source: sasmodels/sasmodels/models/star_polymer.py @ 58c3367

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 58c3367 was 40a87fa, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

lint and latex cleanup

  • Property mode set to 100644
File size: 2.2 KB
Line 
1r"""
2The Benoit model for a simple star polymer, with Gaussian coils arms from
3a common point.
4
5Definition
6----------
7
8For a star with $f$ arms the scattering intensity $I(q)$ is calculated as
9
10.. math::
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]
14
15where
16
17.. math:: v=\frac{u^2f}{(3f-2)}
18
19and
20
21.. math:: u = \left\langle R_{g}^2\right\rangle q^2
22
23contains the square of the ensemble average radius-of-gyration of an arm.
24Note that when there is only one arm, $f = 1$, the Debye Gaussian coil
25equation is recovered. Star polymers in solutions tend to have strong
26interparticle and osmotic effects, so the Benoit equation may not work well.
27At small $q$ the Guinier term and hence $I(q=0)$ is the same as for $f$ arms
28of radius of gyration $R_g$, as described for the :ref:`mono-gauss-coil` model.
29
30References
31----------
32
33H Benoit *J. Polymer Science*, 11, 596-599 (1953)
34"""
35
36from numpy import inf
37
38name = "star_polymer"
39title = "Star polymer model with Gaussian statistics"
40description = """
41        Benoit 'Star polymer with Gaussian statistics'
42        with
43        P(q) = 2/{fv^2} * (v - (1-exp(-v)) + {f-1}/2 * (1-exp(-v))^2)
44        where
45        - v = u^2f/(3f-2)
46        - u = <R_g^2>q^2, where <R_g^2> is the ensemble average radius of
47        gyration squared of an arm
48        - f is the number of arms on the star
49        """
50category = "shape-independent"
51single = False
52# pylint: disable=bad-whitespace, line-too-long
53#             ["name", "units", default, [lower, upper], "type","description"],
54parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of an arm"],
55              ["arms",    "",      3,   [1.0, 6.0], "", "Number of arms in the model"],
56             ]
57# pylint: enable=bad-whitespace, line-too-long
58
59source = ["star_polymer.c"]
60
61demo = dict(scale=1, background=0,
62            rg_squared=100.0,
63            arms=3.0)
64
65tests = [[{'rg_squared': 2.0,
66           'arms':    3.3,
67          }, 0.5, 0.851646091108],
68
69         [{'rg_squared':    1.0,
70           'arms':       2.0,
71           'background': 1.8,
72          }, 1.0, 2.53575888234],
73        ]
74# 23Mar2016  RKH edited docs, would this better use rg not rg^2 ? Numerical noise at extremely small q.rg
Note: See TracBrowser for help on using the repository browser.