Application of the scaling approach to particles having simple, fundamental shapes, in the Rayleigh–Debye–Gans diffraction limit

Abstract

Presented is a scaling approach for understanding features, such as power laws and crossover points, of the light scattered in the m → 1, ρ = 2kRveq|m − 1| < 1, Rayleigh–Debye–Gans diffraction limit. The scaling approach is based on comparison of the length scale of the scattering, which is the inverse of the scattering wave vector, and the various length scales of the scattering entity. It will be shown that the scaling approach correctly predicts the exponents of the power law regions and the locations of the first and second Guinier regimes which define the boundaries of the power laws. Furthermore, the scaling approach yields a semi-quantitative prediction of the coefficients of the power laws. These Guinier boundaries and power law coefficients are described by a single parameter, the aspect ratio of the scattering object.