# gauss_lorentz_gel

Gauss Lorentz Gel model of scattering from a gel structure

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

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
0.001 |

gauss_scale |
Gauss scale factor |
None |
100 |

cor_length_static |
Static correlation length |
Å |
100 |

lorentz_scale |
Lorentzian scale factor |
None |
50 |

cor_length_dynamic |
Dynamic correlation length |
Å |
20 |

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

This model calculates the scattering from a gel structure, but typically a physical rather than chemical network. It is modeled as a sum of a low-q exponential decay (which happens to give a functional form similar to Guinier scattering, so interpret with care) plus a Lorentzian at higher-q values. See also the gel_fit model.

**Definition**

The scattering intensity \(I(q)\) is calculated as (Eqn. 5 from the reference)

\(\Xi\) is the length scale of the static correlations in the gel, which can be attributed to the “frozen-in” crosslinks. \(\xi\) is the dynamic correlation length, which can be attributed to the fluctuating polymer chains between crosslinks. \(I_G(0)\) and \(I_L(0)\) are the scaling factors for each of these structures. Think carefully about how these map to your particular system!

Note

The peaked structure at higher \(q\) values (Figure 2 from the reference) is not reproduced by the model. Peaks can be introduced into the model by summing this model with the gaussian_peak model.

For 2D data the scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as

**Source**

**References**

G Evmenenko, E Theunissen, K Mortensen, H Reynaers,

*Polymer*, 42 (2001) 2907-2913

**Authorship and Verification**

**Author:****Last Modified by:****Last Reviewed by:**