# flexible_cylinder

Flexible cylinder where the form factor is normalized by the volumeof the cylinder.

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
0.001 |

length | Length of the flexible cylinder | Å | 1000 |

kuhn_length | Kuhn length of the flexible cylinder | Å | 100 |

radius | Radius of the flexible cylinder | Å | 20 |

sld | Cylinder scattering length density | 10^{-6}Å^{-2} |
1 |

sld_solvent | Solvent scattering length density | 10^{-6}Å^{-2} |
6.3 |

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

This model provides the form factor, \(P(q)\), for a flexible cylinder
where the form factor is normalized by the volume of the cylinder.
**Inter-cylinder interactions are NOT provided for.**

where the averaging \(\left<\ldots\right>\) is applied only for the 1D calculation

The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as

**Definitions**

The chain of contour length, \(L\), (the total length) can be described as a chain of some number of locally stiff segments of length \(l_p\), the persistence length (the length along the cylinder over which the flexible cylinder can be considered a rigid rod). The Kuhn length \((b = 2*l_p)\) is also used to describe the stiffness of a chain.

The returned value is in units of \(cm^{-1}\), on absolute scale.

In the parameters, the sld and sld_solvent represent the SLD of the cylinder and solvent respectively.

Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006).

From the reference:

‘Method 3 With Excluded Volume’ is used. The model is a parametrization of simulations of a discrete representation of the worm-like chain model of Kratky and Porod applied in the pseudocontinuous limit. See equations (13,26-27) in the original reference for the details.

**References**

J S Pedersen and P Schurtenberger. *Scattering functions of semiflexible
polymers with and without excluded volume effects.* Macromolecules,
29 (1996) 7602-7612

Correction of the formula can be found in

W R Chen, P D Butler and L J Magid, *Incorporating Intermicellar Interactions
in the Fitting of SANS Data from Cationic Wormlike Micelles.* Langmuir,
22(15) 2006 6539-6548