source: sasmodels/sasmodels/models/mono_gauss_coil.py @ 0507e09

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Last change on this file since 0507e09 was 0507e09, checked in by smk78, 5 months ago

Added link to source code to each model. Closes #883

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1#mono_gauss_coil model
2#conversion of DebyeModel.py
3#converted by Steve King, Mar 2016
4r"""
5This Debye Gaussian coil model strictly describes the scattering from
6*monodisperse* polymer chains in theta solvents or polymer melts, conditions
7under which the distances between segments follow a Gaussian distribution.
8Provided the number of segments is large (ie, high molecular weight polymers)
9the single-chain form factor P(Q) is that described by Debye (1947).
10
11To describe the scattering from *polydisperse* polymer chains see the
12:ref:`poly-gauss-coil` model.
13
14Definition
15----------
16
17.. math::
18
19     I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background}
20
21where
22
23.. math::
24
25     I_0 &= \phi_\text{poly} \cdot V
26            \cdot (\rho_\text{poly} - \rho_\text{solv})^2 \\
27     P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\
28     Z &= (q R_g)^2 \\
29     V &= M / (N_A \delta)
30
31Here, $\phi_\text{poly}$ is the volume fraction of polymer, $V$ is the
32volume of a polymer coil, *M* is the molecular weight of the polymer,
33$N_A$ is Avogadro's Number, $\delta$ is the bulk density of the polymer,
34$\rho_\text{poly}$ is the sld of the polymer, $\rho\text{solv}$ is the
35sld of the solvent, and $R_g$ is the radius of gyration of the polymer coil.
36
37The 2D scattering intensity is calculated in the same way as the 1D,
38but where the *q* vector is redefined as
39
40.. math::
41
42    q = \sqrt{q_x^2 + q_y^2}
43
44References
45----------
46
47.. [#] P Debye, *J. Phys. Colloid. Chem.*, 51 (1947) 18.
48.. [#] R J Roe, *Methods of X-Ray and Neutron Scattering in Polymer Science*, Oxford University Press, New York (2000).
49.. [#] http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf
50
51Source
52------
53
54`mono_gauss_coil.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/mono_gauss_coil.py>`_
55
56`mono_gauss_coil.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/mono_gauss_coil.c>`_
57
58Authorship and Verification
59----------------------------
60
61* **Author:**
62* **Last Modified by:**
63* **Last Reviewed by:**
64* **Source added by :** Steve King **Date:** March 25, 2019"""
65
66import numpy as np
67from numpy import inf
68
69name = "mono_gauss_coil"
70title = "Scattering from monodisperse polymer coils"
71
72description = """
73    Evaluates the scattering from
74    monodisperse polymer chains.
75    """
76category = "shape-independent"
77
78# pylint: disable=bad-whitespace, line-too-long
79#   ["name", "units", default, [lower, upper], "type", "description"],
80parameters = [
81    ["i_zero", "1/cm", 70.0, [0.0, inf], "", "Intensity at q=0"],
82    ["rg", "Ang", 75.0, [0.0, inf], "volume", "Radius of gyration"],
83    ]
84# pylint: enable=bad-whitespace, line-too-long
85
86source = ["mono_gauss_coil.c"]
87have_Fq = False
88effective_radius_type = ["R_g", "2R_g", "3R_g", "sqrt(5/3)*R_g"]
89
90
91def random():
92    """Return a random parameter set for the model."""
93    rg = 10**np.random.uniform(0, 4)
94    #rg = 1e3
95    pars = dict(
96        #scale=1, background=0,
97        i_zero=1e7, # i_zero is a simple scale
98        rg=rg,
99    )
100    return pars
101
102demo = dict(scale=1.0, i_zero=70.0, rg=75.0, background=0.0)
103
104# these unit test values taken from SasView 3.1.2
105tests = [
106    [{'scale': 1.0, 'i_zero': 70.0, 'rg': 75.0, 'background': 0.0},
107     [0.0106939, 0.469418], [57.1241, 0.112859]],
108    ]
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