Electromagnetic coupling and determination of the structure factor of fractal aggregates

The Rayleigh-Debye-Gans approximation for fractal aggregates (RDG-FA) is commonly used to evaluate the radiative properties of soot aerosols composed of nano-spheres due to its analytical character. Despite neglecting electromagnetic coupling within an aggregate, the RDG-FA provides a simple interpretation of angular light-scattering measurements in terms of a structure factor. This factor, in turn, enables the de-termination of the aggregate's fractal dimension Df and radius of gyration Rg. The structure factor can be expressed as the Fourier transform of a purely morphological autocorrelation function. Here we em-ploy the discrete dipole approximation and phasor analysis of the internal electric field in an aggregate to study the role of coupling for the specific case of soot particle refractive index. An optical autocorre-lation function is defined in terms of an aggregate's phasors rather than simply its physical distribution of material. The new function conveys the effect of the non-uniformity of the internal field distribution, due to coupling, to the angular scattering. A correction term is then introduced explaining why coupling tends to decrease the structure factor inferred in the power-law regime. Such decrease impacts the de-termination of the fractal dimension from scattering data. Finally, it is shown that the inferred structure factor is mainly affected by a so-called internal trapping effect associated with a large imaginary part of the refractive index. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

The Rayleigh-Debye-Gans approximation is widely used to evaluate the radiative properties of soot aerosols. Although it neglects electromagnetic coupling within an aggregate, it provides a simple interpretation of light-scattering measurements in terms of a structure factor. In this study, the role of coupling for the refractive index of soot particles is investigated using the discrete dipole approximation. A new optical autocorrelation function is defined, which takes into account the non-uniformity of the internal field distribution due to coupling. The study also shows that the inferred structure factor is mainly affected by an internal trapping effect associated with a large imaginary part of the refractive index.