Changeset 33e475a in sasmodels for sasmodels/models
- Timestamp:
- Aug 26, 2017 8:17:30 PM (7 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:
- 573ffab
- Parents:
- d439007 (diff), bedb9b0 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent. - Location:
- sasmodels/models
- Files:
-
- 2 edited
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- Unmodified
- Added
- Removed
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sasmodels/models/multilayer_vesicle.py
r5d23de2 r870a2f4 71 71 sufficiently fine grained in certain cases. Please report any such occurences 72 72 to the SasView team. Generally, for the best possible experience: 73 * Start with the best possible guess 74 * Using a priori knowledge, hold as many parameters fixed as possible 75 * if N=1, tw (water thickness) must by definition be zero. Both N and tw should 73 74 - Start with the best possible guess 75 - Using a priori knowledge, hold as many parameters fixed as possible 76 - if N=1, tw (water thickness) must by definition be zero. Both N and tw should 76 77 be fixed during fitting. 77 *If N>1, use constraints to keep N > 178 *Because N only really moves in integer steps, it may get "stuck" if the78 - If N>1, use constraints to keep N > 1 79 - Because N only really moves in integer steps, it may get "stuck" if the 79 80 optimizer step size is too small so care should be taken 80 81 If you experience problems with this please contact the SasView team and let -
sasmodels/models/star_polymer.py
r40a87fa rd439007 1 1 r""" 2 The Benoit model for a simple star polymer, with Gaussian coils arms from3 a common point.4 5 2 Definition 6 3 ---------- 4 5 Calcuates the scattering from a simple star polymer with f equal Gaussian coil 6 arms. A star being defined as a branched polymer with all the branches 7 emanating from a common central (in the case of this model) point. It is 8 derived as a special case of on the Benoit model for general branched 9 polymers\ [#CITBenoit]_ as also used by Richter ''et. al.''\ [#CITRichter]_ 7 10 8 11 For a star with $f$ arms the scattering intensity $I(q)$ is calculated as … … 15 18 where 16 19 17 .. math:: v=\frac{u ^2f}{(3f-2)}20 .. math:: v=\frac{uf}{(3f-2)} 18 21 19 22 and … … 21 24 .. math:: u = \left\langle R_{g}^2\right\rangle q^2 22 25 23 contains the square of the ensemble average radius-of-gyration of an arm. 26 contains the square of the ensemble average radius-of-gyration of the full 27 polymer while v contains the radius of gyration of a single arm $R_{arm}$. 28 The two are related as: 29 30 .. math:: R_{arm}^2 = \frac{f}{3f-2} R_{g}^2 31 24 32 Note that when there is only one arm, $f = 1$, the Debye Gaussian coil 25 equation is recovered. Star polymers in solutions tend to have strong 26 interparticle and osmotic effects, so the Benoit equation may not work well. 27 At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms 28 of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil` model. 33 equation is recovered. 34 35 .. note:: 36 Star polymers in solutions tend to have strong interparticle and osmotic 37 effects. Thus the Benoit equation may not work well for many real cases. 38 At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms 39 of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil` 40 model. A newer model for star polymer incorporating excluded volume has been 41 developed by Li et al in arXiv:1404.6269 [physics.chem-ph]. 29 42 30 43 References 31 44 ---------- 32 45 33 H Benoit *J. Polymer Science*, 11, 596-599 (1953) 46 .. [#CITBenoit] H Benoit *J. Polymer Science*, 11, 507-510 (1953) 47 .. [#CITRichter] D Richter, B. Farago, J. S. Huang, L. J. Fetters, 48 B Ewen *Macromolecules*, 22, 468-472 (1989) 49 50 Authorship and Verification 51 ---------------------------- 52 53 * **Author:** Kieran Campbell **Date:** July 24, 2012 54 * **Last Modified by:** Paul Butler **Date:** Auguts 26, 2017 55 * **Last Reviewed by:** Ziang Li and Richard Heenan **Date:** May 17, 2017 34 56 """ 35 57 … … 45 67 - v = u^2f/(3f-2) 46 68 - u = <R_g^2>q^2, where <R_g^2> is the ensemble average radius of 47 gyration squared of an arm69 gyration squared of the entire polymer 48 70 - f is the number of arms on the star 71 - the radius of gyration of an arm is given b 72 Rg_arm^2 = R_g^2 * f/(3f-2) 49 73 """ 50 74 category = "shape-independent" … … 52 76 # pylint: disable=bad-whitespace, line-too-long 53 77 # ["name", "units", default, [lower, upper], "type","description"], 54 parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of an arm"],78 parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of the full polymer"], 55 79 ["arms", "", 3, [1.0, 6.0], "", "Number of arms in the model"], 56 80 ]
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