Light scattering shape diagnostics for nano-agglomerates

Abstract

Motivated by light scattering experiments showing enhanced intensity of electric field aligned nano-agglomerates vs. randomly oriented nano-agglomerates, we address the theoretical basis for this effect by applying the theory of small angle Rayleigh-Debye-Gans light scattering to oriented nano-clusters generated by classical diffusion–limited cluster-cluster aggregation (DLCA). Based on more than 100 nano-clusters with 30 monomers and with 100 monomers, the ratio of the slopes of the inverse of the structure factor vs. the momentum transfer squared (S(q)ˉ¹ vs. q² ) for the partially aligned (aligned along the major axis but free to rotate about that axis) and randomly oriented clusters is well correlated with a linear fit to the shape anisotropy, defined as the ratio of the square of the major to minor principle radii of gyration. It is also shown that state of the art small-angle aerosol scattering measurements would have the angular resolution required to measure the shape anisotropy with 30 to 1000 nano-monomers with a size parameter of 0.15. For large q for nano-clusters with 30 to1000 monomers, it is shown from the simulations that S(q) for the partially aligned clusters is not proportional to q[suberscript -Df] , where D[subscript f] is the fractal dimension, as it is for randomly oriented clusters. Nano-clusters with a fixed orientation are shown to result in a structure factor with multiple peaks, which could be used to obtain more detailed information about particle structure than shape anisotropy. The measurements reported in the literature showing enhanced scattering for partially aligned soot agglomerates were for angle integrated measurements. Calculation of the integrated light scattering cross section for the same range of angles and polarization direction as the experiments indicate a significant enhancement of 70 % and 120 % for two representative aspect ratios. The smaller value overlaps with measured values of the scattering enhancement for oriented soot agglomerates in an electric field.