# Changeset 4f9e288 in sasmodels

Ignore:
Timestamp:
Mar 12, 2017 10:39:37 PM (3 years ago)
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
5d23de2
Parents:
5e2fd41
Message:

update RPA documentation

File:
1 edited

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Unmodified
 reb63414 These case numbers are different from those in the NIST SANS package! The models are based on the papers by Akcasu et al. [#Akcasu]_ and by Hammouda [#Hammouda]_ assuming the polymer follows Gaussian statistics such that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is the number of statistical segment lengths. A nice tutorial on how these are constructed and implemented can be found in chapters 28 and 39 of Boualem Hammouda's 'SANS Toolbox'[#toolbox]_. In brief the macroscopic cross sections are derived from the general forms for homopolymer scattering and the multiblock cross-terms while the inter polymer cross terms are described in the usual way by the $\chi$ parameter. USAGE NOTES: for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:2. * Depending on which case is being used, the number of fitting parameters can vary.  Note that in general the degrees of polymerization, the volume fractions, the molar volumes, and the neutron scattering lengths for each component are obtained from other methods and held fixed while the segment lengths (b\ :sub:a, b\ :sub:b, etc) and $\chi$ parameters (K\ :sub:ab, K\ :sub:ac, etc). The *scale* parameter should be held equal to unity. vary. .. Note:: * In general the degrees of polymerization, the volume fractions, the molar volumes, and the neutron scattering lengths for each component are obtained from other methods and held fixed while The *scale* parameter should be held equal to unity. * The variables are normally the segment lengths (b\ :sub:a, b\ :sub:b, etc) and $\chi$ parameters (K\ :sub:ab, K\ :sub:ac, etc). ---------- .. [#] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136 .. [#Akcasu] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136. .. [#Hammouda] B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. .. [#toolbox] https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf Authorship and Verification ---------------------------- * **Author:** Boualem Hammouda - NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Paul Kienzle **Date:** July 18, 2016 * **Last Modified by:** Paul Butler **Date:** March 12, 2017 * **Last Reviewed by:** Paul Butler **Date:** March 12, 2017 """