Dielectric Response of a Chain of Disordered Polarizable Spheres: Numerical Simulation and Theory
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DIELECTRIC RESPONSE OF A CHAIN OF DISORDERED POLARIZABLE SPHERES: NUMERICAL SIMULATION AND THEORY t PEDRO VILLASEINOR-GONZALEZ , CECILIA NOGUEZ*t AND RUBEN G. BARRERAt t Instituto de F(sica, Universidad Aut6noma de San Luis Potosi, 78000 San Luis Potos(, Mexico. * Facultad de Ciencias, Universidad Nacional Aut6noma de M~xico, 01000 Mexico D.F., Mixico. t Instituto de Fisica, Universidad Nacional Aut6noma de Mexico, Apdo. Postal 20-364, 01000 M~xico D.F., MWxico.
ABSTRACT We applied to a one-dimensional system (1D) a recently developed diagrammatic formalism, in order to calculate the effective dielectric response of a chain of polarizable spheres embeded in an homogeneous host. The effective response is calculated within the dipolar, quasi-static approximation, through the summation of selected classes of diagrams. We compared our results with a numerical simulation, where the position of each sphere was generated at random and the induced dipole moment of each sphere was calculated by solving a set of linear equations through matrix inversion and using periodic boundary conditions. INTRODUCTION The optical properties of a composite systems are determined through the knowledge of its dielectric response. Here we are interested in composites with a separate-grain topology and the simplest and most recurrent [1] 3D system is the one containing a homogeneous matrix within identical spherical inclusions. A pioneering work towards the calculation of the effective dielectric response of this system was done at the beginning of this century by JC Maxwell Garnett [2]. In his work he assumed that ,(i) only the dipolar moment is induced at each sphere (dipolar-approximation) and that (ii) the local field is the same in all the spheres and equal to its average (mean-field-approximation). The objective of actual theories is to improve the mean-field-approximation, thus we are interested in taking into account the fluctuations of the local field and exploring their effects on the effective dielectric response. One source of these fluctuations is the disorder in the position of the spheres and its mathematical treatment has been the main subject of recently developed theories. An ample variety of procedures like multiple scattering [3], cluster expansions [4], numerical simulations [5], renormalization [6], diagrammatic techniques [7,8], etc., have been devised in order to calculate the effective dielectric response of a disordered system. On the other hand, the comparision with experiment has been a painful task because the samples used by the experimentalist do not resemble properly the models used in the theoretical work. Problems like clustering and distributions of shapes and sizes of the inclusions make the interpretation of the absorption spectra more difficult. Moreover until recently, the experimentalists have not been aware of the need to report more information about microstructure of their samples. Therefore, the only fair test of the present theories is the comparision of their results with recently reported numeri
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