1 | r""" |
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2 | Calculates the macroscopic scattering intensity for a multi-component |
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3 | homogeneous mixture of polymers using the Random Phase Approximation. |
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4 | This general formalism contains 10 specific cases |
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5 | |
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6 | Case 0: C/D binary mixture of homopolymers |
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7 | |
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8 | Case 1: C-D diblock copolymer |
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9 | |
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10 | Case 2: B/C/D ternary mixture of homopolymers |
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11 | |
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12 | Case 3: C/C-D mixture of a homopolymer B and a diblock copolymer C-D |
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13 | |
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14 | Case 4: B-C-D triblock copolymer |
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15 | |
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16 | Case 5: A/B/C/D quaternary mixture of homopolymers |
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17 | |
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18 | Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D |
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19 | |
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20 | Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D |
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21 | |
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22 | Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D |
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23 | |
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24 | Case 9: A-B-C-D tetra-block copolymer |
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25 | |
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26 | **NB: these case numbers are different from those in the NIST SANS package!** |
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27 | |
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28 | Only one case can be used at any one time. |
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29 | |
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30 | The RPA (mean field) formalism only applies only when the multicomponent |
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31 | polymer mixture is in the homogeneous mixed-phase region. |
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32 | |
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33 | **Component D is assumed to be the "background" component (ie, all contrasts |
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34 | are calculated with respect to component D).** So the scattering contrast |
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35 | for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`. |
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36 | |
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37 | Depending on which case is being used, the number of fitting parameters - the |
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38 | segment lengths (ba, bb, etc) and $\chi$ parameters (Kab, Kac, etc) - vary. |
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39 | The *scale* parameter should be held equal to unity. |
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40 | |
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41 | The input parameters are the degrees of polymerization, the volume fractions, |
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42 | the specific volumes, and the neutron scattering length densities for each |
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43 | component. |
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44 | |
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45 | .. figure:: img/rpa_1d.jpg |
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46 | |
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47 | 1D plot using the default values (w/500 data points). |
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48 | |
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49 | References |
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50 | ---------- |
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51 | |
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52 | A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136 |
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53 | """ |
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54 | |
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55 | from numpy import inf |
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56 | |
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57 | name = "rpa" |
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58 | title = "Random Phase Approximation" |
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59 | description = """ |
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60 | This formalism applies to multicomponent polymer mixtures in the |
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61 | homogeneous (mixed) phase region only. |
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62 | Case 0: C/D binary mixture of homopolymers |
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63 | Case 1: C-D diblock copolymer |
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64 | Case 2: B/C/D ternary mixture of homopolymers |
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65 | Case 3: B/C-D mixture of homopolymer b and diblock copolymer C-D |
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66 | Case 4: B-C-D triblock copolymer |
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67 | Case 5: A/B/C/D quaternary mixture of homopolymers |
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68 | Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D |
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69 | Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D |
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70 | Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D |
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71 | Case 9: A-B-C-D four-block copolymer |
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72 | See details in the model function help |
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73 | """ |
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74 | category = "" |
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75 | |
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76 | CASES = [ |
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77 | "C+D binary mixture", |
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78 | "C:D diblock copolymer", |
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79 | "B+C+D ternary mixture", |
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80 | "B+C:D binary mixture", |
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81 | "B:C:D triblock copolymer", |
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82 | "A+B+C+D quaternary mixture", |
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83 | "A+B+C:D ternary mixture", |
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84 | "A+B:C:D binary mixture", |
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85 | "A:B+C:D binary mixture", |
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86 | "A:B:C:D quadblock copolymer", |
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87 | ] |
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88 | |
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89 | # ["name", "units", default, [lower, upper], "type","description"], |
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90 | parameters = [ |
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91 | ["case_num", CASES, 0, [0, 10], "", "Component organization"], |
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92 | |
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93 | ["Na", "", 1000.0, [1, inf], "", "Degree of polymerization"], |
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94 | ["Phia", "", 0.25, [0, 1], "", "volume fraction"], |
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95 | ["va", "mL/mol", 100.0, [0, inf], "", "specific volume"], |
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96 | ["La", "fm", 10.0, [-inf, inf], "", "scattering length"], |
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97 | ["ba", "Ang", 5.0, [0, inf], "", "segment length"], |
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98 | |
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99 | ["Nb", "", 1000.0, [1, inf], "", "Degree of polymerization"], |
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100 | ["Phib", "", 0.25, [0, 1], "", "volume fraction"], |
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101 | ["vb", "mL/mol", 100.0, [0, inf], "", "specific volume"], |
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102 | ["Lb", "fm", 10.0, [-inf, inf], "", "scattering length"], |
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103 | ["bb", "Ang", 5.0, [0, inf], "", "segment length"], |
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104 | |
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105 | ["Nc", "", 1000.0, [1, inf], "", "Degree of polymerization"], |
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106 | ["Phic", "", 0.25, [0, 1], "", "volume fraction"], |
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107 | ["vc", "mL/mol", 100.0, [0, inf], "", "specific volume"], |
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108 | ["Lc", "fm", 10.0, [-inf, inf], "", "scattering length"], |
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109 | ["bc", "Ang", 5.0, [0, inf], "", "segment length"], |
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110 | |
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111 | ["Nd", "", 1000.0, [1, inf], "", "Degree of polymerization"], |
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112 | ["Phid", "", 0.25, [0, 1], "", "volume fraction"], |
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113 | ["vd", "mL/mol", 100.0, [0, inf], "", "specific volume"], |
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114 | ["Ld", "fm", 10.0, [-inf, inf], "", "scattering length"], |
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115 | ["bd", "Ang", 5.0, [0, inf], "", "segment length"], |
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116 | |
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117 | ["Kab", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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118 | ["Kac", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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119 | ["Kad", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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120 | ["Kbc", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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121 | ["Kbd", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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122 | ["Kcd", "", -0.0004, [-inf, inf], "", "Interaction parameter"], |
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123 | ] |
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124 | |
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125 | category = "shape-independent" |
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126 | |
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127 | source = ["rpa.c"] |
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128 | |
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129 | HIDE_NONE = set() |
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130 | HIDE_A = set("Na Phia va La Kab Kac Kad".split()) |
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131 | HIDE_AB = set("Nb Phib vb Lb Kbc Kbd".split()).union(HIDE_A) |
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132 | def hidden(pars): |
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133 | case_num = pars.get("case_num", parameters[0][2]) |
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134 | if case_num < 2: |
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135 | return HIDE_AB |
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136 | elif case_num < 5: |
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137 | return HIDE_A |
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138 | else: |
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139 | return HIDE_NONE |
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140 | |
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141 | oldname = 'RPAModel' |
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142 | oldpars = dict( |
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143 | case_num="lcase_n", |
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144 | ) |
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