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 will 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. The counterions are also assumed to be monovalent. |
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18 | |
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19 | For 2D data, the scattering intensity is calculated in the same way as 1D, |
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20 | where the $q$ vector is defined as |
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21 | |
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22 | .. math:: |
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23 | |
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24 | q = \sqrt{q_x^2 + q_y^2} |
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25 | |
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26 | .. figure:: img/HayterMSAsq_227.jpg |
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27 | |
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28 | 1D plot using the default values (in linear scale). |
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29 | |
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30 | References |
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31 | ---------- |
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32 | |
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33 | J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118 |
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34 | |
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35 | J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656 |
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36 | """ |
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37 | |
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38 | # dp[0] = 2.0*effect_radius(); |
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39 | # dp[1] = fabs(charge()); |
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40 | # dp[2] = volfraction(); |
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41 | # dp[3] = temperature(); |
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42 | # dp[4] = saltconc(); |
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43 | # dp[5] = dielectconst(); |
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44 | |
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45 | from numpy import inf |
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46 | |
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47 | source = ["HayterMSAsq_kernel.c"] |
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48 | |
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49 | name = "HayterMSAsq" |
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50 | title = "Hayter-Penfold MSA charged sphere interparticle S(Q) structure factor" |
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51 | description = """\ |
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52 | [Hayter-Penfold MSA charged sphere interparticle S(Q) structure factor] |
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53 | Interparticle structure factor S(Q)for a charged hard spheres. |
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54 | Routine takes absolute value of charge, use HardSphere if charge goes to zero. |
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55 | In sasview the effective radius will be calculated from the |
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56 | parameters used in P(Q). |
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57 | """ |
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58 | # [ "name", "units", default, [lower, upper], "type", "description" ], |
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59 | parameters = [["effect_radius", "Ang", 20.75, [0, inf], "volume", |
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60 | "effective radius of hard sphere"], |
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61 | ["charge", "e", 19.0, [0, inf], "", |
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62 | "charge on sphere (in electrons)"], |
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63 | ["volfraction", "", 0.0192, [0, 0.74], "", |
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64 | "volume fraction of spheres"], |
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65 | ["temperature", "K", 318.16, [0, inf], "", |
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66 | "temperature, in Kelvin, for Debye length calculation"], |
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67 | ["saltconc", "M", 0.0, [-inf, inf], "", |
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68 | "conc of salt, 1:1 electolyte, for Debye length"], |
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69 | ["dielectconst", "", 71.08, [-inf, inf], "", |
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70 | "dielectric constant of solvent (default water), for Debye length"], |
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71 | ] |
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72 | category = "structure-factor" |
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73 | |
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74 | # No volume normalization despite having a volume parameter |
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75 | # This should perhaps be volume normalized? |
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76 | form_volume = """ |
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77 | return 1.0; |
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78 | """ |
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79 | Iqxy = """ |
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80 | // never called since no orientation or magnetic parameters. |
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81 | return Iq(sqrt(qx*qx+qy*qy), IQ_PARAMETERS); |
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82 | """ |
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83 | # ER defaults to 0.0 |
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84 | # VR defaults to 1.0 |
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85 | |
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86 | oldname = 'HayterMSAStructure' |
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87 | oldpars = dict() |
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88 | # default parameter set, use compare.sh -midQ -linear |
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89 | # note the calculation varies in different limiting cases so a wide range of parameters will be required for a thorough test! |
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90 | # odd that the default st has saltconc zero |
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91 | demo = dict(effect_radius = 20.75,charge=19.0,volfraction = 0.0192,temperature=318.16,saltconc=0.05,dielectconst=71.08,effect_radius_pd = 0.1,effect_radius_pd_n = 40) |
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92 | # |
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93 | # attempt to use same values as old sasview unit test |
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94 | tests = [ |
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95 | [ {'scale': 1.0, 'background' : 0.0, 'effect_radius' : 20.75, 'charge' : 19.0, 'volfraction' : 0.0192, 'temperature' : 298.0, |
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96 | 'saltconc' : 0,'dielectconst' : 78.0, 'effect_radius_pd' : 0}, [0.0010], [0.0712928]] |
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97 | ] |
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98 | |
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