Changeset 5df888c in sasmodels


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

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  • sasmodels/models/be_polyelectrolyte.py

    rb0c4271 r5df888c  
    33---------- 
    44This model calculates the structure factor of a polyelectrolyte solution with 
    5 the RPA expression derived by Borue and Erukhimovich\ [#Borue]_.  The scattering intensity 
    6 $I(q)$ is calculated as 
     5the RPA expression derived by Borue and Erukhimovich\ [#Borue]_.  Note however 
     6that the fitting procedure here does not follow the notation in that reference 
     7as 's' and 't' are **not** decoupled. Instead the scattering intensity $I(q)$ 
     8is calculated as 
    79 
    810.. math:: 
    911 
    10     I(q) = K\frac{q^2+k^2}{4\pi L\alpha ^2} 
     12    I(q) = K\frac{q^2+k^2}{4\pi L_b\alpha ^2} 
    1113    \frac{1}{1+r_{0}^2(q^2+k^2)(q^2-12hC_a/b^2)} + background 
    1214 
    13     k^2 = 4\pi L(2C_s + \alpha C_a) 
     15    k^2 = 4\pi L_b(2C_s + \alpha C_a) 
    1416 
    1517    r_{0}^2 = \frac{1}{\alpha \sqrt{C_a} \left( b/\sqrt{48\pi L_b}\right)} 
    1618 
    17 where $K$ is the contrast factor for the polymer, $L_b$ is the Bjerrum length, 
    18 $h$ is the virial parameter, $b$ is the monomer length, 
    19 $C_s$ is the concentration of monovalent salt, $\alpha$ is the ionization 
    20 degree, $C_a$ is the polymer molar concentration, and $background$ is the 
    21 incoherent background. 
     19where  
     20 
     21$K$ is the contrast factor for the polymer which is defined differently than in 
     22other models and is given in barns where $1 barn = 10^{-24} cm^2$.  $K$ is 
     23defined as: 
     24 
     25.. math:: 
     26 
     27    K = a^2 
     28 
     29    a = b_p - (v_p/v_s) b_s 
     30     
     31where $b_p$ and $b_s$ are sum of the scattering lengths of the atoms 
     32constituting the monomer of the polymer and the sum of the scattering lengths 
     33of the atoms constituting the solvent molecules respectively, and $v_p$ and 
     34$v_s$ are the partial molar volume of the polymer and the solvent respectively 
     35 
     36$L_b$ is the Bjerrum length(|Ang|) - **Note:** This parameter needs to be 
     37kept constant for a given solvent and temperature!  
     38 
     39$h$ is the virial parameter (|Ang^3|/mol) - **Note:** See [#Borue]_ for the 
     40correct interpretation of this parameter.  It incorporates second and third 
     41virial coefficients and can be Negative. 
     42 
     43$b$ is the monomer length(|Ang|), $C_s$ is the concentration of monovalent 
     44salt(mol/L), $\alpha$ is the ionization degree (ionization degree : ratio of 
     45charged monomers  to total number of monomers), $C_a$ is the polymer molar 
     46concentration(mol/L), and $background$ is the incoherent background. 
    2247 
    2348For 2D data the scattering intensity is calculated in the same way as 1D, 
    24 where the $q$ vector is defined as 
     49where the $\vec q$ vector is defined as 
    2550 
    2651.. math:: 
    2752 
    2853    q = \sqrt{q_x^2 + q_y^2} 
    29  
    30  
    31 NB: $1 barn = 10^{-24} cm^2$ 
    3254 
    3355References 
     
    6991    ["contrast_factor",       "barns",   10.0,  [-inf, inf], "", "Contrast factor of the polymer"], 
    7092    ["bjerrum_length",        "Ang",      7.1,  [0, inf],    "", "Bjerrum length"], 
    71     ["virial_param",          "1/Ang^2", 12.0,  [-inf, inf], "", "Virial parameter"], 
     93    ["virial_param",          "Ang^3/mol", 12.0,  [-inf, inf], "", "Virial parameter"], 
    7294    ["monomer_length",        "Ang",     10.0,  [0, inf],    "", "Monomer length"], 
    7395    ["salt_concentration",    "mol/L",    0.0,  [-inf, inf], "", "Concentration of monovalent salt"], 
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