Effective Dielectric Response of Composites: A New Diagrammatic Approach

Abstract

The interest in the dielectric response of composites has been renewed by the application of a wide variety of mathematical techniques borrowed from other fields of physics. The use of these materials as selective absorbers in solar energy devices [1] and the study of fluids in rocks and porous materials for oil exploration [2], has also contributed to the revival of the actual research in composites. It has been recognized that the topology of thecomposite plays a crucial role in the response of the system to an external perturbation [3]. Here we treat the dielectric response of a system composed by spherical inclusions located at random in an otherwise homogeneous matrix. Although the problem was posed more than a century ago [4] only until recently, theories beyond the mean field approximation started to be developed. Multiple scattering theory [5], cluster expansions [6], lattice gas models[7], numerical simulations [8], homogenization theory [9], renormalization [10] and diagrammatic techniques [11] have been the main ingredients of the recently developed theories. Comparison with experiment has been troublesome because the experiments have been done in samples with a poorly characterized microstructure.