#correlation length model # Note: model title and parameter table are inserted automatically Definition

The scattering intensity I(q) is calculated as

$$ I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + \text{background}

$$

The first term describes Porod scattering from clusters (exponent = $n$) and the second term is a Lorentzian function describing scattering from polymer chains (exponent = $m$). This second term characterizes the polymer/solvent interactions and therefore the thermodynamics. The two multiplicative factors $A$ and $C$, and the two exponents $n$ and $m$ are used as fitting parameters. (Respectively *porod_scale*, *lorentz_scale*, *porod_exp* and *lorentz_exp* in the parameter list.) The remaining parameter $\xi$ (*cor_length* in the parameter list) is a correlation length for the polymer chains. Note that when $m=2$ this functional form becomes the familiar Lorentzian function. Some interpretation of the values of $A$ and $C$ may be possible depending on the values of $m$ and $n$.

For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as

$$ q = \sqrt{q_x^2 + q_y^2}

$$

References

B Hammouda, D L Ho and S R Kline, Insight into Clustering in Poly(ethylene oxide) Solutions, Macromolecules, 37 (2004) 6932-6937

Authorship and Verification

**Author:**

**Last Modified by:**

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Created By |
sasview |

Uploaded |
Sept. 7, 2017, 3:56 p.m. |

Category |
Shape-Independent |

Score |
0 |

Verified |
Verified by SasView Team on 07 Sep 2017 |

In Library |
This model is included in the SasView library by default |

Files |
correlation_length.py |

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