A two-way particle mapping for calculation of the effective dielectric response of graded spherical composites

This work is a study of the dielectric properties of composites where each embedded spherical inclusion is surrounded by an inhomogeneous interphase. This is an extension of work done by Lombardo and Ding [Lombardo N, Ding Y. Effect of inhomogeneous interphase on the bulk modulus of a composite containing spherical inclusions. In: Proceedings of the 4th Australasian congress on applied mechanics; 2005] on the bulk modulus of composites. Here we derive a coupled pair of differential equations using the replacement method [Hill R. Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour. J Mech Phys Solids 1964:12;199] as the foundation. These differential equations model the dielectric properties of composites for a wide class of functions describing the interphase inhomogeneity and are shown to coincide with the equation obtained using DEDA [Yu KW, Gu GQ, Huang JP. Dielectric response of spherical particles of graded materials. cond-mat/0211532; 2002]. It is also shown how the model may be combined with the model of Vo and Shi [Vo HT, Shi FG. Towards model-based engineering of optoelectronic packaging materials: dielectric constant modeling. Microelectron J 2002:33;409] for the dielectric constant. The differential equations are solved for three different profiles and the result of the combined models is compared to experimental data. All three profiles compared excellently to the experimental data.