1 | # Note: model title and parameter table are inserted automatically |
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2 | r""" |
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3 | This calculates the structure factor (the Fourier transform of the pair |
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4 | correlation function $g(r)$) for a system of charged, spheroidal objects |
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5 | in a dielectric medium. When combined with an appropriate form factor |
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6 | (such as sphere, core+shell, ellipsoid, etc), this allows for inclusion |
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7 | of the interparticle interference effects due to screened coulomb repulsion |
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8 | between charged particles. |
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9 | |
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10 | **This routine only works for charged particles**. If the charge is set to |
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11 | zero the routine may self-destruct! For non-charged particles use a hard |
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12 | sphere potential. |
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13 | |
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14 | The salt concentration is used to compute the ionic strength of the solution |
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15 | which in turn is used to compute the Debye screening length. At present |
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16 | there is no provision for entering the ionic strength directly nor for use |
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17 | of any multivalent salts, though it should be possible to simulate the effect |
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18 | of this by increasing the salt concentration. The counterions are also |
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19 | assumed to be monovalent. |
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20 | |
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21 | In sasview the effective radius may be calculated from the parameters |
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22 | used in the form factor $P(q)$ that this $S(q)$ is combined with. |
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23 | |
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24 | The computation uses a Taylor series expansion at very small rescaled $qR$, to |
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25 | avoid some serious rounding error issues, this may result in a minor artefact |
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26 | in the transition region under some circumstances. |
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27 | |
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28 | For 2D data, the scattering intensity is calculated in the same way as 1D, |
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29 | where the $q$ vector is defined as |
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30 | |
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31 | .. math:: |
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32 | |
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33 | q = \sqrt{q_x^2 + q_y^2} |
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34 | |
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35 | |
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36 | References |
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37 | ---------- |
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38 | |
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39 | .. [#] J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118 |
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40 | .. [#] J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656 |
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41 | |
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42 | Source |
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43 | ------ |
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44 | |
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45 | `hayter_msa.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/hayter_msa.py>`_ |
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46 | |
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47 | `hayter_msa.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/hayter_msa.c>`_ |
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48 | |
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49 | Authorship and Verification |
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50 | ---------------------------- |
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51 | |
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52 | * **Author:** |
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53 | * **Last Modified by:** |
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54 | * **Last Reviewed by:** |
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55 | * **Source added by :** Steve King **Date:** March 25, 2019 |
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56 | """ |
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57 | |
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58 | import numpy as np |
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59 | from numpy import inf |
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60 | |
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61 | category = "structure-factor" |
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62 | structure_factor = True |
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63 | single = False # double precision only! |
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64 | |
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65 | # dp[0] = 2.0*radius_effective(); |
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66 | # dp[1] = fabs(charge()); |
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67 | # dp[2] = volfraction(); |
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68 | # dp[3] = temperature(); |
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69 | # dp[4] = concentration_salt(); |
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70 | # dp[5] = dielectconst(); |
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71 | |
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72 | |
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73 | |
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74 | |
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75 | name = "hayter_msa" |
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76 | title = "Hayter-Penfold rescaled MSA, charged sphere, interparticle S(Q) structure factor" |
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77 | description = """\ |
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78 | [Hayter-Penfold RMSA charged sphere interparticle S(Q) structure factor] |
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79 | Interparticle structure factor S(Q)for a charged hard spheres. |
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80 | Routine takes absolute value of charge, use HardSphere if charge |
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81 | goes to zero. |
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82 | In sasview the effective radius and volume fraction may be calculated |
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83 | from the parameters used in P(Q). |
