Microscale Fragmentation and Small-Angle Scattering from Mass Fractals

Abstract

Using the small-angle scattering method, we calculate here the mono- and polydisperse structure factor from an idealized fragmentation model based on the concept of renormalization. The system consists of a large number of fractal microobjects which are randomly oriented and whose positions are uncorrelated. It is shown that, in the fractal region, the monodisperse form factor is characterized by a generalized power-law decay (i.e., a succession of maxima and minima superimposed on a simple power-law decay) and whose scattering exponent coincides with the fractal dimension of the scatterer. The present analysis of the scattering structure factor allows us to obtain the number of fragments resulted at a given iteration. The results could be used to obtain additional structural information about systems obtained through microscale fragmentation processes.