# Changeset 5df888c in sasmodels

Ignore:
Timestamp:
Oct 7, 2016 9:07:26 PM (5 years ago)
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:
1 edited

### Legend:

Unmodified
 rb0c4271 ---------- 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 ["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"],