Calculation of effective electromagnetic parameters of multi-needle zinc oxide whisker based on equivalent spherical particle and strong fluctuation theory

Abstract

Multi-needle zinc oxide whisker (M-ZnOw) includes tetrapod-needle ZnOw (T-ZnOw), flower-shaped ZnOw, and other similar ZnOw architectures. The unique three-dimensional (3D) and multi-needle-shaped structures give the special performance of M-ZnOw, but make it difficult to calculate the effective electromagnetic parameters of M-ZnOw composites. In this paper, based on the equivalent spherical particle and the strong fluctuation theory, three different closed-form expressions are presented to calculate the effective electromagnetic parameters of M-ZnOw composites. To start with, because of the macroscopic isotropic nature of M-ZnOw composites and lossy properties of M-ZnOw itself, an equivalent spherical particle is introduced in the scheme to simplify the unique microscopic structures of M-ZnOw, and the possible limitations of the presented equivalent spherical particle are discussed qualitatively. In addition, different closed-form expressions to calculate the effective electromagnetic parameter are obtained by means of representing the physical situations of conductive network as different correlation functions in the strong fluctuation theory. Finally, the effective permeability of a T-ZnOw/Fe – paraffin composite is calculated by these three expressions in 2–18 GHz frequency range. Very good agreement between the calculated and experimental results on one hand verifies the rationality of presented expressions, and on the other hand indicates that the correlation function plays an important role in improving the performance of the presented expression.