# correlation_length

Calculates an empirical functional form for SAS data characterized by a low-Q signal and a high-Q signal.

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

scale | Source intensity | None | 1 |

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

lorentz_scale | Lorentzian Scaling Factor | None | 10 |

porod_scale | Porod Scaling Factor | None | 1e-06 |

cor_length | Correlation length, xi, in Lorentzian | Å | 50 |

porod_exp | Porod Exponent, n, in q^-n | None | 3 |

lorentz_exp | Lorentzian Exponent, m, in 1/( 1 + (q.xi)^m) | Å^{-2} |
2 |

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

**Definition**

The scattering intensity I(q) is calculated as

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

**References**

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