Changeset 40a87fa in sasmodels for sasmodels/models/star_polymer.py
- Timestamp:
- Aug 8, 2016 9:24:11 AM (8 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 2472141
- Parents:
- 2d65d51
- File:
-
- 1 edited
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sasmodels/models/star_polymer.py
rec45c4f r40a87fa 1 1 r""" 2 The Benoit model for a simple star polymer, with Gaussian coils arms from 2 The Benoit model for a simple star polymer, with Gaussian coils arms from 3 3 a common point. 4 4 … … 10 10 .. math:: 11 11 12 I(q) = \frac{2}{fv^2}\left[ v-1+ exp(-v)+\frac{f-1}{2}13 \left[ 1- exp(-v)\right]^2\right]12 I(q) = \frac{2}{fv^2}\left[ v-1+\exp(-v)+\frac{f-1}{2} 13 \left[ 1-\exp(-v)\right]^2\right] 14 14 15 15 where 16 16 17 .. math:: 18 19 v=\frac{u^2f}{(3f-2)} 17 .. math:: v=\frac{u^2f}{(3f-2)} 20 18 21 19 and 22 20 23 .. math:: 21 .. math:: u = \left\langle R_{g}^2\right\rangle q^2 24 22 25 u = \left\langle R_{g}^2\right\rangle q^2 26 27 contains the square of the ensemble average radius-of-gyration of an arm. Note that 28 when there is only one arm, $f$ = 1, the Debye Gaussian coil equation is recovered. 29 Star polymers in solutions tend to have strong interparticle and osmotic effects, so 30 the Benoit equation may not work well. At small q the Guinier term and hence I(q=0) 31 is the same as for $f$ arms of radius of gyration $R_g$, as described for the :ref:`mono_gauss_coil <mono-gauss-coil>`. 32 23 contains the square of the ensemble average radius-of-gyration of an arm. 24 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 29 34 30 References … … 36 32 37 33 H Benoit *J. Polymer Science*, 11, 596-599 (1953) 38 39 40 34 """ 41 35
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