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

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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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1r"""
2Definition
3----------
4
5This model describes the scattering from a layer of surfactant or polymer
6adsorbed on large, smooth, notionally spherical particles under the conditions
7that (i) the particles (cores) are contrast-matched to the dispersion medium,
8(ii) $S(Q) \sim 1$ (ie, the particle volume fraction is dilute), (iii) the
9particle radius is >> layer thickness (ie, the interface is locally flat),
10and (iv) scattering from excess unadsorbed adsorbate in the bulk medium is
11absent or has been corrected for.
12
13Unlike many other core-shell models, this model does not assume any form
14for the density distribution of the adsorbed species normal to the interface
15(cf, a core-shell model normally assumes the density distribution to be a
16homogeneous step-function). For comparison, if the thickness of a (traditional
17core-shell like) step function distribution is $t$, the second moment about
18the mean of the density distribution (ie, the distance of the centre-of-mass
19of the distribution from the interface), $\sigma = \sqrt{t^2/12}$.
20
21.. math::
22
23     I(q) = \text{scale} \cdot (\rho_\text{poly}-\rho_\text{solvent})^2
24         \left[
25             \frac{6\pi\phi_\text{core}}{Q^2}
26             \frac{\Gamma^2}{\delta_\text{poly}^2R_\text{core}}
27             \exp(-Q^2\sigma^2)
28         \right] + \text{background}
29
30where *scale* is a scale factor, $\rho_\text{poly}$ is the sld of the
31polymer (or surfactant) layer, $\rho_\text{solv}$ is the sld of the
32solvent/medium and cores, $\phi_\text{core}$ is the volume fraction of
33the core particles, $\delta_\text{poly}$ is the bulk density of the
34polymer, $\Gamma$ is the adsorbed amount, and $\sigma$ is the second
35moment of the thickness distribution.
36
37Note that all parameters except $\sigma$ are correlated so fitting more
38than one of these parameters will generally fail. Also note that unlike
39other shape models, no volume normalization is applied to this model (the
40calculation is exact).
41
42The code for this model is based originally on a a fortran implementation by
43Steve King at ISIS in the SANDRA package c. 1990.
44
45References
46----------
47
48.. [#] S King, P Griffiths, J Hone, and T Cosgrove, *SANS from Adsorbed Polymer
49   Layers*, *Macromol. Symp.*, 190 (2002) 33-42.
50
51Source
52------
53
54`adsorbed_layer.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/adsorbed_layer.py>`_
55
56Authorship and Verification
57----------------------------
58
59* **Author:** Jae-Hi Cho **Date:** pre 2010
60* **Last Modified by:** Paul Kienzle **Date:** April 14, 2016
61* **Last Reviewed by:** Steve King **Date:** March 18, 2016
62* **Source added by :** Steve King **Date:** March 25, 2019
63"""
64
65import numpy as np
66from numpy import inf, pi, exp, errstate
67
68name = "adsorbed_layer"
69title = "Scattering from an adsorbed layer on particles"
70
71description = """
72    Evaluates the scattering from large particles
73    with an adsorbed layer of surfactant or
74    polymer, independent of the form of the
75    density distribution.
76    """
77category = "shape:sphere"
78
79# pylint: disable=bad-whitespace, line-too-long
80#   ["name", "units", default, [lower, upper], "type", "description"],
81parameters = [
82    ["second_moment", "Ang", 23.0, [0.0, inf], "", "Second moment of polymer distribution"],
83    ["adsorbed_amount", "mg/m^2", 1.9, [0.0, inf], "", "Adsorbed amount of polymer"],
84    ["density_shell", "g/cm^3", 0.7, [0.0, inf], "", "Bulk density of polymer in the shell"],
85    ["radius", "Ang", 500.0, [0.0, inf], "", "Core particle radius"],
86    ["volfraction", "None", 0.14, [0.0, inf], "", "Core particle volume fraction"],
87    ["sld_shell", "1e-6/Ang^2", 1.5, [-inf, inf], "sld", "Polymer shell SLD"],
88    ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent SLD"],
89]
90# pylint: enable=bad-whitespace, line-too-long
91
92# NB: Scale and Background are implicit parameters on every model
93def Iq(q, second_moment, adsorbed_amount, density_shell, radius,
94       volfraction, sld_shell, sld_solvent):
95    """Return I(q) for adsorbed layer model."""
96    with errstate(divide='ignore'):
97        aa = ((sld_shell - sld_solvent)/density_shell * adsorbed_amount) / q
98    bb = q * second_moment
99    #scale by 10^-2 for units conversion to cm^-1
100    inten = 6.0e-02 * pi * volfraction * aa**2 * exp(-bb**2) / radius
101    return inten
102Iq.vectorized = True  # Iq accepts an array of q values
103
104def random():
105    """Return a random parameter set for the model."""
106    # only care about the value of second_moment:
107    #    curve = scale * e**(-second_moment^2 q^2)/q^2
108    #    scale = 6 pi/100 (contrast/density*absorbed_amount)^2 * Vf/radius
109    # the remaining parameters can be randomly generated from zero to
110    # twice the default value as done by default in compare.py
111    pars = dict(
112        scale=1,
113        second_moment=10**np.random.uniform(1, 3),
114    )
115    return pars
116
117# unit test values taken from SasView 3.1.2
118tests = [
119    [{'scale': 1.0, 'second_moment': 23.0, 'adsorbed_amount': 1.9,
120      'density_shell': 0.7, 'radius': 500.0, 'volfraction': 0.14,
121      'sld_shell': 1.5, 'sld_solvent': 6.3, 'background': 0.0},
122     [0.0106939, 0.1], [73.741, 4.51684e-3]],
123]
124
125# 2016-03-16 SMK converted from sasview, checked vs SANDRA
126# 2016-03-18 RKH some edits & renaming
127# 2016-04-14 PAK reformatting
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