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)

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

$\Xi$ 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

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

Fig. 100 1D plot corresponding to the default parameters of the model.

Source

gauss_lorentz_gel.py

References

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

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