Changeset 5df888c in sasmodels for sasmodels/models/be_polyelectrolyte.py

Timestamp:

Oct 7, 2016 7:07:26 PM (8 years ago)

Author:

butler

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

462a115

Parents:

416f5c7

Message:

added defintions, fixed units and gnerally cleaned up
be_polyelectrolyte.py model documentation. closes #553

File:

• sasmodels/models/be_polyelectrolyte.py (modified) (2 diffs)

sasmodels/models/be_polyelectrolyte.py

@@ -3 +3 @@
 ----------
 This model calculates the structure factor of a polyelectrolyte solution with
-the RPA expression derived by Borue and Erukhimovich\ [#Borue]_.  The scattering intensity
-$I(q)$ is calculated as
+the RPA expression derived by Borue and Erukhimovich\ [#Borue]_.  Note however
+that the fitting procedure here does not follow the notation in that reference
+as 's' and 't' are **not** decoupled. Instead the scattering intensity $I(q)$
+is calculated as
 
 .. math::
 
-    I(q) = K\frac{q^2+k^2}{4\pi L\alpha ^2}
+    I(q) = K\frac{q^2+k^2}{4\pi L_b\alpha ^2}
     \frac{1}{1+r_{0}^2(q^2+k^2)(q^2-12hC_a/b^2)} + background
 
-    k^2 = 4\pi L(2C_s + \alpha C_a)
+    k^2 = 4\pi L_b(2C_s + \alpha C_a)
 
     r_{0}^2 = \frac{1}{\alpha \sqrt{C_a} \left( b/\sqrt{48\pi L_b}\right)}
 
-where $K$ is the contrast factor for the polymer, $L_b$ is the Bjerrum length,
-$h$ is the virial parameter, $b$ is the monomer length,
-$C_s$ is the concentration of monovalent salt, $\alpha$ is the ionization
-degree, $C_a$ is the polymer molar concentration, and $background$ is the
-incoherent background.
+where 
+
+$K$ is the contrast factor for the polymer which is defined differently than in
+other models and is given in barns where $1 barn = 10^{-24} cm^2$.  $K$ is
+defined as:
+
+.. math::
+
+    K = a^2
+
+    a = b_p - (v_p/v_s) b_s
+    
+where $b_p$ and $b_s$ are sum of the scattering lengths of the atoms
+constituting the monomer of the polymer and the sum of the scattering lengths
+of the atoms constituting the solvent molecules respectively, and $v_p$ and
+$v_s$ are the partial molar volume of the polymer and the solvent respectively
+
+$L_b$ is the Bjerrum length(|Ang|) - **Note:** This parameter needs to be
+kept constant for a given solvent and temperature! 
+
+$h$ is the virial parameter (|Ang^3|/mol) - **Note:** See [#Borue]_ for the
+correct interpretation of this parameter.  It incorporates second and third
+virial coefficients and can be Negative.
+
+$b$ is the monomer length(|Ang|), $C_s$ is the concentration of monovalent
+salt(mol/L), $\alpha$ is the ionization degree (ionization degree : ratio of
+charged monomers  to total number of monomers), $C_a$ is the polymer molar
+concentration(mol/L), and $background$ is the incoherent background.
 
 For 2D data the scattering intensity is calculated in the same way as 1D,
-where the $q$ vector is defined as
+where the $\vec q$ vector is defined as
 
 .. math::
 
     q = \sqrt{q_x^2 + q_y^2}
-
-
-NB: $1 barn = 10^{-24} cm^2$
 
 References
@@ -69 +91 @@
     ["contrast_factor",       "barns",   10.0,  [-inf, inf], "", "Contrast factor of the polymer"],
     ["bjerrum_length",        "Ang",      7.1,  [0, inf],    "", "Bjerrum length"],
-    ["virial_param",          "1/Ang^2", 12.0,  [-inf, inf], "", "Virial parameter"],
+    ["virial_param",          "Ang^3/mol", 12.0,  [-inf, inf], "", "Virial parameter"],
     ["monomer_length",        "Ang",     10.0,  [0, inf],    "", "Monomer length"],
     ["salt_concentration",    "mol/L",    0.0,  [-inf, inf], "", "Concentration of monovalent salt"],