Gauss Lorentz Gel

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)

$$ I(q) = I_G(0) \exp(-q^2\Xi ^2/2) + I_L(0)/(1+q^2\xi^2)
$$
$\Xi$ 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

$$ q = \sqrt{q_x^2 + q_y^2}
$$
References

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

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