Difference between revisions of "Example:Polymer clustering"
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Polymer solutions frequently exhibit some degree of clustering of the polymer chains. A more extreme case are hydrogels, where the polymer chains may be strongly-associated, or even crosslinked, into a network or mesh. | Polymer solutions frequently exhibit some degree of clustering of the polymer chains. A more extreme case are hydrogels, where the polymer chains may be strongly-associated, or even crosslinked, into a network or mesh. | ||
| − | Hammouda ''et al.'' proposed the following functional form to describe [[scattering]] | + | Hammouda ''et al.'' proposed the following functional form to describe [[scattering]] [[Scattering intensity|intensity]] from such systems: |
:<math> | :<math> | ||
I(q) = \frac{A}{q^n} + \frac{C}{1 + (q \xi)^m} + B | I(q) = \frac{A}{q^n} + \frac{C}{1 + (q \xi)^m} + B | ||
Revision as of 11:54, 14 January 2015
Polymer solutions frequently exhibit some degree of clustering of the polymer chains. A more extreme case are hydrogels, where the polymer chains may be strongly-associated, or even crosslinked, into a network or mesh.
Hammouda et al. proposed the following functional form to describe scattering intensity from such systems:
where B is a constant background. The first term represents the Porod scattering from clusters, while the second term is a Lorentzian function ascribed tot he scattering of the polymer chains themselves. In the context of a gel, represents the average mesh size. The parameters A, C, n, and m may be used as fitting parameters.
See Also
- Diffuse scattering
- Boualem Hammouda, Derek L. Ho, and Steve Kline Insight into Clustering in Poly(ethylene oxide) Solutions Macromolecules 2004, 37 (18), 6932-6937. doi: 10.1021/ma049623d
- S.R. Kline "Reduction and Analysis of SANS and USANS Data using Igor Pro", J. Appl. Cryst. 2006, 39, 6, 895. doi:10.1107/S0021889806035059
- Erika M. Saffer, Melissa A. Lackey, David M. Griffin, Suhasini Kishore, Gregory N. Tewb and Surita R. Bhatia SANS study of highly resilient poly(ethylene glycol) hydrogels Soft Matter 2014, 10,1905-1916. doi: 10.1039/C3SM52395K
