Journal
ISRAEL JOURNAL OF CHEMISTRY
Volume 56, Issue 8, Pages 622-628Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/ijch.201500037
Keywords
density functional calculations; generalized electron density; SAXS; self-assembly; solution X-ray scattering
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Funding
- Israel Science Foundation [1372/13]
- US-Israel Binational Science Foundation [2009271]
- Israel Ministry of Economy
- Planning and Budgeting Committee of the Israel Council of Higher Education
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We present a method to calculate solution X-ray scattering form-factors of various geometries with generalized electron density and polydispersity profiles. We create arbitrary and physically relevant electron density profiles using a set of smooth hyperbolic tangent functions. To numerically calculate arbitrary electron density profiles, we formulate an algorithm that adaptively transforms the functions to a series of uniform discrete steps. We solve the models both numerically and analytically for the case of multiple spherical shells and compare the results to show the consistency of the algorithm. Other geometries are solved numerically. Various form-factors are analysed and compared with earlier results. We then compare polydispersity probability density functions (uniform, normal, and Cauchy distributions) of concentric hollow cylinder thicknesses. The relationship of the shape of arbitrary electron density profiles to the features of the scattering form-factor is discussed.
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