The influence of particle shape on dielectric enhancement in metal-insulator composites

Abstract

Disordered suspensions of conducting particles exhibit substantial permittivity enhancements beyond the predictions of the Clausius–Mossotti equation and other purely dipolar approximations. The magnitude of the enhancement depends upon the shape of the particles. A recently developed effective cluster model for spherical particles [Phys. Rev. B 42, 9319 (1990)] that treats a disordered suspension as a mixture, or mesosuspension, of isolated spheres and close-packed spherical clusters of arbitrary size is in excellent agreement with experiments on well-stirred suspensions of spheres over the entire accessible range of volume loading. In this paper, the effective cluster model is extended to be applicable to disordered suspensions of arbitrarily shaped conducting particles. Two physical parameters are used to characterize a general suspension: the angular average polarizability of an isolated particle, and the volume loading at closest packing of the suspension. Multipole interactions within the clusters are treated exactly. External particle-shape-dependent interactions between clusters and isolated particles are treated in the dipole approximation in two ways: explicitly, using the Clausius–Mossotti equation, and implicitly, using the Wiener equation. Both versions of the model are used to find the permittivity of a monodisperse suspension of conducting spheroids, for which the model parameters can be determined independently. The two versions are in good agreement when the axial ratio of the particles is not extreme. The Clausius–Mossotti version of the model yields a mesoscopic analogue of the dielectric virial expansion. It is limited to small volume loadings when the particles have an extremely nonspherical shape. The Wiener equation version of the model holds at all volume loadings for particles of arbitrary shape. Comparison of the two versions of the model leads to a simple physical interpretation of Wiener’s equation. The models are compared with experiments of Kelly, Stenoien, and Isbell [J. Appl. Phys. 24, 258 (1953)] on aluminum and zinc particles in paraffin, with Nasuhoglu’s experiments on iron particles in oil [Commun. Fac. Sci. Univ. Ankara 4, 108 (1952)], and with new X-band and Kα-band permittivity measurements on Ni-Cr alloy particles in a polyurethane binder.

Unified Spectral Technique Application for Study of Radiator Behavior Near Planar Layered Composites

“…However, its electromagnetic parameters may be homogenized using an effective medium theory (EMT). There are many effective media theories (EMT) allowing for homogenization of composite media [19][20][21][22][23]. This layer contains conductive fibers in Electric dipole Figure 8.…”

Frequency-Dependent Effective Material Parameters of Composites as a Function of Inclusion Shape

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“…Historically, the first theories describing the effective properties of fiber-filled composites have been suggested in [37] and [50]. However, the theory [37] describes the case of infinite conductivity of inclusions and is not suitable for describing of frequency dependences in metal-dielectric composites.…”

“…However, the theory [37] describes the case of infinite conductivity of inclusions and is not suitable for describing of frequency dependences in metal-dielectric composites. Theory [50] is a modification of the EMT.…”

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