Controllable effective complex permittivity of functionally graded composite materials: A numerical investigation

Abstract

A ubiquitous issue in dielectric heterostructures is to understand the relation between unconventional materials and their effective polarization properties (complex permittivity, polarizability, factor of depolarization). In this context, graded composite materials (GCMs), in which the constituent material properties can vary continuously in space, provide an interesting playground. We report effective permittivity calculations of two-phase GCM, using finite-element (FE) calculations, to understand the effects of shape, size, and intrinsic permittivity of the different components of the material. Our analysis shows that purposely introduced gradients in the permittivity of inclusion can be used to tune the effective permittivity of the GCM. Our FE calculations quantitatively test recent predictions of the effective permittivity of GCM having general power-law gradient inclusions based on the recently developed Wei-Poon-Shin theory [Phys. Lett. A 336, 264 (2005)]. The agreement between the FE data and the predicted curves is excellent only in the dilute limit. In addition, we quantify the complex effective permittivity of several representative GCMs and show that Maxwell Garnett equation is not, in general, appropriate to represent its volume fraction dependence. Numerics furthermore show that selected lossy GCM with negative permittivity can have specific features which distinguish them from composite materials (CMs) containing homogeneous isotropic inclusions. This information is potentially useful for understanding the dielectric properties of GCM which are abundant in nature. Collectively, the results are also relevant for exploiting artificially engineered CM in technologies for such applications as microwave biosensors, nanophotonics, and heterogeneous catalysis.