# source:sasmodels/sasmodels/models/hayter_msa.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, 9 months ago

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1# Note: model title and parameter table are inserted automatically
2r"""
3This calculates the structure factor (the Fourier transform of the pair
4correlation function $g(r)$) for a system of charged, spheroidal objects
5in a dielectric medium. When combined with an appropriate form factor
6(such as sphere, core+shell, ellipsoid, etc), this allows for inclusion
7of the interparticle interference effects due to screened coulomb repulsion
8between charged particles.
9
10**This routine only works for charged particles**. If the charge is set to
11zero the routine may self-destruct! For non-charged particles use a hard
12sphere potential.
13
14The salt concentration is used to compute the ionic strength of the solution
15which in turn is used to compute the Debye screening length. At present
16there is no provision for entering the ionic strength directly nor for use
17of any multivalent salts, though it should be possible to simulate the effect
18of this by increasing the salt concentration. The counterions are also
19assumed to be monovalent.
20
21In sasview the effective radius may be calculated from the parameters
22used in the form factor $P(q)$ that this $S(q)$ is combined with.
23
24The computation uses a Taylor series expansion at very small rescaled $qR$, to
25avoid some serious rounding error issues, this may result in a minor artefact
26in the transition region under some circumstances.
27
28For 2D data, the scattering intensity is calculated in the same way as 1D,
29where the $q$ vector is defined as
30
31.. math::
32
33    q = \sqrt{q_x^2 + q_y^2}
34
35
36References
37----------
38
39.. [#] J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118
40.. [#] J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656
41
42Source
43------
44
45hayter_msa.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/hayter_msa.py>_
46
47hayter_msa.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/hayter_msa.c>_
48
49Authorship and Verification
50----------------------------
51
52* **Author:**
54* **Last Reviewed by:**
55* **Source added by :** Steve King **Date:** March 25, 2019
56"""
57
58import numpy as np
59from numpy import inf
60
61category = "structure-factor"
62structure_factor = True
63single = False  # double precision only!
64
66#  dp = fabs(charge());
67#  dp = volfraction();
68#  dp = temperature();
69#  dp = concentration_salt();
70#  dp = dielectconst();
71
72
73
74
75name = "hayter_msa"
76title = "Hayter-Penfold rescaled MSA, charged sphere, interparticle S(Q) structure factor"
77description = """\
78    [Hayter-Penfold RMSA charged sphere interparticle S(Q) structure factor]
79        Interparticle structure factor S(Q)for a charged hard spheres.
80        Routine takes absolute value of charge, use HardSphere if charge
81        goes to zero.
82        In sasview the effective radius and volume fraction may be calculated
83        from the parameters used in P(Q).
84"""
85
86
88#             [ "name", "units", default, [lower, upper], "type", "description" ],
89parameters = [
90    ["radius_effective", "Ang", 20.75,   [0, inf],    "volume", "effective radius of charged sphere"],
91    ["volfraction",   "None",     0.0192, [0, 0.74],   "", "volume fraction of spheres"],
92    ["charge",        "e",   19.0,    [0, 200],    "", "charge on sphere (in electrons)"],
93    ["temperature",   "K",  318.16,   [0, 450],    "", "temperature, in Kelvin, for Debye length calculation"],
94    ["concentration_salt",      "M",    0.0,    [0, inf], "", "conc of salt, moles/litre, 1:1 electolyte, for Debye length"],
95    ["dielectconst",  "None",    71.08,   [-inf, inf], "", "dielectric constant (relative permittivity) of solvent, default water, for Debye length"]
96    ]
98
99source = ["hayter_msa.c"]
100# No volume normalization despite having a volume parameter
101# This should perhaps be volume normalized?
102form_volume = """
103    return 1.0;
104    """
105
106def random():
107    """Return a random parameter set for the model."""
108    # TODO: too many failures for random hayter_msa parameters
109    pars = dict(
110        scale=1, background=0,
112        volfraction=10**np.random.uniform(-2, 0),  # high volume fraction
113        charge=min(int(10**np.random.uniform(0, 1.3)+0.5), 200),
114        temperature=10**np.random.uniform(0, np.log10(450)), # max T = 450
115        #concentration_salt=10**np.random.uniform(-3, 1),
116        dialectconst=10**np.random.uniform(0, 6),
117        #charge=10,
118        #temperature=318.16,
119        concentration_salt=0.0,
120        #dielectconst=71.08,
121    )
122    return pars
123
124# default parameter set,  use  compare.sh -midQ -linear
125# note the calculation varies in different limiting cases so a wide range of
126# parameters will be required for a thorough test!
127# odd that the default st has concentration_salt zero
129            charge=19.0,
130            volfraction=0.0192,
131            temperature=318.16,
132            concentration_salt=0.05,
133            dielectconst=71.08,
136#
137# attempt to use same values as old sasview unit test at Q=.001 was 0.0712928,
138# then add lots new ones assuming values from new model are OK, need some
139# low Q values to test the small Q Taylor expansion
140tests = [
141    [{'scale': 1.0,
142      'background': 0.0,
144      'charge': 19.0,
145      'volfraction': 0.0192,
146      'temperature': 298.0,
147      'concentration_salt': 0,
148      'dielectconst': 78.0,
150     [0.00001, 0.0010, 0.01, 0.075], [0.0711646, 0.0712928, 0.0847006, 1.07150]],
151    [{'scale': 1.0,
152      'background': 0.0,