[3330bb4] | 1 | #mono_gauss_coil model |
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| 2 | #conversion of DebyeModel.py |
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| 3 | #converted by Steve King, Mar 2016 |
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| 4 | r""" |
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| 5 | This Debye Gaussian coil model strictly describes the scattering from |
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| 6 | *monodisperse* polymer chains in theta solvents or polymer melts, conditions |
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| 7 | under which the distances between segments follow a Gaussian distribution. |
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| 8 | Provided the number of segments is large (ie, high molecular weight polymers) |
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| 9 | the single-chain form factor P(Q) is that described by Debye (1947). |
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| 10 | |
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| 11 | To describe the scattering from *polydisperse* polymer chains see the |
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| 12 | :ref:`poly-gauss-coil` model. |
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| 13 | |
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| 14 | Definition |
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| 15 | ---------- |
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| 16 | |
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| 17 | .. math:: |
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| 18 | |
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| 19 | I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background} |
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| 20 | |
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| 21 | where |
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| 22 | |
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| 23 | .. math:: |
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| 24 | |
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| 25 | I_0 &= \phi_\text{poly} \cdot V |
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[ca04add] | 26 | \cdot (\rho_\text{poly} - \rho_\text{solv})^2 \\ |
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| 27 | P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\ |
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| 28 | Z &= (q R_g)^2 \\ |
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[3330bb4] | 29 | V &= M / (N_A \delta) |
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| 30 | |
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| 31 | Here, $\phi_\text{poly}$ is the volume fraction of polymer, $V$ is the |
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| 32 | volume of a polymer coil, *M* is the molecular weight of the polymer, |
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| 33 | $N_A$ is Avogadro's Number, $\delta$ is the bulk density of the polymer, |
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| 34 | $\rho_\text{poly}$ is the sld of the polymer, $\rho\text{solv}$ is the |
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| 35 | sld of the solvent, and $R_g$ is the radius of gyration of the polymer coil. |
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| 36 | |
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| 37 | The 2D scattering intensity is calculated in the same way as the 1D, |
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| 38 | but where the *q* vector is redefined as |
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| 39 | |
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| 40 | .. math:: |
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| 41 | |
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| 42 | q = \sqrt{q_x^2 + q_y^2} |
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| 43 | |
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| 44 | References |
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| 45 | ---------- |
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| 46 | |
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[0507e09] | 47 | .. [#] P Debye, *J. Phys. Colloid. Chem.*, 51 (1947) 18. |
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| 48 | .. [#] R J Roe, *Methods of X-Ray and Neutron Scattering in Polymer Science*, Oxford University Press, New York (2000). |
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| 49 | .. [#] http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf |
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[3330bb4] | 50 | |
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[0507e09] | 51 | Source |
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| 52 | ------ |
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[3330bb4] | 53 | |
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[0507e09] | 54 | `mono_gauss_coil.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/mono_gauss_coil.py>`_ |
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| 55 | |
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| 56 | `mono_gauss_coil.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/mono_gauss_coil.c>`_ |
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| 57 | |
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| 58 | Authorship and Verification |
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| 59 | ---------------------------- |
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| 60 | |
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[a34b811] | 61 | * **Author:** |
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| 62 | * **Last Modified by:** |
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| 63 | * **Last Reviewed by:** |
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[0507e09] | 64 | * **Source added by :** Steve King **Date:** March 25, 2019""" |
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[3330bb4] | 65 | |
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[2d81cfe] | 66 | import numpy as np |
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[d277229] | 67 | from numpy import inf |
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[3330bb4] | 68 | |
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| 69 | name = "mono_gauss_coil" |
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| 70 | title = "Scattering from monodisperse polymer coils" |
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| 71 | |
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| 72 | description = """ |
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[404ebbd] | 73 | Evaluates the scattering from |
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[3330bb4] | 74 | monodisperse polymer chains. |
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| 75 | """ |
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| 76 | category = "shape-independent" |
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| 77 | |
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| 78 | # pylint: disable=bad-whitespace, line-too-long |
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| 79 | # ["name", "units", default, [lower, upper], "type", "description"], |
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| 80 | parameters = [ |
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| 81 | ["i_zero", "1/cm", 70.0, [0.0, inf], "", "Intensity at q=0"], |
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[d277229] | 82 | ["rg", "Ang", 75.0, [0.0, inf], "volume", "Radius of gyration"], |
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[3330bb4] | 83 | ] |
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[ee60aa7] | 84 | # pylint: enable=bad-whitespace, line-too-long |
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[3330bb4] | 85 | |
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[d277229] | 86 | source = ["mono_gauss_coil.c"] |
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| 87 | have_Fq = False |
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[a34b811] | 88 | radius_effective_modes = ["R_g", "2R_g", "3R_g", "sqrt(5/3)*R_g"] |
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[3330bb4] | 89 | |
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| 90 | |
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[404ebbd] | 91 | def random(): |
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[b297ba9] | 92 | """Return a random parameter set for the model.""" |
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[404ebbd] | 93 | rg = 10**np.random.uniform(0, 4) |
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| 94 | #rg = 1e3 |
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| 95 | pars = dict( |
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| 96 | #scale=1, background=0, |
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| 97 | i_zero=1e7, # i_zero is a simple scale |
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| 98 | rg=rg, |
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| 99 | ) |
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| 100 | return pars |
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| 101 | |
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[3330bb4] | 102 | demo = dict(scale=1.0, i_zero=70.0, rg=75.0, background=0.0) |
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| 103 | |
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| 104 | # these unit test values taken from SasView 3.1.2 |
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| 105 | tests = [ |
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| 106 | [{'scale': 1.0, 'i_zero': 70.0, 'rg': 75.0, 'background': 0.0}, |
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| 107 | [0.0106939, 0.469418], [57.1241, 0.112859]], |
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| 108 | ] |
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