Effects of clustering in binary composites: Random fractals

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Abstract
The effects of random-fractal clustering on the electromagnetic properties of two-dimensional binary composites at low frequencies are studied within a random-admittance-network model consisting of metallic and insulating bonds. The diffusion-limited cluster-cluster aggregation model is used for fractal-cluster formation. The effective admittance of the random network is calculated using the Y-Δ transformation algorithm. The real part of the effective admittance per metallic bond, which is proportional to the absorption coefficient of a dilute composite, is calculated at different states of the aggregation process. As particles join together to form clusters and clusters join together to form larger ones, the absorption coefficient gradually increases and reaches its highest value when all the particles aggregate into a single cluster. Results are compared to those obtained within a differential effective-medium approximation.