Small-angle X-ray scattering is an important method for studying the structure of fractals and other disordered systems on a scale of lengths from about 1 to 200 nm. This review begins with a short outline of some properties of fractals. Next the X-ray scattering from fractal systems is discussed. The intensity of small-angle scattering from fractals and other disordered systems often obeys so called power-law scattering. According to this, the scattering intensity is proportional to a negative power of the quantity s equals 4(pi) (lambda) -1sin(theta) , where 2(theta) is the scattering angle and (lambda) is the X-ray wavelength. From the magnitude of the exponent much important information can be obtained. To illustrate the scattering from fractals, several experimental investigations of surface fractals in styrene based ionomers are reviewed.
"Fractal structure of polymer particles", Proc. SPIE 3095, X-Ray Investigations of Polymer Structures, (18 February 1997); doi: 10.1117/12.267198; https://doi.org/10.1117/12.267198