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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 integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and 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 theories were presented as error contour charts in the ‖m - 1‖x(p) domains for various size aggregates, emphasizing fractal properties representative 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 general 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) ≈ 1.0) to compact clusters (D(f) ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m - 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x(p) ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.

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ABSTRACT. While the fractal dimension of cluster -cluster aggregates, D f , appears to be a well-established property, the fractal prefactor, kg (also known as structural coef cient), continues to exhibit a large range of possible values. In the present paper, an attempt is made to clarify this issue which leads to conclusive results concerning the value to adopt for the fractal prefactor of simulated aggregates. Starting from a large population of "free" numerically simulated aggregates (i.e., where no restrictions to aggregate formation were imposed) the fractal properties obtained were estimated both using morphological concepts as well as light scattering theories. Furthermore, studies for aggregates having prede ned morphological k g values (namely, k g > 2 and ca. 1) were also performed in order to check the viability of these values. The results obtained for the three different populations of aggregates considered were used to infer, through a best-t analysis, the fractal properties. Our best estimates are k g ¼ 1.27 and D f ¼ 1.82, which are approximately independent of aggregate size and composition. These results are in very good agreement with numerical predictions reported by previous authors. However, experimental results systematically indicate k g > 2. This motivated the present authors to identify possible reasons for these large discrepancies. Present calculations indicate that partial sintering in conjunction with the polydispersity of aggregates (resulting in a cut-off function coef cient, k p , >1) contributes to a systematic increase in k g , possibly justifying the differences between numerical and experimental results.

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