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.


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

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




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

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.


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