Changeset 4f9e288 in sasmodels


Ignore:
Timestamp:
Mar 12, 2017 10:39:37 PM (2 years ago)
Author:
butler
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

Legend:

Unmodified
Added
Removed
  • sasmodels/models/rpa.py

    reb63414 r4f9e288  
    3030    These case numbers are different from those in the NIST SANS package! 
    3131 
     32The models are based on the papers by Akcasu et al. [#Akcasu]_ and by 
     33Hammouda [#Hammouda]_ assuming the polymer follows Gaussian statistics such 
     34that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is 
     35the number of statistical segment lengths. A nice tutorial on how these are 
     36constructed and implemented can be found in chapters 28 and 39 of Boualem 
     37Hammouda's 'SANS Toolbox'[#toolbox]_. 
     38 
     39In brief the macroscopic cross sections are derived from the general forms 
     40for homopolymer scattering and the multiblock cross-terms while the inter 
     41polymer cross terms are described in the usual way by the $\chi$ parameter. 
     42 
    3243USAGE NOTES: 
    3344 
     
    3950  for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`. 
    4051* 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). 
    4661 
    4762 
     
    4964---------- 
    5065 
    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 
     71Authorship 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 
    5278""" 
    5379 
Note: See TracChangeset for help on using the changeset viewer.