Changeset caddb14 in sasmodels

Timestamp:

Oct 1, 2016 7:48:49 AM (8 years ago)

Author:

ajj

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

69ef533

Parents:

a807206

Message:

Updated and re-parameterised Teubner-Strey model.

Closes #472
Closes #530

File:

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

sasmodels/models/teubner_strey.py

@@ -5 +5 @@
 This model calculates the scattered intensity of a two-component system
 using the Teubner-Strey model. Unlike :ref:`dab` this function generates
-a peak.
+a peak. A two-phase material can be characterised by two length scales -
+a correlation length and a domain size (periodicity).
+
+The original paper by Teubner and Strey defined the function as:
 
 .. math::
 
-    I(q) = \frac{1}{a_2 + c_1 q^2 + c_2 q^4} + \text{background}
+    I(q) \propto \frac{1}{a_2 + c_1 q^2 + c_2 q^4} + \text{background}
 
-The parameters $a_2$, $c_1$ and $c_2$ can be used to determine the
-characteristic domain size $d$,
+where the parameters $a_2$, $c_1$ and $c_2$ are defined in terms of the
+periodicity, $d$, and correlation length $\xi$ as:
+
+.. math::
+
+    a_2 &= \biggl[1+\bigl(\frac{2\pi\xi}{d}\bigr)^2\biggr]\\
+    c_1 &= -2\xi^2\bigl(\frac{2\pi\xi}{d}\bigr)^2+2\xi^2\\
+    c_2 &= \xi^4
+
+and thus, the periodicity, $d$ is given by
 
 .. math::
 
     d = 2\pi\left[\frac12\left(\frac{a_2}{c_2}\right)^{1/2}
-                  + \frac14\frac{c_1}{c_2}\right]^{-1/2}
+                  - \frac14\frac{c_1}{c_2}\right]^{-1/2}
 
-
-and the correlation length $\xi$,
+and the correlation length, $\xi$, is given by
 
 .. math::
 
     \xi = \left[\frac12\left(\frac{a_2}{c_2}\right)^{1/2}
-                  - \frac14\frac{c_1}{c_2}\right]^{-1/2}
+                  + \frac14\frac{c_1}{c_2}\right]^{-1/2}
 
+Here the model is parameterised in terms of  $d$ and $\xi$ and with an explicit
+volume fraction for one phase, $\phi_a$, and contrast,
+$\delta\rho^2 = (\rho_a - \rho_b)^2$ :
+
+.. math::
+
+    I(q) = \frac{8\pi\phi_a(1-\phi_a)(\Delta\rho)^2c_2/\xi}
+        {a_2 + c_1q^2 + c_2q^4}
+
+where :math:`8\pi\phi_a(1-\phi_a)(\Delta\rho)^2c_2/\xi` is the constant of
+proportionality from the first equation above.
+
+In the case of a microemulsion, $a_2 > 0$, $c_1 < 0$, and $c_2 >0$.
 
 For 2D data, scattering intensity is calculated in the same way as 1D,
@@ -34 +57 @@
 
     q = \sqrt{q_x^2 + q_y^2}
-
 
 References
@@ -44 +66 @@
 *J. Chem. Phys.*, 101 (1994) 5343
 
+H Endo, M Mihailescu, M. Monkenbusch, J Allgaier, G Gompper, D Richter,
+B Jakobs, T Sottmann, R Strey, and I Grillo, *J. Chem. Phys.*, 115 (2001), 580
 """
 
 import numpy as np
-from numpy import inf
+from numpy import inf,power,pi
 
 name = "teubner_strey"
 title = "Teubner-Strey model of microemulsions"
 description = """\
-   Scattering model class for the Teubner-Strey model given by
-    Provide F(x) = 1/( a2 + c1 q^2+  c2 q^4 ) + background
-    a2>0, c1<0, c2>0, 4 a2 c2 - c1^2 > 0
+    Calculates scattering according to the Teubner-Strey model
 """
 category = "shape-independent"
@@ -60 +82 @@
 #   ["name", "units", default, [lower, upper], "type","description"],
 parameters = [
-    ["a2", "", 0.1, [0, inf], "", "a2"],
-    ["c1", "1e-6/Ang^2", -30., [-inf, 0], "", "c1"],
-    ["c2", "Ang", 5000., [0, inf], "volume", "c2"],
+    ["volfraction_a", "", 0.5, [0, 1.0], "", "Volume fraction of phase a"],
+    ["sld_a", "1e-6/Ang^2", 0.3, [-inf, inf], "", "SLD of phase a"],
+    ["sld_b", "1e-6/Ang^2", 6.3, [-inf, inf], "", "SLD of phase b"],
+    ["d", "Ang", 100.0, [0, inf], "", "Domain size (periodicity)"],
+    ["xi", "Ang", 30.0, [0, inf], "", "Correlation length"],
     ]
 
-def Iq(q, a2, c1, c2):
+def Iq(q, volfraction, sld, sld_solvent,d,xi):
     """SAS form"""
-    return 1. / np.polyval([c2, c1, a2], q**2)
+    drho2 = (sld-sld_solvent)*(sld-sld_solvent)
+    a2 = power(1.0+power(2.0*pi*xi/d,2.0),2.0)
+    c1 = -2.0*xi*xi*power(2.0*pi*xi/d,2.0)+2*xi*xi
+    c2 = power(xi,4.0)
+    prefactor = 8.0*pi*volfraction*(1.0-volfraction)*drho2*c2/xi
+    #k2 = (2.0*pi/d)*(2.0*pi/d)
+    #xi2 = 1/(xi*xi)
+    #q2 = q*q
+    #result = prefactor/((xi2+k2)*(xi2+k2)+2.0*(xi2-k2)*q2+q2*q2)
+    return 1.0e-4*prefactor / np.polyval([c2, c1, a2], q**2)
+
 Iq.vectorized = True  # Iq accepts an array of q values
 
-demo = dict(scale=1, background=0, a2=0.1, c1=-30.0, c2=5000.0)
-tests = [[{}, 0.2, 0.145927536232]]
+demo = dict(scale=1, background=0, volfraction_a=0.5,
+                     sld_a=0.3, sld_b=6.3,
+                     d=100.0, xi=30.0)
+tests = [[{}, 0.06, 41.5918888453]]