Generalized effective medium theory and dielectric relaxation in particle-filled polymeric resins

Dielectric relaxation in disordered solids continue to be in the focus due to the important technological applications in the context of microwave and optical remote sensing and communication. The pragmatic philosophy of the present article is to use a combination of Jonscher's phenomenological equations with a generalized effective medium equation, due to McLachlan, to study the microwave relaxation dynamics in a technologically interesting system, i.e., a particle-filled polymeric resin. The introduction of a small number of parameters (critical exponents s and t, conductivity threshold phi(c)) into the standard Bruggeman effective medium equation dramatically improves its predictive power. This approach, termed the McLachlan-Jonscher model, has the potential to be quite flexible and is very sensitive to the values of the critical exponents s, t and of the conductivity threshold phi(c). Furthermore, a comparison of the calculated complex effective permittivity for a series of carbon black-filled polymers with experimental results shows that it can accurately describe the microwave response over a broad range of volume fraction of carbon black. These considerations illustrate the potential for using this coarse grained model to help understand the dielectric relaxation of particle dispersions in polymeric matrixes. (C) 2002 American Institute of Physics.