source: sasmodels/sasmodels/models/gel_fit.py @ ef07e95

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since ef07e95 was 2d81cfe, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

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1r"""
2*This model was implemented by an interested user!*
3
4Unlike a concentrated polymer solution, the fine-scale polymer distribution
5in a gel involves at least two characteristic length scales,
6a shorter correlation length ( $a1$ ) to describe the rapid fluctuations
7in the position of the polymer chains that ensure thermodynamic equilibrium,
8and a longer distance (denoted here as $a2$ ) needed to account for the static
9accumulations of polymer pinned down by junction points or clusters of such
10points. The latter is derived from a simple Guinier function. Compare also the
11gauss_lorentz_gel model.
12
13
14Definition
15----------
16
17The scattered intensity $I(q)$ is calculated as
18
19.. math::
20
21    I(Q) = I(0)_L \frac{1}{\left( 1+\left[ ((D+1/3)Q^2a_{1}^2
22    \right]\right)^{D/2}} + I(0)_G exp\left( -Q^2a_{2}^2\right) + B
23
24where
25
26.. math::
27
28    a_{2}^2 \approx \frac{R_{g}^2}{3}
29
30Note that the first term reduces to the Ornstein-Zernicke equation
31when $D = 2$; ie, when the Flory exponent is 0.5 (theta conditions).
32In gels with significant hydrogen bonding $D$ has been reported to be
33~2.6 to 2.8.
34
35
36References
37----------
38
39Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C Han,
40*J. Chem. Phys.* 1992, 97 (9), 6829-6841
41
42Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R Rennie, Erik Geissler,
43*Macromolecules* 1991, 24, 543-548
44"""
45
46import numpy as np
47from numpy import inf
48
49name = "gel_fit"
50title = "Fitting using fine-scale polymer distribution in a gel."
51description = """\
52    Structure factor for interacting particles:
53
54    Shibayama-Geissler Two-Length Scale Fit for Gels (GelFit)
55
56    Shibayama; Tanaka; Han J Chem Phys (1992), 97(9), 6829-6841
57    Mallam; Horkay; Hecht; Rennie; Geissler, Macromol (1991), 24, 543
58"""
59category = "shape-independent"
60
61# pylint: disable=bad-whitespace, line-too-long
62#             ["name", "units", default, [lower, upper], "type","description"],
63parameters = [["guinier_scale",    "cm^-1",   1.7, [-inf, inf], "", "Guinier length scale"],
64              ["lorentz_scale", "cm^-1",   3.5, [-inf, inf], "", "Lorentzian length scale"],
65              ["rg",  "Ang",     104.0, [2, inf],    "", "Radius of gyration"],
66              ["fractal_dim",      "",          2.0, [0, inf],    "", "Fractal exponent"],
67              ["cor_length",       "Ang",      16.0, [0, inf],    "", "Correlation length"]
68             ]
69# pylint: enable=bad-whitespace, line-too-long
70
71source = ["gel_fit.c"]
72
73def random():
74    guinier_scale = 10**np.random.uniform(1, 3)
75    lorentz_scale = 10**np.random.uniform(1, 3)
76    rg = 10**np.random.uniform(1, 5)
77    fractal_dim = np.random.uniform(0, 6)
78    cor_length = 10**np.random.uniform(0, 3)
79    pars = dict(
80        #background=0,
81        scale=1,
82        guinier_scale=guinier_scale,
83        lorentz_scale=lorentz_scale,
84        rg=rg,
85        fractal_dim=fractal_dim,
86        cor_length=cor_length
87    )
88    return pars
89
90demo = dict(background=0.01,
91            guinier_scale=1.7,
92            lorentz_scale=3.5,
93            rg=104,
94            fractal_dim=2.0,
95            cor_length=16.0)
96
97tests = [[{'guinier_scale': 1.0,
98           'lorentz_scale': 1.0,
99           'rg': 10.0,
100           'fractal_dim': 10.0,
101           'cor_length': 20.0,
102           'background': 0.0,
103          }, 0.1, 0.716532],
104
105         [{'guinier_scale': 4.0,
106           'lorentz_scale': 10.0,
107           'rg': 500.0,
108           'fractal_dim': 1.0,
109           'cor_length': 20.0,
110           'background': 20.0,
111          }, 5.0, 20.1224653026],
112        ]
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