Size distribution effect on the power law regime of the structure factor of fractal aggregates

We consider the large 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(q) similar to 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=1.0. 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. [S1063-651X(99)05112-0].