# source:sasmodels/sasmodels/models/multilayer_vesicle.py@68f45cb

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 68f45cb was 68f45cb, checked in by Paul Kienzle <pkienzle@…>, 4 years ago

multilayer vesicle: add doc on how to use array distribution

• Property mode set to 100644
File size: 5.3 KB
Line
1r"""
2Definition
3----------
4
5This model is a trivial extension of the core_shell_sphere function to include
6*N* shells where the core is filled with solvent and the shells are interleaved
7with layers of solvent. For $N = 1$, this returns the same as the vesicle model,
8except for the normalisation, which here is to outermost volume.
9The shell thicknessess and SLD are constant for all shells as expected for
10a multilayer vesicle.
11
12.. figure:: img/multi_shell_geometry.jpg
13
14    Geometry of the multilayer_vesicle model.
15
16See the :ref:core-shell-sphere model for more documentation.
17
18The 1D scattering intensity is calculated in the following way (Guinier, 1955)
19
20.. math::
21    P(q) = \text{scale} \cdot \frac{\phi}{V(R_N)} F^2(q) + \text{background}
22
23where
24
25.. math::
26     F(q) = (\rho_\text{shell}-\rho_\text{solv}) \sum_{i=1}^{N} \left[
27     3V(r_i)\frac{\sin(qr_i) - qr_i\cos(qr_i)}{(qr_i)^3}
28     - 3V(R_i)\frac{\sin(qR_i) - qR_i\cos(qR_i)}{(qR_i)^3}
29     \right]
30
31for
32
33.. math::
34
35     r_i &= r_c + (i-1)(t_s + t_w) && \text{ solvent radius before shell } i \\
36     R_i &= r_i + t_s && \text{ shell radius for shell } i
37
38$\phi$ is the volume fraction of particles, $V(r)$ is the volume of a sphere
39of radius $r$, $r_c$ is the radius of the core, $t_s$ is the thickness of
40the shell, $t_w$ is the thickness of the solvent layer between the shells,
41$\rho_\text{shell}$ is the scattering length density of a shell, and
42$\rho_\text{solv}$ is the scattering length density of the solvent.
43
44The outer-most shell radius $R_N$ is used as the effective radius
45for $P(Q)$ when $P(Q) * S(Q)$ is applied.
46
47For mixed systems in which some vesicles have 1 shell, some have 2,
48etc., use polydispersity on $N$ to model the data.  For example,
49create a file such as *shell_dist.txt* containing the relative portion
50of each vesicle size::
51
52    1 20
53    2  4
54    3  1
55
56Turn on polydispersity and select an array distribution for the *n_shells*
57parameter.  Choose the above *shell_dist.txt* file, and the model will be
58computed with 80% 1-shell vesicles, 16% 2-shell vesicles and 4%
593-shell vesicles.
60
61The 2D scattering intensity is the same as 1D, regardless of the orientation
62of the q vector which is defined as:
63
64.. math::
65
66    q = \sqrt{q_x^2 + q_y^2}
67
68For information about polarised and magnetic scattering, see
69the :ref:magnetism documentation.
70
71This code is based on the form factor calculations implemented in the NIST
72Center for Neutron Research provided c-library (Kline, 2006).
73
74References
75----------
76
77B Cabane, *Small Angle Scattering Methods*,
78in *Surfactant Solutions: New Methods of Investigation*,
79Ch.2, Surfactant Science Series Vol. 22, Ed. R Zana and M Dekker,
80New York, (1987).
81
82**Author:** NIST IGOR/DANSE **on:** pre 2010
83
85
86**Last Reviewed by:** Paul Butler **on:** March 20, 2016
87
88"""
89
90from numpy import inf
91
92name = "multilayer_vesicle"
93title = "P(Q) for a Multi-lamellar vesicle"
94description = """
95    multilayer_vesicle model parameters;
96    scale : scale factor for abs intensity if needed else 1.0
97    volfraction: volume fraction
99    thick_shell: shell thickness
100    thick_solvent: water thickness
101    sld_solvent: solvent scattering length density
102    sld: shell scattering length density
103    n_shells:number of "shell plus solvent" layer pairs
104    background: incoherent background
105        """
106category = "shape:sphere"
107
109#   ["name", "units", default, [lower, upper], "type","description"],
110parameters = [
111    ["volfraction", "",  0.05, [0.0, 1],  "", "volume fraction of vesicles"],
112    ["radius", "Ang", 60.0, [0.0, inf],  "volume", "radius of solvent filled core"],
113    ["thick_shell", "Ang",        10.0, [0.0, inf],  "volume", "thickness of one shell"],
114    ["thick_solvent", "Ang",        10.0, [0.0, inf],  "volume", "solvent thickness between shells"],
115    ["sld_solvent",    "1e-6/Ang^2",  6.4, [-inf, inf], "sld", "solvent scattering length density"],
116    ["sld",   "1e-6/Ang^2",  0.4, [-inf, inf], "sld", "Shell scattering length density"],
117    ["n_shells",     "",            2.0, [1.0, inf],  "volume", "Number of shell plus solvent layer pairs"],
118    ]
120
121# TODO: proposed syntax for specifying which parameters can be polydisperse
123
124source = ["lib/sas_3j1x_x.c", "multilayer_vesicle.c"]
125
127    n_shells = int(n_shells+0.5)
128    return radius + n_shells * (thick_shell + thick_solvent) - thick_solvent
129
130demo = dict(scale=1, background=0,
131            volfraction=0.05,
133            thick_shell=10.0,
134            thick_solvent=10.0,
135            sld_solvent=6.4,
136            sld=0.4,
137            n_shells=2.0)
138
139tests = [
140    # Accuracy tests based on content in test/utest_other_models.py
142      'thick_shell': 10.0,
143      'thick_solvent': 10.0,
144      'sld_solvent': 6.4,
145      'sld': 0.4,
146      'n_shells': 2.0,
147      'scale': 1.0,
148      'background': 0.001,
149     }, 0.001, 122.1405],
150
151    [{'volfraction': 1.0,