1 | r""" |
---|
2 | Definition |
---|
3 | ---------- |
---|
4 | |
---|
5 | Calculates the macroscopic scattering intensity for a multi-component |
---|
6 | homogeneous mixture of polymers using the Random Phase Approximation. |
---|
7 | This general formalism contains 10 specific cases |
---|
8 | |
---|
9 | Case 0: C/D binary mixture of homopolymers |
---|
10 | |
---|
11 | Case 1: C-D diblock copolymer |
---|
12 | |
---|
13 | Case 2: B/C/D ternary mixture of homopolymers |
---|
14 | |
---|
15 | Case 3: C/C-D mixture of a homopolymer B and a diblock copolymer C-D |
---|
16 | |
---|
17 | Case 4: B-C-D triblock copolymer |
---|
18 | |
---|
19 | Case 5: A/B/C/D quaternary mixture of homopolymers |
---|
20 | |
---|
21 | Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D |
---|
22 | |
---|
23 | Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D |
---|
24 | |
---|
25 | Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D |
---|
26 | |
---|
27 | Case 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 | |
---|
32 | The models are based on the papers by Akcasu *et al.* [1] and by |
---|
33 | Hammouda [2] assuming the polymer follows Gaussian statistics such |
---|
34 | that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is |
---|
35 | the number of statistical segment lengths. A nice tutorial on how these are |
---|
36 | constructed and implemented can be found in chapters 28, 31 and 34, and Part H, |
---|
37 | of Hammouda's 'SANS Toolbox' [3]. |
---|
38 | |
---|
39 | In brief, the macroscopic cross sections are derived from the general forms |
---|
40 | for homopolymer scattering and the multiblock cross-terms while the inter, |
---|
41 | polymer cross terms are described in the usual way by the $\chi$ parameter. |
---|
42 | |
---|
43 | USAGE 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 $\rho_{C/D} = [\rho_C - \rho_D]$\ :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 | |
---|
62 | References |
---|
63 | ---------- |
---|
64 | |
---|
65 | .. [#] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136 |
---|
66 | .. [#] B. Hammouda, *Advances in Polymer Science* 106 (1993) 87 |
---|
67 | .. [#] B. Hammouda, *SANS Toolbox* https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf. |
---|
68 | |
---|
69 | Source |
---|
70 | ------ |
---|
71 | |
---|
72 | `rpa.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/rpa.py>`_ |
---|
73 | |
---|
74 | `rpa.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/rpa.c>`_ |
---|
75 | |
---|
76 | Authorship and Verification |
---|
77 | ---------------------------- |
---|
78 | |
---|
79 | * **Author:** Boualem Hammouda - NIST IGOR/DANSE **Date:** pre 2010 |
---|
80 | * **Converted to sasmodels by:** Paul Kienzle **Date:** July 18, 2016 |
---|
81 | * **Last Modified by:** Paul Butler **Date:** March 12, 2017 |
---|
82 | * **Last Reviewed by:** Steve King **Date:** March 27, 2019 |
---|
83 | * **Source added by :** Steve King **Date:** March 25, 2019 |
---|
84 | """ |
---|
85 | |
---|
86 | from numpy import inf |
---|
87 | |
---|
88 | name = "rpa" |
---|
89 | title = "Random Phase Approximation" |
---|
90 | description = """ |
---|
91 | This formalism applies to multicomponent polymer mixtures in the |
---|
92 | homogeneous (mixed) phase region only. |
---|
93 | Case 0: C/D binary mixture of homopolymers |
---|
94 | Case 1: C-D diblock copolymer |
---|
95 | Case 2: B/C/D ternary mixture of homopolymers |
---|
96 | Case 3: B/C-D mixture of homopolymer b and diblock copolymer C-D |
---|
97 | Case 4: B-C-D triblock copolymer |
---|
98 | Case 5: A/B/C/D quaternary mixture of homopolymers |
---|
99 | Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D |
---|
100 | Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D |
---|
101 | Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D |
---|
102 | Case 9: A-B-C-D four-block copolymer |
---|
103 | See details in the model function help |
---|
104 | """ |
---|
105 | category = "shape-independent" |
---|
106 | |
---|
107 | CASES = [ |
---|
108 | "C+D binary mixture", |
---|
109 | "C:D diblock copolymer", |
---|
110 | "B+C+D ternary mixture", |
---|
111 | "B+C:D binary mixture", |
---|
112 | "B:C:D triblock copolymer", |
---|
113 | "A+B+C+D quaternary mixture", |
---|
114 | "A+B+C:D ternary mixture", |
---|
115 | "A+B:C:D binary mixture", |
---|
116 | "A:B+C:D binary mixture", |
---|
117 | "A:B:C:D quadblock copolymer", |
---|
118 | ] |
---|
119 | |
---|
120 | # ["name", "units", default, [lower, upper], "type","description"], |
---|
121 | parameters = [ |
---|
122 | ["case_num", "", 1, [CASES], "", "Component organization"], |
---|
123 | |
---|
124 | ["N[4]", "", 1000.0, [1, inf], "", "Degree of polymerization"], |
---|
125 | ["Phi[4]", "", 0.25, [0, 1], "", "volume fraction"], |
---|
126 | ["v[4]", "mL/mol", 100.0, [0, inf], "", "molar volume"], |
---|
127 | ["L[4]", "fm", 10.0, [-inf, inf], "", "scattering length"], |
---|
128 | ["b[4]", "Ang", 5.0, [0, inf], "", "segment length"], |
---|
129 | |
---|
130 | ["K12", "", -0.0004, [-inf, inf], "", "A:B interaction parameter"], |
---|
131 | ["K13", "", -0.0004, [-inf, inf], "", "A:C interaction parameter"], |
---|
132 | ["K14", "", -0.0004, [-inf, inf], "", "A:D interaction parameter"], |
---|
133 | ["K23", "", -0.0004, [-inf, inf], "", "B:C interaction parameter"], |
---|
134 | ["K24", "", -0.0004, [-inf, inf], "", "B:D interaction parameter"], |
---|
135 | ["K34", "", -0.0004, [-inf, inf], "", "C:D interaction parameter"], |
---|
136 | ] |
---|
137 | |
---|
138 | |
---|
139 | source = ["rpa.c"] |
---|
140 | single = False |
---|
141 | |
---|
142 | control = "case_num" |
---|
143 | HIDE_ALL = set("Phi4".split()) |
---|
144 | HIDE_A = set("N1 Phi1 v1 L1 b1 K12 K13 K14".split()).union(HIDE_ALL) |
---|
145 | HIDE_AB = set("N2 Phi2 v2 L2 b2 K23 K24".split()).union(HIDE_A) |
---|
146 | def hidden(case_num): |
---|
147 | """ |
---|
148 | Return a list of parameters to hide depending on the multiplicity parameter. |
---|
149 | """ |
---|
150 | case_num = int(case_num+0.5) |
---|
151 | if case_num < 2: |
---|
152 | return HIDE_AB |
---|
153 | elif case_num < 5: |
---|
154 | return HIDE_A |
---|
155 | else: |
---|
156 | return HIDE_ALL |
---|
157 | |
---|
158 | # TODO: no random parameters generated for RPA |
---|