We consider the large ${\mathrm{qR}}_g,$ where q is the magnitude of the scattering wave vector and $R_g$ is the aggregate radius of gyration, part of the structure factor of fractal aggregates, and quantify the coefficient C of the power law, $S\left(q\right)\mathrm{}\sim {C(qR}_g{)}^{-D},$ where D is the fractal dimension, for various structure factors proposed in the literature. With the aid of earlier work, we conclude the most accurate structure factors have $C=\mathrm{1.0.}\mathrm{}$ We then calculate the effects of polydispersity on this coefficient, and show the effects are significant, enough so to allow a measurement of the distribution width. These concepts are accurately supported with scattering data from a diffusion limited aerosol and a reaction limited colloid.

• Received 18 February 1999

DOI:https://doi.org/10.1103/PhysRevE.60.7143