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84 | """ |
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85 | |
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86 | |
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87 | # pylint: disable=bad-whitespace, line-too-long |
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88 | # [ "name", "units", default, [lower, upper], "type", "description" ], |
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89 | parameters = [ |
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90 | ["radius_effective", "Ang", 20.75, [0, inf], "volume", "effective radius of charged sphere"], |
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91 | ["volfraction", "None", 0.0192, [0, 0.74], "", "volume fraction of spheres"], |
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92 | ["charge", "e", 19.0, [0, 200], "", "charge on sphere (in electrons)"], |
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93 | ["temperature", "K", 318.16, [0, 450], "", "temperature, in Kelvin, for Debye length calculation"], |
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94 | ["concentration_salt", "M", 0.0, [0, inf], "", "conc of salt, moles/litre, 1:1 electolyte, for Debye length"], |
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95 | ["dielectconst", "None", 71.08, [-inf, inf], "", "dielectric constant (relative permittivity) of solvent, default water, for Debye length"] |
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96 | ] |
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97 | # pylint: enable=bad-whitespace, line-too-long |
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98 | |
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99 | source = ["hayter_msa.c"] |
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100 | # No volume normalization despite having a volume parameter |
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101 | # This should perhaps be volume normalized? |
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102 | form_volume = """ |
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103 | return 1.0; |
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104 | """ |
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105 | |
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106 | def random(): |
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107 | """Return a random parameter set for the model.""" |
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108 | # TODO: too many failures for random hayter_msa parameters |
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109 | pars = dict( |
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110 | scale=1, background=0, |
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111 | radius_effective=10**np.random.uniform(1, 4.7), |
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112 | volfraction=10**np.random.uniform(-2, 0), # high volume fraction |
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113 | charge=min(int(10**np.random.uniform(0, 1.3)+0.5), 200), |
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114 | temperature=10**np.random.uniform(0, np.log10(450)), # max T = 450 |
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115 | #concentration_salt=10**np.random.uniform(-3, 1), |
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116 | dialectconst=10**np.random.uniform(0, 6), |
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117 | #charge=10, |
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118 | #temperature=318.16, |
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119 | concentration_salt=0.0, |
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120 | #dielectconst=71.08, |
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121 | ) |
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122 | return pars |
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123 | |
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124 | # default parameter set, use compare.sh -midQ -linear |
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125 | # note the calculation varies in different limiting cases so a wide range of |
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126 | # parameters will be required for a thorough test! |
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127 | # odd that the default st has concentration_salt zero |
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128 | demo = dict(radius_effective=20.75, |
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129 | charge=19.0, |
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130 | volfraction=0.0192, |
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131 | temperature=318.16, |
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132 | concentration_salt=0.05, |
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133 | dielectconst=71.08, |
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134 | radius_effective_pd=0.1, |
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135 | radius_effective_pd_n=40) |
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136 | # |
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137 | # attempt to use same values as old sasview unit test at Q=.001 was 0.0712928, |
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138 | # then add lots new ones assuming values from new model are OK, need some |
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139 | # low Q values to test the small Q Taylor expansion |
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140 | tests = [ |
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141 | [{'scale': 1.0, |
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142 | 'background': 0.0, |
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143 | 'radius_effective': 20.75, |
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144 | 'charge': 19.0, |
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145 | 'volfraction': 0.0192, |
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146 | 'temperature': 298.0, |
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147 | 'concentration_salt': 0, |
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148 | 'dielectconst': 78.0, |
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149 | 'radius_effective_pd': 0}, |
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150 | [0.00001, 0.0010, 0.01, 0.075], [0.0711646, 0.0712928, 0.0847006, 1.07150]], |
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151 | [{'scale': 1.0, |
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152 | 'background': 0.0, |
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153 | 'radius_effective': 20.75, |
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154 | 'charge': 19.0, |
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155 | 'volfraction': 0.0192, |
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156 | 'temperature': 298.0, |
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157 | 'concentration_salt': 0.05, |
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158 | 'dielectconst': 78.0, |
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159 | 'radius_effective_pd': 0.1, |
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160 | 'radius_effective_pd_n': 40}, |
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161 | [0.00001, 0.0010, 0.01, 0.075], [0.450272, 0.450420, 0.465116, 1.039625]] |
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162 | ] |
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163 | # ADDED by: RKH ON: 16Mar2016 converted from sasview, new Taylor expansion at smallest rescaled Q |
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