Q-space analysis of the orientationally averaged light scattering by particles of various shapes

Abstract

The scaling approach for determining the orientationally averaged light scattering in the 3d Rayleigh-Debye-Gans diffraction limit is reviewed and extended, and applied to spheroids, cylinders, hexagonal prisms, rectangular prisms, Gaussian random spheres, and droxtals. It will be shown that the scaling approach is not only able to predict the power laws that describe the diffractive light scattering by a variety of shapes, but also the coefficients to the power laws. It will also be demonstrated that the scaling approach is able to identify the crossover points between distinct scattering regimes with different power laws, due extreme aspect ratios. Application of the scaling approach to inhomogeneous spheres, and the effects on the scattering will also be demonstrated. The internal coupling parameter ρ' for any arbitrary shape will be derived and a numerical approach for calculating ρ' and the proper Rayleigh normalization for any arbitrary shape will be presented. The Rayleigh normalized orientationally averaged light scattered by spheroids, cylinders, hexagonal prisms, rectangular prisms, Gaussian random spheres, and droxtals was systematically studied. It will be shown that despite having different shapes, aspect ratios, refractive indexes, and sizes, there is an overall description of how particles scatter light. The internal coupling parameter ρ' will be shown to describe the region that the light scattering is in from the 3d Rayleigh-Debye-Gans diffraction limit to the 2d Rayleigh-Debye-Gans diffraction limit. It will also be shown that when the light scattering is in the 2d Rayleigh-Debye-Gans diffraction limit, ρ' describes the separation between the diffraction dominated region and the refraction dominated region of the scattering in q-space. Finally, it will be shown that the absorption parameter κkR, where κ is the imaginary part of the refractive index, and kR is the size parameter, is a universal parameter that describes the reduction in the refractive effects, such as the refraction hump, generalized rainbows, and glories in the scattered light as the absorption increases.