Changes in / [59994557:ec8b9a3] in sasmodels


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sasmodels/models
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  • sasmodels/models/polymer_micelle.py

    rbba9361 ra807206  
    1111 
    1212The 1D scattering intensity for this model is calculated according to 
    13 the equations given by Pedersen (Pedersen, 2000), summarised briefly here. 
    14  
    15 The micelle core is imagined as $N\_aggreg$ polymer heads, each of volume $v\_core$, 
    16 which then defines a micelle core of $radius\_core$, which is a separate parameter 
    17 even though it could be directly determined. 
    18 The Gaussian random coil tails, of gyration radius $rg$, are imagined uniformly  
    19 distributed around the spherical core, centred at a distance $radius\_core + d\_penetration.rg$ 
    20 from the micelle centre, where $d\_penetration$ is of order unity. 
    21 A volume $v\_corona$ is defined for each coil. 
    22 The model in detail seems to separately parametrise the terms for the shape of I(Q) and the 
    23 relative intensity of each term, so use with caution and check parameters for consistency. 
    24 The spherical core is monodisperse, so it's intensity and the cross terms may have sharp 
    25 oscillations (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  
    34 where $N = n\_aggreg$, and for the spherical core of radius $R$  
    35  
    36 .. math::    
    37    \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3} 
    38  
    39 whilst 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  
    47 The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are 
    48 approximated 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} 
     13the equations given by Pedersen (Pedersen, 2000). 
    5714 
    5815Validation 
    5916---------- 
    6017 
    61 $P(q)$ above is multiplied by $ndensity$, and a units conversion of 10^{-13}, so $scale$ 
    62 is likely 1.0 if the scattering data is in absolute units. This model has not yet been  
    63 independently validated. 
     18This model has not yet been validated. Feb2015 
    6419 
    6520 
     
    7631title = "Polymer micelle model" 
    7732description = """ 
    78 This model provides the form factor, $P(q)$, for a micelle with a spherical 
    79 core and Gaussian polymer chains attached to the surface, thus may be applied 
    80 to block copolymer micelles. To work well the Gaussian chains must be much 
    81 smaller than the core, which is often not the case.  Please study the 
    82 reference to Pedersen and full documentation carefully.  
     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. 
    8335    """ 
    84  
    85  
    8636category = "shape:sphere" 
    8737 
  • sasmodels/models/spinodal.py

    rbba9361 r43fe34b  
    55This model calculates the SAS signal of a phase separating solution under spinodal decomposition.  
    66The scattering intensity $I(q)$ is calculated as 
    7  
    8 .. math::  
    9     I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
    10  
    11 where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length  
    12 scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to  
     7.. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 
     8where $x=q/q_0$ 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  
    1310$d+1$ with d the dimensionality of the off-critical concentration mixtures. 
    14 A transition to $\gamma=2d$ is seen near the percolation threshold into the  
     11A transition to $\gamma=2 d$is seen near the percolation treshold into the  
    1512critical concentration regime. 
    1613 
     
    4643# pylint: disable=bad-whitespace, line-too-long 
    4744#             ["name", "units", default, [lower, upper], "type", "description"], 
    48 parameters = [["scale",    "",      1.0, [-inf, inf], "", "Scale factor"], 
    49               ["gamma",      "",    3.0, [-inf, inf], "", "Exponent"], 
     45parameters = [["scale",    "",  1.0, [-inf, inf], "", "Scale factor"], 
     46              ["gamma",      "",      3.0, [-inf, inf], "", "Exponent"], 
    5047              ["q_0",  "1/Ang",     0.1, [-inf, inf], "", "Correlation peak position"] 
    5148             ] 
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