Effective Dielectric function of a Composite with Aligned Spheroidal Inclusions
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EFFECTIVE DIELECTRIC FUNCTION OF A COMPOSITE WITH ALIGNED SPHEROIDAL INCLUSIONS RUBEN G. BARRERA*, JAIRO GIRALDOt AND W. LUIS MOCHANt * Instituto de Fisica, UNAM, Apdo. Postal 20-364, 01000 Mixico D.F., M~xico. t Departamento de Fiesica, Universidad Nacional de Colombia, Bogoti, Colombia. t Laboratorio de Cuernavaca, Instituto de Frsica, UNAM, Apartado Postal 139-8, 62190 Cuernavaca, M~xico. ABSTRACT The effective dielectric response eM of a composite with aligned spheroidal inclusions is calculated. Using the dipolar and the mean-field approximation (MFA) an 2 analytical expression for eM as a functional of the two-particle distribution function p( ) is obtained. It is shown that previous expressions reported in the literature correspond to different choices of p( 2 ), thus, clarifying the origin of their discrepancies. The theory is further extended beyond the MFA by including the dipolar fluctuations through a renormalization of the polarizability tensor of the inclusions. The absorption peaks are diminished and broadened by the spatial disorder, which also yields an easily identified coupling among electromagnetic modes with perpendicular polarizations. INTRODUCTION Owing to the intrinsic fundamental importance of composite materials as well as to their ample variety of applications, the study of their linear electromagnetic response has attracted the attention of many researchers since the beginning of electrodynamics [1]. This interest has been recently renewed due to the development of new theoretical methods for dealing with disordered systems (2] and also to the potential applications of composite materials in solar energy conversion [3], earth sciences [4], biology [5] and other fields [6]. It has been established by now that the dielectric response of composites is very sensitive to the topology of its microstructure. Here we restrict ourselves to the separate-grain topology, that is, to composites prepared as small inclusions embedded in an otherwise homogeneous, isotropic host material. The simplest model regards the inclusions as identical spheres, even though one expects a distribution of sizes and shapes in actual samples. Although the results obtained so far for this model cover a wide range of methods and approximations [7], extensions to non-spherical inclusions have been restricted, almost entirely, to the mean-field approximation (MFA). Even in this case the problem has not been thoroughly examined. For a system with spherical inclusions, one of the first expressions for eM which appears in the literature was derived by J.C. Maxwell Garnett [8]. It can be shown that the Maxwell Garnett theory (MGT) is a mean-field theory equivalent to the celebrated Clausius-Mossotti-Lorenz-Lorentz relation [9]. From the several derivations of eM in the MFA, the most popular one is, probably, the one introduced by Lorentz [10] for the case of fluids and which now appears in almost all textbooks. In the Lorentz's method (LM) one considers a fictitious spherical cavity in the system, known as the Lorentz sphere,
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