Example:Polymer clustering

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:

$I(q)={\frac {A}{q^{n}}}+{\frac {C}{1+(q\xi )^{m}}}+B$

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, $\scriptstyle \xi$ 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
• Takuro Matsunaga, Takamasa Sakai, Yuki Akagi, Ung-il Chung and Mitsuhiro Shibayama SANS and SLS Studies on Tetra-Arm PEG Gels in As-Prepared and Swollen States Macromolecules 2009, 42 (16), 6245–6252. doi: 10.1021/ma901013q
• 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