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

Evaluation of the small-angle X-ray scattering of two-phase systems leads to the determination of the Porod length l_p and the correlation length l_c. In dilute systems, the parameter κ_l = l_c/l_p − 1 is a measure of the polydispersity of the chord lengths l within the dilute phase, which depends on the size distribution and the shape of the particles forming this phase. As an example, the change of κ_l with the size distribution is calculated for spheres and spheroids. For dense two-phase systems, κ_l depends not only on the polydispersities of the chord lengths l₁ and l₂ of 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.