This is the Pringle-Schmidt equation for fitting the helical form factor of an infinitely long helix formed from two helical tapes wrapped around each other at an angle $\epsilon$. The two helices are assumed to have the same width and thickness. Please see Figure 1 in Reference [1]. Note that this figure uses $\phi$ in place of the $\epsilon$ used here (because $\phi$ has another meaning in SasView).

This model can also be used to model a single helical tape. To do this, set $\epsilon$ = 0.

$$I(q) = \frac{\pi}{q L} \sum^{\inf}_{n = 0} \epsilon_{n} \cos^2 \left( \frac{n \epsilon}{2} \right) \frac{\sin^{2} \left( n \omega / 2 \right)}{\left( n \omega / 2 \right)^2} \left[ g_{n} \left( q, R, a \right) \right]^2$$

where

$$g_{n} \left( q, R, a \right) = 2 R^{-2} \left(1 - a^{2} \right) \times \int^{R}_{aR} r dr J_{n} \left[ q r \left( 1 - q^{2}_{n}) \right)^{1/2} \right]$$

$$q_{n} = \frac{2 \pi n}{P q}$$

and $L$ is the total length of the tape, $\epsilon$ is the angle of separation between the helices, $\omega$ is the angle of the helical cross section occupied by a tape, $n$ is the order of the layer line, $R$ is the outer radius of the tape, $aR$ is the inner radius of the tape, and $P$ is the helical pitch.

References

----------

1) O. A. Pringle and P. W. Schmidt, Journal of Applied Crystallography, 1971, 4, 290-293, DOI: 10.1107/S002188987100699X

2) C. V. Teixeira, H. Amenitsch, T. Fukushima et al., Journal of Applied Crystallography, 2010, 43, 850-857, DOI: 10.1107/S0021889810015736

The fitting equation can be found in Reference [2] as Equations 15 & 16.

Authorship and Verification

----------------------------

* **Author:** Tim Snow **Date:** November 25, 2016

* **Last Modified by:** Tim Snow **Date:** January 23, 2016

* **Last Reviewed by:** Steve King **Date:** November 18, 2022

Created By |
smk78 |

Uploaded |
Nov. 18, 2022, 6:02 p.m. |

Category |
Cylinder |

Score |
0 |

Verified |
This model has not been verified by a member of the SasView team |

In Library |
This model is not currently included in the SasView library. You must download the files and install it yourself. |

Files |
pringle_schmidt_helices.py |

smk78:

Fri 18 Nov 2022 at 18:08

This is a revision of the model originally posted to the old Marketplace. The description has been updated to clarify that the model can be used to fit a single helical tape. In testing it was also discovered that the model would not compile because one of the angle parameters was called phi. Phi has a special meaning in SasView, being one of the orientational parameters. All references to phi in this model were therefore changed to epsilon. The model now works, but it remains untested!

Please log in to add a comment.