source: sasmodels/sasmodels/models/mono_gauss_coil.py @ c5f7aa9

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Last change on this file since c5f7aa9 was c5f7aa9, checked in by richardh, 13 months ago

changed ER option name in mono_gauss_coil

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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
47P Debye, *J. Phys. Colloid. Chem.*, 51 (1947) 18.
48
49R J Roe, *Methods of X-Ray and Neutron Scattering in Polymer Science*,
50Oxford University Press, New York (2000).
51
52http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf
53"""
54
55import numpy as np
56from numpy import inf
57
58name = "mono_gauss_coil"
59title = "Scattering from monodisperse polymer coils"
60
61description = """
62    Evaluates the scattering from
63    monodisperse polymer chains.
64    """
65category = "shape-independent"
66
67# pylint: disable=bad-whitespace, line-too-long
68#   ["name", "units", default, [lower, upper], "type", "description"],
69parameters = [
70    ["i_zero", "1/cm", 70.0, [0.0, inf], "", "Intensity at q=0"],
71    ["rg", "Ang", 75.0, [0.0, inf], "volume", "Radius of gyration"],
72    ]
73# pylint: enable=bad-whitespace, line-too-long
74
75source = ["mono_gauss_coil.c"]
76have_Fq = False
77effective_radius_type = ["R_g", "2R_g", "3R_g", "sqrt(5/3)*R_g"]
78
79
80def random():
81    rg = 10**np.random.uniform(0, 4)
82    #rg = 1e3
83    pars = dict(
84        #scale=1, background=0,
85        i_zero=1e7, # i_zero is a simple scale
86        rg=rg,
87    )
88    return pars
89
90demo = dict(scale=1.0, i_zero=70.0, rg=75.0, background=0.0)
91
92# these unit test values taken from SasView 3.1.2
93tests = [
94    [{'scale': 1.0, 'i_zero': 70.0, 'rg': 75.0, 'background': 0.0},
95     [0.0106939, 0.469418], [57.1241, 0.112859]],
96    ]
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