Correlation Length

#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:** NIST IGOR/DANSE **Date:** pre 2010
**Last Modified by:** Steve King **Date:** September 24, 2019
**Last Reviewed by:**