[0433203] | 1 | r""" |
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| 2 | Definition |
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| 3 | ---------- |
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| 4 | |
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| 5 | The large and small spheres have their own SLD, as well as the solvent. The |
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| 6 | surface coverage term is a fractional coverage (maximum of approximately 0.9 |
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| 7 | for hexagonally-packed spheres on a surface). Since not all of the small |
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| 8 | spheres are necessarily attached to the surface, the excess free (small) |
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| 9 | spheres scattering is also included in the calculation. The function calculate |
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| 10 | follows equations (8)-(12) of the reference below, and the equations are not |
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| 11 | reproduced here. |
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| 12 | |
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| 13 | No inter-particle scattering is included in this model. |
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| 14 | |
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| 15 | |
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| 16 | .. figure:: img/raspberry_geometry.jpg |
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| 17 | |
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| 18 | Schematic of the raspberry model |
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| 19 | |
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| 20 | where *Ro* is the radius of the large sphere, *Rp* the radius of the smaller |
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| 21 | spheres on the surface and |delta| = the fractional penetration depth. |
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| 22 | |
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| 23 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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| 24 | where the *q* vector is defined as |
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| 25 | |
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| 26 | .. math:: |
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| 27 | |
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| 28 | q = \sqrt{q_x^2 + q_y^2} |
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| 29 | |
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| 30 | |
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| 31 | References |
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| 32 | ---------- |
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| 33 | |
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| 34 | K Larson-Smith, A Jackson, and D C Pozzo, *Small angle scattering model for Pickering emulsions and raspberry* |
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| 35 | *particles*, *Journal of Colloid and Interface Science*, 343(1) (2010) 36-41 |
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| 36 | |
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| 37 | **Author:** Andrew jackson **on:** 2008 |
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| 38 | |
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| 39 | **Modified by:** Paul Butler **on:** March 18, 2016 |
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| 40 | |
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| 41 | **Reviewed by:** Paul Butler **on:** March 18, 2016 |
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| 42 | """ |
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| 43 | |
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| 44 | from numpy import pi, inf |
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| 45 | |
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| 46 | name = "raspberry_surface_coverage" |
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| 47 | title = "Calculates the form factor, *P(q)*, for a 'Raspberry-like' structure \ |
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| 48 | where there are smaller spheres at the surface of a larger sphere, such as the \ |
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| 49 | structure of a Pickering emulsion. This version takes the suface coverage \ |
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| 50 | of small spheres as a parameter." |
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| 51 | description = """ |
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| 52 | RaspBerryModel: |
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| 53 | volfraction_lg = volume fraction large spheres |
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| 54 | radius_lg = radius large sphere (A) |
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| 55 | sld_lg = sld large sphere (A-2) |
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| 56 | volfraction_sm = volume fraction small spheres |
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| 57 | radius_sm = radius small sphere (A) |
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| 58 | surface_coverage = fraction of small spheres at surface |
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| 59 | sld_sm = sld small sphere |
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| 60 | penetration = small sphere penetration (A) |
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| 61 | sld_solvent = sld solvent |
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| 62 | background = background (cm-1) |
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| 63 | Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41.""" |
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| 64 | category = "shape:sphere" |
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| 65 | |
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| 66 | # [ "name", "units", default, [lower, upper], "type", "description"], |
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| 67 | parameters = [["sld_lg", "1e-6/Ang^2", -0.4, [-inf, inf], "", |
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| 68 | "large particle scattering length density"], |
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| 69 | ["sld_sm", "1e-6/Ang^2", 3.5, [-inf, inf], "", |
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| 70 | "small particle scattering length density"], |
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| 71 | ["sld_solvent", "1e-6/Ang^2", 6.36, [-inf, inf], "", |
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| 72 | "solvent scattering length density"], |
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| 73 | ["volfraction_lg", "", 0.05, [-inf, inf], "", |
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| 74 | "volume fraction of large spheres"], |
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| 75 | ["volfraction_sm", "", 0.005, [-inf, inf], "", |
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| 76 | "volume fraction of small spheres"], |
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| 77 | ["surface_coverage", "", 0.4, [-inf, inf], "", |
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| 78 | "surface coverage fraction of small spheres"], |
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| 79 | ["radius_lg", "Ang", 5000, [0, inf], "volume", |
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| 80 | "radius of large spheres"], |
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| 81 | ["radius_sm", "Ang", 100, [0, inf], "", |
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| 82 | "radius of small spheres"], |
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| 83 | ["penetration", "Ang", 0.0, [0, inf], "", |
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| 84 | "penetration depth of small spheres into large sphere"], |
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| 85 | ] |
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| 86 | |
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| 87 | source = ["lib/sph_j1c.c", "raspberry_surface_coverage.c"] |
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| 88 | |
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| 89 | # parameters for demo |
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| 90 | demo = dict(scale=1, background=0.001, |
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| 91 | sld_lg=-0.4, sld_sm=3.5, sld_solvent=6.36, |
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| 92 | volfraction_lg=0.05, volfraction_sm=0.005, surf_fraction=0.4, |
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| 93 | radius_lg=5000, radius_sm=100, penetration=0.0, |
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| 94 | radius_lg_pd=.2, radius_lg_pd_n=10) |
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| 95 | |
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| 96 | # For testing against the old sasview models, include the converted parameter |
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| 97 | # names and the target sasview model name. |
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| 98 | oldname = 'RaspBerryModel' |
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| 99 | oldpars = dict(sld_lg='sld_Lsph', sld_sm='sld_Ssph', sld_solvent='sld_solv', |
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| 100 | volfraction_lg='volf_Lsph', volfraction_sm='volf_Ssph', |
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| 101 | surf_fraction='surfrac_Ssph', |
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| 102 | radius_lg='radius_Lsph', radius_sm='radius_Ssph', |
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| 103 | penetration='delta_Ssph') |
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| 104 | |
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| 105 | |
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| 106 | # NOTE: test results taken from values returned by SasView 3.1.2, with |
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| 107 | # 0.001 added for a non-zero default background. |
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| 108 | tests = [[{}, 0.0412755102041, 0.286669115234], |
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| 109 | [{}, 0.5, 0.00103818393658], |
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| 110 | ] |
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