Metal clusters and model rocks: Electromagnetic properties of conducting fractal aggregates

We present a numerical study of fractal metallic aggregates embedded in a two-dimensional (2D) dielectric host. The metallic clusters are constructed from Drude-like bonds, while the dielectric host is taken to have purely capacitive response. The clusters are either grown randomly [by diffusion-limited aggregation (DLA)] or by a deterministic algorithm which generates self-similar clusters. The effective ac response of the composite is computed using the Y-{Δ} algorithm of Frank and Lobb. For finite clusters, either random or deterministic, the far-infrared absorption per unit mass of metal is found to be greatly increased over that of isolated metallic particles. This provides a possible explanation of the enhancement observed in suspensions of small metal particles, assuming a fractal clustering is present. At higher frequencies, the random fractals lead to a broad surface-plasmon absorption spectrum, while the ordered fractals have an optical conductivity which appears to be self-similar in frequency. When a random 2D DLA cluster is allowed to percolate across the composite, we find a strong low-frequency enhancement of the dielectric constant, similar to the enhancement observed in brine-saturated porous rocks. We discuss the possible relevance of the model, and its probable limitations, as applied to real composites.