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