RANGE OF VALIDITY OF THE RAYLEIGH-DEBYE-GANS THEORY FOR OPTICS OF FRACTAL AGGREGATES

The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integ ral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simula tions were performed to create aggregates that exhibit mass fractallik e characteristics with a wide range of particle and aggregate sizes an d morphologies, including x(p) = 0.01-1.0, \m-1\ = 0.1-2.0, N = 16-256 , and D-f = 1.0-3.0. The percent differences between both scattering t heories were presented as error contour charts in the \m-1\x(p) domain s for various size aggregates, emphasizing fractal properties represen tative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use gene ral guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D-f approximate to 1.0) to compact clusters (D-f approximate to 3.0) were also considered for generalization of the findings. For the present c omputational conditions, the RDG-FA theory yielded accurate prediction s to within 10% for \m-1\ to approximately 1 or more as long as the pr imary particles in aggregates were within the Rayleigh scattering limi t (x(p) less than or equal to 0.3). Additionally, the effect of fracta l dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reas onable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability. (C) 1996 Optical Society of America