Changeset 547c6f0 in sasmodels


Ignore:
Timestamp:
Feb 15, 2018 5:59:45 AM (6 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
aa90015
Parents:
a2ca6e5
Message:

polymer_excl_volume: update eq. to match paper. Refs #1073

File:
1 edited

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  • sasmodels/models/polymer_excl_volume.py

    ra2ca6e5 r547c6f0  
    1818and $n$ is the degree of polymerization. 
    1919 
    20 This integral was later put into an almost analytical form as follows 
     20This integral was put into an almost analytical form as follows 
    2121(Hammouda, 1993) 
    2222 
    2323.. math:: 
    2424 
    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) 
     25    P(Q)=\frac{1}{\nu U^{1/2\nu}} 
     26    \left\{ 
     27        \gamma\left(\frac{1}{2\nu},U\right) - 
     28        \frac{1}{U^{1/2\nu}}\gamma\left(\frac{1}{\nu},U\right) 
     29    \right\} 
    2730 
    28 later recast as (for example, Hore, 2013; Hammouda & Kim, 2017) 
     31and later recast as (for example, Hore, 2013; Hammouda & Kim, 2017) 
    2932 
    3033.. math:: 
     
    3740.. math:: 
    3841 
    39     \gamma(x,U)=\int_0^{U}dt\ exp(-t)t^{x-1} 
     42    \gamma(x,U)=\int_0^{U}dt\ \exp(-t)t^{x-1} 
    4043 
    4144and the variable $U$ is given in terms of the scattering vector $Q$ as 
     
    9295.. math:: 
    9396 
    94     P(Q) = \frac{2}{Q^4R_{g}^4} \left[exp(-Q^2R_{g}^2) - 1 + Q^2R_{g}^2 \right] 
     97    P(Q) = \frac{2}{Q^4R_{g}^4} \left[\exp(-Q^2R_{g}^2) - 1 + Q^2R_{g}^2 \right] 
    9598 
    9699For 2D data: The 2D scattering intensity is calculated in the same way as 1D, 
     
    110113Advances in Polym. Sci.* 106 (1993) 87-133 
    111114 
    112 M Hore et al, *Co-Nonsolvency of Poly(n-isopropylacrylamide) in Deuterated  
     115M Hore et al, *Co-Nonsolvency of Poly(n-isopropylacrylamide) in Deuterated 
    113116Water/Ethanol Mixtures* 46 (2013) 7894-7901 
    114117 
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