Changeset a2ca6e5 in sasmodels


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Timestamp:
Feb 15, 2018 5:01:45 AM (6 years ago)
Author:
smk78
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
547c6f0
Parents:
13bd583
Message:

Updated help doc for polymer_excl_volume model in wake of Ticket 1073

File:
1 edited

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  • sasmodels/models/polymer_excl_volume.py

    r2d81cfe ra2ca6e5  
    1717$a$ is the statistical segment length of the polymer chain, 
    1818and $n$ is the degree of polymerization. 
     19 
    1920This integral was later put into an almost analytical form as follows 
    2021(Hammouda, 1993) 
     22 
     23.. math:: 
     24 
     25    P(Q)=\frac{1}{\nu U^{1/2\nu}}\gamma\left(\frac{1}{2\nu},U\right) - 
     26    \frac{1}{U^{1/2\nu}}\gamma\left(\frac{1}{\nu},U\right) 
     27 
     28later recast as (for example, Hore, 2013; Hammouda & Kim, 2017) 
    2129 
    2230.. math:: 
     
    3745    U=\frac{Q^2a^2n^{2\nu}}{6} = \frac{Q^2R_{g}^2(2\nu+1)(2\nu+2)}{6} 
    3846 
     47The two analytic forms are equivalent. In the 1993 paper 
     48 
     49.. math:: 
     50 
     51    \frac{1}{\nu U^{1/2\nu}} 
     52 
     53has been factored out. 
     54 
     55**SasView implements the 1993 expression**. 
     56 
    3957The square of the radius-of-gyration is defined as 
    4058 
     
    4361    R_{g}^2 = \frac{a^2n^{2\nu}}{(2\nu+1)(2\nu+2)} 
    4462 
    45 Note that this model applies only in the mass fractal range (ie, $5/3<=m<=3$ ) 
    46 and **does not apply** to surface fractals ( $3<m<=4$ ). 
    47 It also does not reproduce the rigid rod limit (m=1) because it assumes chain 
    48 flexibility from the outset. It may cover a portion of the semi-flexible chain 
    49 range ( $1<m<5/3$ ). 
     63.. note:: 
     64    This model applies only in the mass fractal range (ie, $5/3<=m<=3$ ) 
     65    and **does not apply** to surface fractals ( $3<m<=4$ ). 
     66    It also does not reproduce the rigid rod limit (m=1) because it assumes chain 
     67    flexibility from the outset. It may cover a portion of the semi-flexible chain 
     68    range ( $1<m<5/3$ ). 
    5069 
    5170A low-Q expansion yields the Guinier form and a high-Q expansion yields the 
     
    89108 
    90109B Hammouda, *SANS from Homogeneous Polymer Mixtures - A Unified Overview, 
    91 Advances in Polym. Sci.* 106(1993) 87-133 
     110Advances in Polym. Sci.* 106 (1993) 87-133 
     111 
     112M Hore et al, *Co-Nonsolvency of Poly(n-isopropylacrylamide) in Deuterated  
     113Water/Ethanol Mixtures* 46 (2013) 7894-7901 
     114 
     115B Hammouda & M-H Kim, *The empirical core-chain model* 247 (2017) 434-440 
    92116""" 
    93117 
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