source: sasmodels/sasmodels/models/rpa.py @ b297ba9

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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1r"""
2Definition
3----------
4
5Calculates the macroscopic scattering intensity for a multi-component
6homogeneous mixture of polymers using the Random Phase Approximation.
7This general formalism contains 10 specific cases
8
9Case 0: C/D binary mixture of homopolymers
10
11Case 1: C-D diblock copolymer
12
13Case 2: B/C/D ternary mixture of homopolymers
14
15Case 3: C/C-D mixture of a homopolymer B and a diblock copolymer C-D
16
17Case 4: B-C-D triblock copolymer
18
19Case 5: A/B/C/D quaternary mixture of homopolymers
20
21Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D
22
23Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D
24
25Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D
26
27Case 9: A-B-C-D tetra-block copolymer
28
29.. note::
30    These case numbers are different from those in the NIST SANS package!
31
32The models are based on the papers by Akcasu *et al.* and by
33Hammouda assuming the polymer follows Gaussian statistics such
34that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is
35the number of statistical segment lengths. A nice tutorial on how these are
36constructed and implemented can be found in chapters 28 and 39 of Boualem
37Hammouda's 'SANS Toolbox'.
38
39In brief the macroscopic cross sections are derived from the general forms
40for homopolymer scattering and the multiblock cross-terms while the inter
41polymer cross terms are described in the usual way by the $\chi$ parameter.
42
43USAGE NOTES:
44
45* Only one case can be used at any one time.
46* The RPA (mean field) formalism only applies only when the multicomponent
47  polymer mixture is in the homogeneous mixed-phase region.
48* **Component D is assumed to be the "background" component (ie, all contrasts
49  are calculated with respect to component D).** So the scattering contrast
50  for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`.
51* Depending on which case is being used, the number of fitting parameters can
52  vary.
53
54  .. Note::
55    * In general the degrees of polymerization, the volume
56      fractions, the molar volumes, and the neutron scattering lengths for each
57      component are obtained from other methods and held fixed while The *scale*
58      parameter should be held equal to unity.
59    * The variables are normally the segment lengths ($b_a$, $b_b$,
60      etc.) and $\chi$ parameters ($K_{ab}$, $K_{ac}$, etc).
61
62References
63----------
64
65A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136.
66
67B. Hammouda, *Advances in Polymer Science* 106 (1993) 87.
68
69B. Hammouda, *SANS Toolbox*
70https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf.
71
72Authorship and Verification
73----------------------------
74
75* **Author:** Boualem Hammouda - NIST IGOR/DANSE **Date:** pre 2010
76* **Converted to sasmodels by:** Paul Kienzle **Date:** July 18, 2016
77* **Last Modified by:** Paul Butler **Date:** March 12, 2017
78* **Last Reviewed by:** Paul Butler **Date:** March 12, 2017
79"""
80
81from numpy import inf
82
83name = "rpa"
84title = "Random Phase Approximation"
85description = """
86This formalism applies to multicomponent polymer mixtures in the
87homogeneous (mixed) phase region only.
88Case 0: C/D binary mixture of homopolymers
89Case 1: C-D diblock copolymer
90Case 2: B/C/D ternary mixture of homopolymers
91Case 3: B/C-D mixture of homopolymer b and diblock copolymer C-D
92Case 4: B-C-D triblock copolymer
93Case 5: A/B/C/D quaternary mixture of homopolymers
94Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D
95Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D
96Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D
97Case 9: A-B-C-D four-block copolymer
98See details in the model function help
99"""
100category = "shape-independent"
101
102CASES = [
103    "C+D binary mixture",
104    "C:D diblock copolymer",
105    "B+C+D ternary mixture",
106    "B+C:D binary mixture",
107    "B:C:D triblock copolymer",
108    "A+B+C+D quaternary mixture",
109    "A+B+C:D ternary mixture",
110    "A+B:C:D binary mixture",
111    "A:B+C:D binary mixture",
112    "A:B:C:D quadblock copolymer",
113]
114
115#   ["name", "units", default, [lower, upper], "type","description"],
116parameters = [
117    ["case_num", "", 1, [CASES], "", "Component organization"],
118
119    ["N[4]", "", 1000.0, [1, inf], "", "Degree of polymerization"],
120    ["Phi[4]", "", 0.25, [0, 1], "", "volume fraction"],
121    ["v[4]", "mL/mol", 100.0, [0, inf], "", "molar volume"],
122    ["L[4]", "fm", 10.0, [-inf, inf], "", "scattering length"],
123    ["b[4]", "Ang", 5.0, [0, inf], "", "segment length"],
124
125    ["K12", "", -0.0004, [-inf, inf], "", "A:B interaction parameter"],
126    ["K13", "", -0.0004, [-inf, inf], "", "A:C interaction parameter"],
127    ["K14", "", -0.0004, [-inf, inf], "", "A:D interaction parameter"],
128    ["K23", "", -0.0004, [-inf, inf], "", "B:C interaction parameter"],
129    ["K24", "", -0.0004, [-inf, inf], "", "B:D interaction parameter"],
130    ["K34", "", -0.0004, [-inf, inf], "", "C:D interaction parameter"],
131]
132
133
134source = ["rpa.c"]
135single = False
136
137control = "case_num"
138HIDE_ALL = set("Phi4".split())
139HIDE_A = set("N1 Phi1 v1 L1 b1 K12 K13 K14".split()).union(HIDE_ALL)
140HIDE_AB = set("N2 Phi2 v2 L2 b2 K23 K24".split()).union(HIDE_A)
141def hidden(case_num):
142    """
143    Return a list of parameters to hide depending on the multiplicity parameter.
144    """
145    case_num = int(case_num+0.5)
146    if case_num < 2:
147        return HIDE_AB
148    elif case_num < 5:
149        return HIDE_A
150    else:
151        return HIDE_ALL
152
153# TODO: no random parameters generated for RPA
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