Revised scattering exponents for a power-law distribution of surface and mass fractals

We consider scattering exponents arising in small-angle scattering from power-law polydisperse surface and mass fractals. It is shown that a set of fractals, whose sizes are distributed according to a power law, can change its fractal dimension when the power-law exponent is sufficiently big. As a result, the scattering exponent corresponding to this dimension appears due to the spatial correlations between positions of different fractals. For large values of the momentum transfer, the correlations do not play any role, and the resulting scattering intensity is given by a sum of intensities of all composing fractals. The restrictions imposed on the power-law exponents are found. The obtained results generalize Martin's formulas for the scattering exponents of the polydisperse fractals.

Automated summary

This article considers the scattering exponents in small-angle scattering from power-law polydisperse surface and mass fractals. It is demonstrated that a set of fractals, with sizes distributed according to a power law, can alter its fractal dimension when the power-law exponent is sufficiently large. Consequently, a scattering exponent corresponding to this dimension arises due to spatial correlations among the positions of different fractals. For high values of momentum transfer, the correlations have no impact, and the resulting scattering intensity is determined by the sum of intensities of all constituent fractals. Restrictions on the power-law exponents are identified. The obtained results generalize Martin's formulas for the scattering exponents of polydisperse fractals.