Changeset d439007 in sasmodels

Timestamp:

Aug 26, 2017 8:16:53 PM (7 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:

33e475a

Parents:

997c9ca

Message:

Corrected errors in star_polymer documentation identified by MN student
checked carefully against code, benoit paper and Richter paper cited in
ticket. Also took the opportuinty to generally udated and standardize
the documentation as per ongoing process addresses #646. fixes #962

File:

• sasmodels/models/star_polymer.py (modified) (5 diffs)

sasmodels/models/star_polymer.py

@@ -1 +1 @@
 r"""
-The Benoit model for a simple star polymer, with Gaussian coils arms from
-a common point.
-
 Definition
 ----------
+
+Calcuates the scattering from a simple star polymer with f equal Gaussian coil
+arms. A star being defined as a branched polymer with all the branches
+emanating from a common central (in the case of this model) point.  It is
+derived as a special case of on the Benoit model for general branched
+polymers\ [#CITBenoit]_ as also used by Richter ''et. al.''\ [#CITRichter]_
 
 For a star with $f$ arms the scattering intensity $I(q)$ is calculated as
@@ -15 +18 @@
 where
 
-.. math:: v=\frac{u^2f}{(3f-2)}
+.. math:: v=\frac{uf}{(3f-2)}
 
 and
@@ -21 +24 @@
 .. math:: u = \left\langle R_{g}^2\right\rangle q^2
 
-contains the square of the ensemble average radius-of-gyration of an arm.
+contains the square of the ensemble average radius-of-gyration of the full
+polymer while v contains the radius of gyration of a single arm $R_{arm}$.
+The two are related as:
+
+.. math:: R_{arm}^2 = \frac{f}{3f-2} R_{g}^2
+
 Note that when there is only one arm, $f = 1$, the Debye Gaussian coil
-equation is recovered. Star polymers in solutions tend to have strong
-interparticle and osmotic effects, so the Benoit equation may not work well.
-At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms
-of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil` model.
+equation is recovered.
+
+.. note::
+   Star polymers in solutions tend to have strong interparticle and osmotic
+   effects. Thus the Benoit equation may not work well for many real cases.
+   At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms
+   of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil`
+   model. A newer model for star polymer incorporating excluded volume has been
+   developed by Li et al in arXiv:1404.6269 [physics.chem-ph].
 
 References
 ----------
 
-H Benoit *J. Polymer Science*, 11, 596-599 (1953)
+.. [#CITBenoit] H Benoit *J. Polymer Science*, 11, 507-510 (1953)
+.. [#CITRichter] D Richter, B. Farago, J. S. Huang, L. J. Fetters,
+   B Ewen *Macromolecules*, 22, 468-472 (1989)
+
+Authorship and Verification
+----------------------------
+
+* **Author:** Kieran Campbell **Date:** July 24, 2012
+* **Last Modified by:** Paul Butler **Date:** Auguts 26, 2017
+* **Last Reviewed by:** Ziang Li and Richard Heenan **Date:** May 17, 2017
 """
 
@@ -45 +67 @@
         - v = u^2f/(3f-2)
         - u = <R_g^2>q^2, where <R_g^2> is the ensemble average radius of
-        gyration squared of an arm
+        gyration squared of the entire polymer
         - f is the number of arms on the star
+        - the radius of gyration of an arm is given b
+        Rg_arm^2 = R_g^2 * f/(3f-2)
         """
 category = "shape-independent"
@@ -52 +76 @@
 # pylint: disable=bad-whitespace, line-too-long
 #             ["name", "units", default, [lower, upper], "type","description"],
-parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of an arm"],
+parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of the full polymer"],
               ["arms",    "",      3,   [1.0, 6.0], "", "Number of arms in the model"],
              ]