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Small‐angle X‐ray scattering of two‐phase systems: significance of polydispersity
Author(s) -
Ruland Wilhelm
Publication year - 2010
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889810031973
Subject(s) - dispersity , chord (peer to peer) , small angle scattering , scattering , microemulsion , small angle x ray scattering , spheres , phase (matter) , hard spheres , physics , chemistry , materials science , optics , thermodynamics , quantum mechanics , polymer chemistry , pulmonary surfactant , distributed computing , astronomy , computer science
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.