source: sasmodels/sasmodels/models/lamellar_hg.py @ 99658f6

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Last change on this file since 99658f6 was 304c775, checked in by Paul Kienzle <pkienzle@…>, 5 years ago

provide method for testing Fq results. Refs #1202.

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1# Note: model title and parameter table are inserted automatically
2r"""
3This model provides the scattering intensity, $I(q)$, for a lyotropic lamellar
4phase where a random distribution in solution are assumed. The SLD of the head
5region is taken to be different from the SLD of the tail region.
6
7Definition
8----------
9
10The scattering intensity $I(q)$ is
11
12.. math::
13
14   I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)}  P(q) \frac{1}{q^2}
15
16The form factor $P(q)$ is
17
18.. math::
19
20    P(q) = \frac{4}{q^2}
21        \left\lbrace
22            \Delta \rho_H
23            \left[\sin[q(\delta_H + \delta_T)\ - \sin(q\delta_T)\right]
24            + \Delta\rho_T\sin(q\delta_T)
25        \right\rbrace^2
26
27where $\delta_T$ is *length_tail*, $\delta_H$ is *length_head*,
28$\Delta\rho_H$ is the head contrast (*sld_head* $-$ *sld_solvent*),
29and $\Delta\rho_T$ is tail contrast (*sld* $-$ *sld_solvent*).
30
31The total thickness of the lamellar sheet is $\delta_H + \delta_T + \delta_T + \delta_H$.
32Note that in a non aqueous solvent the chemical "head" group may be the
33"Tail region" and vice-versa.
34
35The 2D scattering intensity is calculated in the same way as 1D, where
36the $q$ vector is defined as
37
38.. math:: q = \sqrt{q_x^2 + q_y^2}
39
40References
41----------
42
43F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502
44
45also in J. Phys. Chem. B, 105, (2001) 11081-11088
46
47*2014/04/17 - Description reviewed by S King and P Butler.*
48"""
49
50import numpy as np
51from numpy import inf
52
53name = "lamellar_hg"
54title = "Random lamellar phase with Head and Tail Groups"
55description = """\
56    [Random lamellar phase with Head and Tail Groups]
57        I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where
58        P(q)= see manual
59        layer thickness =(H+T+T+H) = 2(Head+Tail)
60        sld = Tail scattering length density
61        sld_head = Head scattering length density
62        sld_solvent = solvent scattering length density
63        background = incoherent background
64        scale = scale factor
65"""
66category = "shape:lamellae"
67
68# pylint: disable=bad-whitespace, line-too-long
69#             ["name", "units", default, [lower, upper], "type","description"],
70parameters = [["length_tail", "Ang",       15,   [0, inf],  "volume",  "Tail thickness ( total = H+T+T+H)"],
71              ["length_head", "Ang",       10,   [0, inf],  "volume",  "Head thickness"],
72              ["sld",         "1e-6/Ang^2", 0.4, [-inf,inf], "sld",    "Tail scattering length density"],
73              ["sld_head",    "1e-6/Ang^2", 3.0, [-inf,inf], "sld",    "Head scattering length density"],
74              ["sld_solvent", "1e-6/Ang^2", 6,   [-inf,inf], "sld",    "Solvent scattering length density"]]
75# pylint: enable=bad-whitespace, line-too-long
76
77# No volume normalization despite having a volume parameter
78# This should perhaps be volume normalized?
79form_volume = """
80    return 1.0;
81    """
82
83Iq = """
84    const double qsq = q*q;
85    const double drh = sld_head - sld_solvent;
86    const double drt = sld - sld_solvent;    //correction 13FEB06 by L.Porcar
87    const double qT = q*length_tail;
88    double Pq, inten;
89    Pq = drh*(sin(q*(length_head+length_tail))-sin(qT)) + drt*sin(qT);
90    Pq *= Pq;
91    Pq *= 4.0/(qsq);
92
93    inten = 2.0e-4*M_PI*Pq/qsq;
94
95    // normalize by the bilayer thickness
96    inten /= 2.0*(length_head+length_tail);
97
98    return inten;
99    """
100
101def random():
102    thickness = 10**np.random.uniform(1, 4)
103    length_head = thickness * np.random.uniform(0, 1)
104    length_tail = thickness - length_head
105    pars = dict(
106        length_head=length_head,
107        length_tail=length_tail,
108    )
109    return pars
110
111demo = dict(scale=1, background=0,
112            length_tail=15, length_head=10,
113            sld=0.4, sld_head=3.0, sld_solvent=6.0,
114            length_tail_pd=0.2, length_tail_pd_n=40,
115            length_head_pd=0.01, length_head_pd_n=40)
116
117#
118tests = [
119    [{'scale': 1.0, 'background': 0.0, 'length_tail': 15.0, 'length_head': 10.0,
120      'sld': 0.4, 'sld_head': 3.0, 'sld_solvent': 6.0},
121     [0.001], [653143.9209]],
122]
123# ADDED by: RKH  ON: 18Mar2016  converted from sasview previously, now renaming everything & sorting the docs
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