Changeset 2d81cfe in sasmodels for sasmodels/models/polymer_micelle.py

Timestamp:

Nov 29, 2017 1:13:23 PM (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:

237b800f

Parents:

a839b22

Message:

lint

File:

• sasmodels/models/polymer_micelle.py (modified) (4 diffs)

sasmodels/models/polymer_micelle.py

@@ -13 +13 @@
 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).
+The micelle core is imagined as $N$ = *n_aggreg* polymer heads, each of volume
+$V_\text{core}$, which then defines a micelle core of radius $r$ = *r_core*,
+which is a separate parameter even though it could be directly determined.
+The Gaussian random coil tails, of gyration radius $R_g$, are imagined
+uniformly distributed around the spherical core, centred at a distance
+$r + d \cdot R_g$ from the micelle centre, where $d$ = *d_penetration* is
+of order unity. A volume $V_\text{corona}$ 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)
+    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_\text{core}(\rho_\text{core} - \rho_\text{solvent}) \\
+    \beta_c &= V_\text{corona}(\rho_\text{corona} - \rho_\text{solvent})
 
-where $N = n\_aggreg$, and for the spherical core of radius $R$
+where $\rho_\text{core}$, $\rho_\text{corona}$ and $\rho_\text{solvent}$ are
+the scattering length densities *sld_core*, *sld_corona* and *sld_solvent*.
+For the spherical core of radius $r$
 
 .. math::
-   \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3}
+   \Phi(qr)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3}
 
 whilst for the Gaussian coils
@@ -42 +46 @@
    Z &= (q R_g)^2
 
-The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are
-approximated by:
+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}
+   S_{sc}(q) &= \Phi(qr)\psi(Z)
+       \frac{\sin(q(r+d \cdot R_g))}{q(r+d \cdot R_g)} \\
+   S_{cc}(q) &= \psi(Z)^2
+       \left[\frac{\sin(q(r+d \cdot R_g))}{q(r+d \cdot R_g)} \right]^2 \\
+   \psi(Z) &= \frac{[1-\exp^{-Z}]}{Z}
 
 Validation
 ----------
 
-$P(q)$ 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.
+$P(q)$ 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.
 
 
@@ -63 +69 @@
 
 J Pedersen, *J. Appl. Cryst.*, 33 (2000) 637-640
-
 """
 
+import numpy as np
 from numpy import inf, pi
 
@@ -102 +108 @@
 
 def random():
-    import numpy as np
     radius_core = 10**np.random.uniform(1, 3)
     rg = radius_core * 10**np.random.uniform(-2, -0.3)