A semi-empirical correction for the Rayleigh-Debye-Gans approximation for fractal aggregates based on phasor analysis: Application to soot particles

Abstract

The Rayleigh Debye-Gans approximation for Fractal Aggregates (RDG-FA) is commonly used for the evaluation of the radiative properties of fractal aggregates of nanometer-scale nearly spherical particles as soot particles. The cost of its simplicity, however, is the precision of the aggregate cross sections when the refractive index deviates from unity and when the aggregate’s spheres, or monomers, are not sufficiently small compared to the wavelength. While correction factors have been highlighted before, their physical origin is not clear and no universal correction factors are proposed. The present study develops an approach based on phasor analysis of the aggregate’s internal electric field rigorously determined by the discrete dipole approximation. Aggregates representative of the Diffusion Limited Cluster Aggregation (DLCA) regime having a fractal dimension of Df=1.78 are considered as representative of a soot aggregate. The results reveal that correction factors to the RDG-FA for forward scattering (A) and the absorption cross section (h) are due to a competition between internal-field hot-spots caused by point contact between the spherical monomers and a decrease of the field amplitude as the field propagates through the aggregate. Both phenomena are neglected in the RDF-FA by definition. The absorption phenomenon explains the aggregate-size dependence of A and h. These effects are then studied as the aggregate size varies according to the number of monomers Nm ranging from 10 to 1000, as the monomer radius varies from Rm=5nm - 30nm, and as the wavelength varies from λ=266nm - 1064nm. Both constant and wavelength dependent refractive indices for organic, graphitic, and amorphous soot are considered. Finally, a semi-empirical model is proposed intended to correct the RDG-FA theory based on the analysis.