A pair-correlation-based structure factor for fractal agglomerates accounting for primary-particle polydispersity

The precise optical characterization of fractal agglomerates as soot, or Black Carbon, relies on accurate modelling of light-particle interaction with non-spherical particles. The structure factor which predicts the angular or spectral dependence of the scattered light is crucial for interpreting measured signals to assess their size or shape. This can be accurately determined by numerically solving Maxwell’s equations, which is costly. For that reason, many analytical and simplified models have been proposed and integrated in the Rayleigh-Debye-Gans model for Fractal Aggregates (RDG–FA) in the visible range to assess the agglomerate size, which can be extended to a larger range of wavelengths including X-rays to characterize smaller scales typically the primary spheres. These structure factors generally rely on the agglomerate size (gyration radii) and morphology (fractal dimension) but rarely consider the effect of primary sphere polydispersity. The present work pursues a recent approach relying on the modelling of the pair-correlation function by incorporating the role played by primary sphere polydispersity. This model is compared with classical formulations (Mie theory, Dobbins and Megaridis and Fisher’s). The impact of primary sphere polydispersity is finally discussed for visible LIDAR applications as well as X-ray scattering. The results show that Mie theory can overestimate the backscattering structure factor by a factor larger than 9 for agglomerates gyration radius reaching 200 nm independently of primary-particle polydispersity. Dobbins and Megaridis model through RDG–FA shows better results. Finally a recently proposed expression of the polydispersity index used for the interpretation of SAXS data is validated.