Effects of aggregation on the permittivity of random media containing monodisperse spheres

Numerical simulations were used to calculate the effective permittivities of three-dimensional random particle suspensions containing up to 2440 particles and exhibiting two types of particle aggregation. The particles were modeled as 200 mu m spheres that were aggregated into either large spherical clusters or into foam-type microstructures with large spherical voids. Multiple scattering of 0.01-10.0 GHz electromagnetic fields was simulated using a first-principles iterative multipole approach with matrix and particle permittivities of 1.0 and 8.5, respectively. The computational results showed both significant and highly significant trends. Aggregation into spherical clusters decreased the effective permittivity by up to 3.2 +/- 0.2%, whereas aggregation into foam-type microstructures increased the effective permittivity by up to 3.0 +/- 1.6%. The effective permittivity trends exhibited little change with frequency. These results were compared to effective medium approximations that predicted higher permittivities than those from the simulations and showed opposite trends for cluster aggregation. Three theories are proposed to explain the simulation results. The first theory invokes a waveguidelike mechanism. The simulations indicate that the wave fields propagate more through the continuous paths of greater or lesser particle density created by aggregation, rather than through the isolated particle clusters or large voids. This quasicontinuous phase, or quasimatrix, therefore behaves like a random waveguide structure in the material. A second theory is proposed where the quasicontinuous phase governs the behavior of the system by a percolationlike process. In this theory, the multipole interactions are modeled as the percolation of virtual charges tunneling from one particle to another. A third mechanism for the permittivity changes is also proposed involving collective polarization effects associated with the particle clusters or large voids. The simulation results challenge the general applicability of the quasistatic limit for heterogeneous media by showing how microstructural changes much smaller than the electromagnetic wavelength can alter the effective permittivity by a statistically significant degree. The results also provide a quantitative indication of the effects of aggregation and hierarchical microstructures on the electromagnetic properties of random media and have application to the remote and in situ sensing of soils, the rational design and nondestructive evaluation of composites, and the study of biological tissues and other random materials.