Small-angle X-ray scattering of two-phase systems: significance of polydispersity

Abstract

Evaluation of the small-angle X-ray scattering of two-phase systems leads to the determination of the Porod lengthlpand the correlation lengthlc. In dilute systems, the parameter κl=lc/lp− 1 is a measure of the polydispersity of the chord lengthslwithin the dilute phase, which depends on the size distribution and the shape of the particles forming this phase. As an example, the change of κlwith the size distribution is calculated for spheres and spheroids. For dense two-phase systems, κldepends not only on the polydispersities of the chord lengthsl1andl2of the two phases but also on the spatial order in the system. This is demonstrated by examples related to microemulsions. The appendix contains a short discussion on the relationship between chord-length distributions and Bertrand's paradox.