Changeset 4f9e288 in sasmodels
 Timestamp:
 Mar 12, 2017 10:39:37 PM (2 years ago)
 Branches:
 master, core_shell_microgels, costrafo411, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 5d23de2
 Parents:
 5e2fd41
 File:

 1 edited
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sasmodels/models/rpa.py
reb63414 r4f9e288 30 30 These case numbers are different from those in the NIST SANS package! 31 31 32 The models are based on the papers by Akcasu et al. [#Akcasu]_ and by 33 Hammouda [#Hammouda]_ assuming the polymer follows Gaussian statistics such 34 that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is 35 the number of statistical segment lengths. A nice tutorial on how these are 36 constructed and implemented can be found in chapters 28 and 39 of Boualem 37 Hammouda's 'SANS Toolbox'[#toolbox]_. 38 39 In brief the macroscopic cross sections are derived from the general forms 40 for homopolymer scattering and the multiblock crossterms while the inter 41 polymer cross terms are described in the usual way by the $\chi$ parameter. 42 32 43 USAGE NOTES: 33 44 … … 39 50 for a C/D blend = [SLD(component C)  SLD(component D)]\ :sup:`2`. 40 51 * Depending on which case is being used, the number of fitting parameters can 41 vary. Note that in general the degrees of polymerization, the volume 42 fractions, the molar volumes, and the neutron scattering lengths for each 43 component are obtained from other methods and held fixed while the segment 44 lengths (b\ :sub:`a`, b\ :sub:`b`, etc) and $\chi$ parameters (K\ :sub:`ab`, 45 K\ :sub:`ac`, etc). The *scale* parameter should be held equal to unity. 52 vary. 53 54 .. Note:: 55 * In general the degrees of polymerization, the volume 56 fractions, the molar volumes, and the neutron scattering lengths for each 57 component are obtained from other methods and held fixed while The *scale* 58 parameter should be held equal to unity. 59 * The variables are normally the segment lengths (b\ :sub:`a`, b\ :sub:`b`, 60 etc) and $\chi$ parameters (K\ :sub:`ab`, K\ :sub:`ac`, etc). 46 61 47 62 … … 49 64  50 65 51 .. [#] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136 66 .. [#Akcasu] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 67 4136. 68 .. [#Hammouda] B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. 69 .. [#toolbox] https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf 70 71 Authorship and Verification 72  73 74 * **Author:** Boualem Hammouda  NIST IGOR/DANSE **Date:** pre 2010 75 * **Converted to sasmodels by:** Paul Kienzle **Date:** July 18, 2016 76 * **Last Modified by:** Paul Butler **Date:** March 12, 2017 77 * **Last Reviewed by:** Paul Butler **Date:** March 12, 2017 52 78 """ 53 79
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