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Investigation of non‐ideal two‐phase polymer structures by small‐angle X‐ray scattering
Author(s) -
Vonk C. G.
Publication year - 1973
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/s0021889873008204
Subject(s) - small angle x ray scattering , scattering , reciprocal lattice , intensity (physics) , isotropy , small angle scattering , phase (matter) , materials science , radial distribution function , correlation function (quantum field theory) , molecular physics , physics , crystallography , diffraction , optics , chemistry , quantum mechanics , dielectric , molecular dynamics , optoelectronics
The mean square of the electron‐density gradient, 〈|grad η| 2 〉 in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ∫ s 4 I ( s )d s , as well as to the second derivative of the correlation function in the origin. In the case of two‐phase structures with unsharp phase boundaries, these relations may be used to find the thickness E of the transition regions. As was shown by Ruland [ J. Appl. Cryst. (1971). 4 , 70–73] E can also be determined by analysis of the intensity in the tail of the SAXS pattern. This approach is used here to investigate the effect of E on the one‐dimensional correlation function. In the application of both methods, separation of the SAXS intensity from the continuous background of liquid scattering constitutes a critical step. A procedure in which the background is represented by a curve of the type a + bs n , where n is an even number, is found to work well for a number of polymers.