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.

Fig. 104 1D plot corresponding to the default parameters of the model.

References

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