Changes in / [ec8b9a3:59994557] in sasmodels

Location:

sasmodels/models

Files:

• polymer_micelle.py (modified) (2 diffs)
• spinodal.py (modified) (2 diffs)

sasmodels/models/polymer_micelle.py

@@ -11 +11 @@
 
 The 1D scattering intensity for this model is calculated according to
-the equations given by Pedersen (Pedersen, 2000).
+the equations given by Pedersen (Pedersen, 2000), summarised briefly here.
+
+The micelle core is imagined as $N\_aggreg$ polymer heads, each of volume $v\_core$,
+which then defines a micelle core of $radius\_core$, which is a separate parameter
+even though it could be directly determined.
+The Gaussian random coil tails, of gyration radius $rg$, are imagined uniformly 
+distributed around the spherical core, centred at a distance $radius\_core + d\_penetration.rg$
+from the micelle centre, where $d\_penetration$ is of order unity.
+A volume $v\_corona$ is defined for each coil.
+The model in detail seems to separately parametrise the terms for the shape of I(Q) and the
+relative intensity of each term, so use with caution and check parameters for consistency.
+The spherical core is monodisperse, so it's intensity and the cross terms may have sharp
+oscillations (use q resolution smearing if needs be to help remove them).
+
+.. math::
+    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)
+    
+    \beta_s = v\_core(sld\_core - sld\_solvent)
+    
+    \beta_c = v\_corona(sld\_corona - sld\_solvent)
+
+where $N = n\_aggreg$, and for the spherical core of radius $R$ 
+
+.. math::   
+   \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3}
+
+whilst for the Gaussian coils
+
+.. math::
+
+   P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2
+
+   Z &= (q R_g)^2
+
+The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are
+approximated by:
+
+.. math::
+   
+   S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)}
+   
+   S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2
+   
+   \psi(Z)=\frac{[1-exp^{-Z}]}{Z}
 
 Validation
 ----------
 
-This model has not yet been validated. Feb2015
+$P(q)$ above is multiplied by $ndensity$, and a units conversion of 10^{-13}, so $scale$
+is likely 1.0 if the scattering data is in absolute units. This model has not yet been 
+independently validated.
 
 
@@ -31 +76 @@
 title = "Polymer micelle model"
 description = """
-    This model provides an approximate form factor, P(q), for a micelle with
-    a spherical core with Gaussian polymer chains attached to the surface.
+This model provides the form factor, $P(q)$, for a micelle with a spherical
+core and Gaussian polymer chains attached to the surface, thus may be applied
+to block copolymer micelles. To work well the Gaussian chains must be much
+smaller than the core, which is often not the case.  Please study the
+reference to Pedersen and full documentation carefully. 
     """
+
+
 category = "shape:sphere"
 

sasmodels/models/spinodal.py

@@ -5 +5 @@
 This model calculates the SAS signal of a phase separating solution under spinodal decomposition. 
 The scattering intensity $I(q)$ is calculated as
-.. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B
-where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length
- scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to 
+
+.. math:: 
+    I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B
+
+where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length 
+scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to 
 $d+1$ with d the dimensionality of the off-critical concentration mixtures.
-A transition to $\gamma=2 d$is seen near the percolation treshold into the 
+A transition to $\gamma=2d$ is seen near the percolation threshold into the 
 critical concentration regime.
 
@@ -43 +46 @@
 # pylint: disable=bad-whitespace, line-too-long
 #             ["name", "units", default, [lower, upper], "type", "description"],
-parameters = [["scale",    "",  1.0, [-inf, inf], "", "Scale factor"],
-              ["gamma",      "",      3.0, [-inf, inf], "", "Exponent"],
+parameters = [["scale",    "",      1.0, [-inf, inf], "", "Scale factor"],
+              ["gamma",      "",    3.0, [-inf, inf], "", "Exponent"],
               ["q_0",  "1/Ang",     0.1, [-inf, inf], "", "Correlation peak position"]
              ]