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The absorption, scattering, and differential scattering cross sections are presented for polydisperse aggregates of prescribed fractal dimension and uniform primary particle size. These optical properties are formulated for polydisperse aggregates in terms of the primary particle diameter, the appropriate moments of the discrete size distribution function, and the mean-square radius of gyration. The absorption and scattering cross sections are compared with Rayleigh theory in the small size limit and with the results of the computational simulations of Mountain and Mulholland Langmuir 4, 1321 (1988) for intermediate and large aggregates. The differential scattering cross sections are well correlated by the law of Guinier together with a power-law expression for the larger sizes. The cross sections that are described herein apply in particular to polydisperse fractallike aggregates that are formed by cluster-cluster aggregation and possess a size scale that is pertinent to laboratory experiments and industrial processes.
Dobbins et al. (Wed,) studied this question.