source: sasmodels/sasmodels/models/pearl_necklace.py @ 4b541ac

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 4b541ac was 4b541ac, checked in by wojciech, 7 years ago

sas_Si fixes in py files

  • Property mode set to 100644
File size: 4.7 KB
RevLine 
[cf404cb]1r"""
[841753c]2This model provides the form factor for a pearl necklace composed of two
3elements: *N* pearls (homogeneous spheres of radius *R*) freely jointed by *M*
[cf404cb]4rods (like strings - with a total mass *Mw* = *M* \* *m*\ :sub:`r` + *N* \* *m*\
[841753c]5:sub:`s`, and the string segment length (or edge separation) *l*
[cf404cb]6(= *A* - 2\ *R*)). *A* is the center-to-center pearl separation distance.
7
[2f0c07d]8.. figure:: img/pearl_necklace_geometry.jpg
[cf404cb]9
10    Pearl Necklace schematic
11
12Definition
13----------
14
[a2f9aa2]15The output of the scattering intensity function for the pearl_necklace is
[cf404cb]16given by (Schweins, 2004)
17
18.. math::
19
20    I(q)=\frac{ \text{scale} }{V} \cdot \frac{(S_{ss}(q)+S_{ff}(q)+S_{fs}(q))}
21        {(M \cdot m_f + N \cdot m_s)^2} + \text{bkg}
22
23where
24
25.. math::
26
27    S_{ss}(q) &= sm_s^2\psi^2(q)[\frac{N}{1-sin(qA)/qA}-\frac{N}{2}-
28        \frac{1-(sin(qA)/qA)^N}{(1-sin(qA)/qA)^2}\cdot\frac{sin(qA)}{qA}] \\
29    S_{ff}(q) &= sm_r^2[M\{2\Lambda(q)-(\frac{sin(ql/2)}{ql/2})\}+
30        \frac{2M\beta^2(q)}{1-sin(qA)/qA}-2\beta^2(q)\cdot
31        \frac{1-(sin(qA)/qA)^M}{(1-sin(qA)/qA)^2}] \\
32    S_{fs}(q) &= m_r \beta (q) \cdot m_s \psi (q) \cdot 4[
33        \frac{N-1}{1-sin(qA)/qA}-\frac{1-(sin(qA)/qA)^{N-1}}{(1-sin(qA)/qA)^2}
34        \cdot \frac{sin(qA)}{qA}] \\
35    \psi(q) &= 3 \cdot \frac{sin(qR)-(qR)\cdot cos(qR)}{(qR)^3} \\
36    \Lambda(q) &= \frac{\int_0^{ql}\frac{sin(t)}{t}dt}{ql} \\
37    \beta(q) &= \frac{\int_{qR}^{q(A-R)}\frac{sin(t)}{t}dt}{ql}
38
[841753c]39where the mass *m*\ :sub:`i` is (SLD\ :sub:`i` - SLD\ :sub:`solvent`) \*
[cf404cb]40(volume of the *N* pearls/rods). *V* is the total volume of the necklace.
41
[841753c]42The 2D scattering intensity is the same as $P(q)$ above, regardless of the
[cf404cb]43orientation of the *q* vector.
44
45The returned value is scaled to units of |cm^-1| and the parameters of the
46pearl_necklace model are the following
47
[a807206]48NB: *num_pearls* must be an integer.
[cf404cb]49
[2f0c07d]50References
51----------
[cf404cb]52
[841753c]53R Schweins and K Huber, *Particle Scattering Factor of Pearl Necklace Chains*,
[cf404cb]54*Macromol. Symp.* 211 (2004) 25-42 2004
55"""
56
[f12357f]57from numpy import inf, pi
[cf404cb]58
59name = "pearl_necklace"
[a2f9aa2]60title = "Colloidal spheres chained together with no preferential orientation"
[cf404cb]61description = """
62Calculate form factor for Pearl Necklace Model
63[Macromol. Symp. 2004, 211, 25-42]
64Parameters:
65background:background
66scale: scale factor
67sld: the SLD of the pearl spheres
68sld_string: the SLD of the strings
69sld_solvent: the SLD of the solvent
[a807206]70num_pearls: number of the pearls
[cf404cb]71radius: the radius of a pearl
[a807206]72edge_sep: the length of string segment; surface to surface
73thick_string: thickness (ie, diameter) of the string
[cf404cb]74"""
75category = "shape:cylinder"
76
77#             ["name", "units", default, [lower, upper], "type","description"],
[a2f9aa2]78parameters = [["radius", "Ang", 80.0, [0, inf], "volume",
[cf404cb]79               "Mean radius of the chained spheres"],
[a807206]80              ["edge_sep", "Ang", 350.0, [0, inf], "volume",
[cf404cb]81               "Mean separation of chained particles"],
[a807206]82              ["thick_string", "Ang", 2.5, [0, inf], "volume",
[cf404cb]83               "Thickness of the chain linkage"],
[a807206]84              ["num_pearls", "none", 3, [0, inf], "volume",
[a2f9aa2]85               "Number of pearls in the necklace (must be integer)"],
[42356c8]86              ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld",
[cf404cb]87               "Scattering length density of the chained spheres"],
[42356c8]88              ["sld_string", "1e-6/Ang^2", 1.0, [-inf, inf], "sld",
[cf404cb]89               "Scattering length density of the chain linkage"],
[42356c8]90              ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld",
[cf404cb]91               "Scattering length density of the solvent"],
[841753c]92             ]
[cf404cb]93
[4b541ac]94source = ["lib/sas_Si.c", "lib/sas_3j1x_x.c", "pearl_necklace.c"]
[d18582e]95single = False  # use double precision unless told otherwise
[f12357f]96
[a807206]97def volume(radius, edge_sep, thick_string, num_pearls):
[f12357f]98    """
99    Calculates the total particle volume of the necklace.
100    Redundant with form_volume.
101    """
[a807206]102    number_of_strings = num_pearls - 1.0
103    string_vol = edge_sep * pi * pow((thick_string / 2.0), 2.0)
[f12357f]104    pearl_vol = 4.0 /3.0 * pi * pow(radius, 3.0)
105    total_vol = number_of_strings * string_vol
[a807206]106    total_vol += num_pearls * pearl_vol
[f12357f]107    return total_vol
108
[a807206]109def ER(radius, edge_sep, thick_string, num_pearls):
[f12357f]110    """
111    Calculation for effective radius.
112    """
[a807206]113    tot_vol = volume(radius, edge_sep, thick_string, num_pearls)
[4962519]114    rad_out = (tot_vol/(4.0/3.0*pi)) ** (1./3.)
[f12357f]115    return rad_out
[cf404cb]116
117# parameters for demo
[a807206]118demo = dict(scale=1, background=0, radius=80.0, edge_sep=350.0,
119            num_pearls=3, sld=1, sld_solvent=6.3, sld_string=1,
120            thick_string=2.5,
[cf404cb]121            radius_pd=.2, radius_pd_n=5,
[a807206]122            edge_sep_pd=25.0, edge_sep_pd_n=5,
123            num_pearls_pd=0, num_pearls_pd_n=0,
124            thick_string_pd=0.2, thick_string_pd_n=5,
[cf404cb]125           )
126
[f12357f]127tests = [[{}, 0.001, 17380.245], [{}, 'ER', 115.39502]]
Note: See TracBrowser for help on using the repository browser.