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# Modeling of small angle scattering from branched polymers¶

In this notebook we continue to demonstrate the capabilities of ESCAPE to simulate small-angle scattering data with custom model functions.

The following example implements a single polymer form-factor for branched polymers formulated by B. Hammouda et al. ( https://doi.org/10.1002/mats.201100111)

Without going into details of the (mass)fractal model, the form-factor of branched polymer is given by:

${P}_{B}\left(Q\right)=\frac{1}{Norm}\left[\frac{1}{\nu {U}_{B}^{c/2\nu }}\gamma \left(c/2\nu ,{U}_{B}\right)-\frac{1}{\nu {U}_{B}^{\left(c+1\right)/2\nu }}\gamma \left(\left(c+1\right)/2\nu ,{U}_{B}\right)\right]$

where $Norm=\frac{2}{c\left(c+1\right)}$ - the normalization factor,

${U}_{B}={Q}^{2}{R}_{g}^{2}\left(2\nu +c\right)\left(2\nu +c+1\right)/6$ - scattering variable which expressed in terms of the radii of gyration.

$\nu$ - excluded volume, $c$ - scaling factor and raddi of gyration are the model fit parameters.

The implementation of this model in terms of ESCAPE entities is straightforward.

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