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 l 1 and l 2 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.