Changeset c1e44e5 in sasmodels for sasmodels/models/stickyhardsphere.py
- Timestamp:
- Mar 30, 2019 1:59:45 AM (5 years ago)
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- master
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- a42b091
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- 663d2a8
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sasmodels/models/stickyhardsphere.py
r5f3c534 rc1e44e5 1 1 # Note: model title and parameter table are inserted automatically 2 2 r""" 3 Calculates the interparticle structure factor for a hard sphere fluid 4 with a narrow, attractive, potential well. Unlike the :ref:`squarewell` 5 model, here a perturbative solution of the Percus-Yevick closure 6 relationship is used. The strength of the attractive well is described 3 Calculates the interparticle structure factor for a hard sphere fluid 4 with a narrow, attractive, potential well. Unlike the :ref:`squarewell` 5 model, here a perturbative solution of the Percus-Yevick closure 6 relationship is used. The strength of the attractive well is described 7 7 in terms of "stickiness" as defined below. 8 8 9 9 The perturbation parameter (perturb), $\tau$, should be fixed between 0.01 10 and 0.1 and the "stickiness", $\epsilon$, allowed to vary to adjust the 11 interaction strength. The "stickiness" is defined in the equation below and is 12 a function of both the perturbation parameter and the interaction strength. 13 $\epsilon$ and $\tau$ are defined in terms of the hard sphere diameter $(\sigma = 2 R)$, 14 the width of the square well, $\Delta$ (having the same units as $R$\ ), 15 and the depth of the well, $U_o$, in units of $kT$. From the definition, it 10 and 0.1 and the "stickiness", $\epsilon$, allowed to vary to adjust the 11 interaction strength. The "stickiness" is defined in the equation below and is 12 a function of both the perturbation parameter and the interaction strength. 13 $\epsilon$ and $\tau$ are defined in terms of the hard sphere diameter $(\sigma = 2 R)$, 14 the width of the square well, $\Delta$ (having the same units as $R$\ ), 15 and the depth of the well, $U_o$, in units of $kT$. From the definition, it 16 16 is clear that smaller $\epsilon$ means a stronger attraction. 17 17 … … 37 37 38 38 The true particle volume fraction, $\phi$, is not equal to $h$ which appears 39 in most of reference [1]. The two are related in equation (24). Reference 40 [1] also describes the relationship between this perturbative solution and 39 in most of reference [1]. The two are related in equation (24). Reference 40 [1] also describes the relationship between this perturbative solution and 41 41 the original sticky hard sphere (or "adhesive sphere") model of Baxter [2]. 42 42 … … 47 47 reported to the command window and $S(q)$ is set to -1 (so it will 48 48 disappear on a log-log plot!). 49 50 Use tight bounds to keep the parameters to values that you know are 51 physical (test them), and keep nudging them until the optimization 49 50 Use tight bounds to keep the parameters to values that you know are 51 physical (test them), and keep nudging them until the optimization 52 52 does not hit the constraints. 53 53 54 54 .. note:: 55 55 56 Earlier versions of SasView did not incorporate the so-called 57 $\beta(q)$ ("beta") correction [3] for polydispersity and non-sphericity. 56 Earlier versions of SasView did not incorporate the so-called 57 $\beta(q)$ ("beta") correction [3] for polydispersity and non-sphericity. 58 58 This is only available in SasView versions 4.2.2 and higher. 59 59 60 60 In SasView the effective radius may be calculated from the parameters 61 61 used in the form factor $P(q)$ that this $S(q)$ is combined with. … … 78 78 .. [#] M Kotlarchyk and S-H Chen, *J. Chem. Phys.*, 79 (1983) 2461-2469 79 79 80 Source81 ------82 83 `stickyhardsphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/stickyhardsphere.py>`_84 85 80 Authorship and Verification 86 81 ---------------------------- 87 82 88 * **Author:** 89 * **Last Modified by:** 83 * **Author:** 84 * **Last Modified by:** 90 85 * **Last Reviewed by:** Steve King **Date:** March 27, 2019 91 * **Source added by :** Steve King **Date:** March 25, 201992 86 """ 93 87 … … 101 95 description = """\ 102 96 [Sticky hard sphere structure factor, with Percus-Yevick closure] 103 Interparticle structure factor S(Q) for a hard sphere fluid 97 Interparticle structure factor S(Q) for a hard sphere fluid 104 98 with a narrow attractive well. Fits are prone to deliver non- 105 physical parameters; use with care and read the references in 106 the model documentation.The "beta(q)" correction is available 99 physical parameters; use with care and read the references in 100 the model documentation.The "beta(q)" correction is available 107 101 in versions 4.2.2 and higher. 108 102 """
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