulties when the spheres are randomly distributed in space. For such media the permittivity may be calculated only approximately. If only dipole interactions are present, the permittivity of an isotropic medium is given by the well-known Clausius-Mossotti approximation. For regular arrays this case occurs in the limit of low filling factors. In random distributions close encounters can occur even at low filling factors, so corrections become necessary even at low particle densities. Experiments with nominally "random" media often exhibit substantial departures from the predictions of the approximate formulas, usually of the kinds to be expected from enhanced particle interactions due to particle clustering. In a neutral dielectric medium dipole and higher multipole interactions are present, and all of these particle interactions depend inversely upon increasing powers of the distance between the particles of the medium. As a consequence, the
Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
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multipole interactions grow rapidly with increasing volume filling factor. Because they have a positive angular average, the multipole contributions lead to an increase in the dielectric constant with decreasing interparticle distance. A macroscopic manifestation of this is a strong non-linearity of the dielectric constant when plotted as a function
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