# gauss_lorentz_gel

Gauss Lorentz Gel model of scattering from a gel structure

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

scale | Source intensity | None | 1 |

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

**References**

G Evmenenko, E Theunissen, K Mortensen, H Reynaers, *Polymer*,
42 (2001) 2907-2913