# star_polymer

Star polymer model with Gaussian statistics

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
rg_squared Ensemble radius of gyration SQUARED of an arm Ang^2 100
arms Number of arms in the model None 3

The returned value is scaled to units of cm-1 sr-1, absolute scale.

The Benoit model for a simple star polymer, with Gaussian coils arms from a common point.

Definition

For a star with $$f$$ arms the scattering intensity $$I(q)$$ is calculated as

$I(q) = \frac{2}{fv^2}\left[ v-1+\exp(-v)+\frac{f-1}{2} \left[ 1-\exp(-v)\right]^2\right]$

where

$v=\frac{u^2f}{(3f-2)}$

and

$u = \left\langle R_{g}^2\right\rangle q^2$

contains the square of the ensemble average radius-of-gyration of an arm. Note that when there is only one arm, $$f = 1$$, the Debye Gaussian coil equation is recovered. Star polymers in solutions tend to have strong interparticle and osmotic effects, so the Benoit equation may not work well. At small $$q$$ the Guinier term and hence $$I(q=0)$$ is the same as for $$f$$ arms of radius of gyration $$R_g$$, as described for the mono_gauss_coil model.

References

H Benoit J. Polymer Science, 11, 596-599 (1953)