Changeset c1e44e5 in sasmodels for sasmodels/models/stickyhardsphere.py


Ignore:
Timestamp:
Mar 30, 2019 1:59:45 AM (5 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master
Children:
a42b091
Parents:
663d2a8
Message:

Add local link to source files. Refs #1263.

File:
1 edited

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  • sasmodels/models/stickyhardsphere.py

    r5f3c534 rc1e44e5  
    11# Note: model title and parameter table are inserted automatically 
    22r""" 
    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  
     3Calculates the interparticle structure factor for a hard sphere fluid 
     4with a narrow, attractive, potential well. Unlike the :ref:`squarewell` 
     5model, here a perturbative solution of the Percus-Yevick closure 
     6relationship is used. The strength of the attractive well is described 
    77in terms of "stickiness" as defined below. 
    88 
    99The 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  
     10and 0.1 and the "stickiness", $\epsilon$, allowed to vary to adjust the 
     11interaction strength. The "stickiness" is defined in the equation below and is 
     12a function of both the perturbation parameter and the interaction strength. 
     13$\epsilon$ and $\tau$ are defined in terms of the hard sphere diameter $(\sigma = 2 R)$, 
     14the width of the square well, $\Delta$ (having the same units as $R$\ ), 
     15and the depth of the well, $U_o$, in units of $kT$. From the definition, it 
    1616is clear that smaller $\epsilon$ means a stronger attraction. 
    1717 
     
    3737 
    3838The 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  
     39in most of reference [1]. The two are related in equation (24). Reference 
     40[1] also describes the relationship between this perturbative solution and 
    4141the original sticky hard sphere (or "adhesive sphere") model of Baxter [2]. 
    4242 
     
    4747   reported to the command window and $S(q)$ is set to -1 (so it will 
    4848   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 
    5252   does not hit the constraints. 
    5353 
    5454.. note:: 
    5555 
    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. 
    5858   This is only available in SasView versions 4.2.2 and higher. 
    59     
     59 
    6060In SasView the effective radius may be calculated from the parameters 
    6161used in the form factor $P(q)$ that this $S(q)$ is combined with. 
     
    7878.. [#] M Kotlarchyk and S-H Chen, *J. Chem. Phys.*, 79 (1983) 2461-2469 
    7979 
    80 Source 
    81 ------ 
    82  
    83 `stickyhardsphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/stickyhardsphere.py>`_ 
    84  
    8580Authorship and Verification 
    8681---------------------------- 
    8782 
    88 * **Author:**  
    89 * **Last Modified by:**  
     83* **Author:** 
     84* **Last Modified by:** 
    9085* **Last Reviewed by:** Steve King **Date:** March 27, 2019 
    91 * **Source added by :** Steve King **Date:** March 25, 2019 
    9286""" 
    9387 
     
    10195description = """\ 
    10296    [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 
    10498    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 
    107101    in versions 4.2.2 and higher. 
    108102""" 
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