# be_polyelectrolyte

Polyelectrolyte with the RPA expression derived by Borue and Erukhimovich

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
0.001 |

contrast_factor | Contrast factor of the polymer | barns | 10 |

bjerrum_length | Bjerrum length | Å | 7.1 |

virial_param | Virial parameter | Å^{3}/mol |
12 |

monomer_length | Monomer length | Å | 10 |

salt_concentration | Concentration of monovalent salt | mol/L | 0 |

ionization_degree | Degree of ionization | None | 0.05 |

polymer_concentration | Polymer molar concentration | mol/L | 0.7 |

The returned value is scaled to units of cm^{-1} sr^{-1}, absolute scale.

**Definition**
This model calculates the structure factor of a polyelectrolyte solution with
the RPA expression derived by Borue and Erukhimovich[1]. 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

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:

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(Å) - **Note:** This parameter needs to be
kept constant for a given solvent and temperature!

\(h\) is the virial parameter (Å^{3}/mol) - **Note:** See [1] for the
correct interpretation of this parameter. It incorporates second and third
virial coefficients and can be Negative.

\(b\) is the monomer length(Å), \(C_s\) 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 \(\vec q\) vector is defined as

**References**

[1] | (1, 2) V Y Borue, I Y Erukhimovich, Macromolecules, 21 (1988) 3240 |

[2] | J F Joanny, L Leibler, Journal de Physique, 51 (1990) 545 |

[3] | A Moussaid, F Schosseler, J P Munch, S Candau, J. Journal de Physique
II France, 3 (1993) 573 |

[4] | E Raphael, J F Joanny, Europhysics Letters, 11 (1990) 179 |

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Last Modified by:**Paul Kienzle**Date:**July 24, 2016**Last Reviewed by:**Paul Butler and Richard Heenan**Date:**October 07, 2016