Effect of concentration, lumpiness, aggregation, and cluster compaction on optical properties of particulate media

A four-flux radiative transfer model is used to evaluate diffuse reflectance and transmittance spectra of plane-parallel particulate materials. External parameters, including scattering and absorption cross sections, forward scattering ratios, and average path length parameters, are calculated utilizing Lorenz-Mie theory for independent scattering and a Transition Matrix approach for near-field dependent scattering evaluations. The formalism is applied to sub-micron sized spherical titanium dioxide pigments in an aqueous-polymer matrix to evaluate their reflectance and transmittance spectra in the range of 0.3 to 1.5 m in wavelength. The particle concentration, the degree of lumpiness, the number of particles per cluster and the cluster compaction are varied to quantify the effect of dependent scattering. A novel scheme is introduced to model the morphology of samples in terms of a volume fraction occupied by particles that do not form aggregates and another fraction corresponding to particles that are part of aggregates, as well as the lumpiness of the sample and compaction of the clusters. A more detailed analysis is carried out for specific wavelengths in the ultraviolet, visible, and near infrared to correlate the variation of reflectance and transmittance due to dependent scattering with the propagating fluxes.