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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)

Full article is available here: http://www.sciencetopics.net/5.recent_scientific_publications/4.publications_4/2012_hammouda_macromol_theory_and_simul.pdf

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

PB(Q)=1Norm[1νUBc/2νγ(c/2ν,UB)1νUB(c+1)/2νγ((c+1)/2ν,UB)]

where Norm=2c(c+1) - the normalization factor,

UB=Q2Rg2(2ν+c)(2ν+c+1)/6 - scattering variable which expressed in terms of the radii of gyration.

ν - 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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