# 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

where

and

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)