Changes in / [ec8b9a3:59994557] in sasmodels


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sasmodels/models
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  • sasmodels/models/polymer_micelle.py

    ra807206 rbba9361  
    1111 
    1212The 1D scattering intensity for this model is calculated according to 
    13 the equations given by Pedersen (Pedersen, 2000). 
     13the equations given by Pedersen (Pedersen, 2000), summarised briefly here. 
     14 
     15The micelle core is imagined as $N\_aggreg$ polymer heads, each of volume $v\_core$, 
     16which then defines a micelle core of $radius\_core$, which is a separate parameter 
     17even though it could be directly determined. 
     18The Gaussian random coil tails, of gyration radius $rg$, are imagined uniformly  
     19distributed around the spherical core, centred at a distance $radius\_core + d\_penetration.rg$ 
     20from the micelle centre, where $d\_penetration$ is of order unity. 
     21A volume $v\_corona$ is defined for each coil. 
     22The model in detail seems to separately parametrise the terms for the shape of I(Q) and the 
     23relative intensity of each term, so use with caution and check parameters for consistency. 
     24The spherical core is monodisperse, so it's intensity and the cross terms may have sharp 
     25oscillations (use q resolution smearing if needs be to help remove them). 
     26 
     27.. math:: 
     28    P(q) = N^2\beta^2_s\Phi(qR)^2+N\beta^2_cP_c(q)+2N^2\beta_s\beta_cS_{sc}s_c(q)+N(N-1)\beta_c^2S_{cc}(q) 
     29     
     30    \beta_s = v\_core(sld\_core - sld\_solvent) 
     31     
     32    \beta_c = v\_corona(sld\_corona - sld\_solvent) 
     33 
     34where $N = n\_aggreg$, and for the spherical core of radius $R$  
     35 
     36.. math::    
     37   \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3} 
     38 
     39whilst for the Gaussian coils 
     40 
     41.. math:: 
     42 
     43   P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 
     44 
     45   Z &= (q R_g)^2 
     46 
     47The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are 
     48approximated by: 
     49 
     50.. math:: 
     51    
     52   S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} 
     53    
     54   S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2 
     55    
     56   \psi(Z)=\frac{[1-exp^{-Z}]}{Z} 
    1457 
    1558Validation 
    1659---------- 
    1760 
    18 This model has not yet been validated. Feb2015 
     61$P(q)$ above is multiplied by $ndensity$, and a units conversion of 10^{-13}, so $scale$ 
     62is likely 1.0 if the scattering data is in absolute units. This model has not yet been  
     63independently validated. 
    1964 
    2065 
     
    3176title = "Polymer micelle model" 
    3277description = """ 
    33     This model provides an approximate form factor, P(q), for a micelle with 
    34     a spherical core with Gaussian polymer chains attached to the surface. 
     78This model provides the form factor, $P(q)$, for a micelle with a spherical 
     79core and Gaussian polymer chains attached to the surface, thus may be applied 
     80to block copolymer micelles. To work well the Gaussian chains must be much 
     81smaller than the core, which is often not the case.  Please study the 
     82reference to Pedersen and full documentation carefully.  
    3583    """ 
     84 
     85 
    3686category = "shape:sphere" 
    3787 
  • sasmodels/models/spinodal.py

    r43fe34b rbba9361  
    55This model calculates the SAS signal of a phase separating solution under spinodal decomposition.  
    66The scattering intensity $I(q)$ is calculated as 
    7 .. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
    8 where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length 
    9  scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to  
     7 
     8.. math::  
     9    I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
     10 
     11where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length  
     12scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to  
    1013$d+1$ with d the dimensionality of the off-critical concentration mixtures. 
    11 A transition to $\gamma=2 d$is seen near the percolation treshold into the  
     14A transition to $\gamma=2d$ is seen near the percolation threshold into the  
    1215critical concentration regime. 
    1316 
     
    4346# pylint: disable=bad-whitespace, line-too-long 
    4447#             ["name", "units", default, [lower, upper], "type", "description"], 
    45 parameters = [["scale",    "",  1.0, [-inf, inf], "", "Scale factor"], 
    46               ["gamma",      "",      3.0, [-inf, inf], "", "Exponent"], 
     48parameters = [["scale",    "",      1.0, [-inf, inf], "", "Scale factor"], 
     49              ["gamma",      "",    3.0, [-inf, inf], "", "Exponent"], 
    4750              ["q_0",  "1/Ang",     0.1, [-inf, inf], "", "Correlation peak position"] 
    4851             ] 
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