Example:Polymer clustering - Revision history

KevinYager at 15:25, 4 May 2016

2016-05-04T15:25:32Z

KevinYager at 18:26, 27 October 2015

2015-10-27T18:26:58Z

KevinYager: /* See Also */

2015-01-14T16:13:09Z

‎See Also

KevinYager at 16:09, 14 January 2015

2015-01-14T16:09:18Z

KevinYager: /* See Also */

2015-01-14T15:56:54Z

‎See Also

KevinYager at 15:54, 14 January 2015

2015-01-14T15:54:33Z

KevinYager: Created page with "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, o..."

2015-01-14T15:49:19Z

Created page with "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, o..."

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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.

Hammouda ''et al.'' proposed the following functional form to describe [[scattering]] data from such systems:
:<math>
I(q) = \frac{A}{q^n} + \frac{C}{1 + (q \xi)^m} + B
</math>
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, <math>\scriptstyle \xi</math> 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 [http://pubs.acs.org/doi/abs/10.1021/ma049623d Insight into Clustering in Poly(ethylene oxide) Solutions] ''Macromolecules'' '''2004''', 37 (18), 6932-6937. [http://dx.doi.org/10.1021/ma049623d doi: 10.1021/ma049623d]
* S.R. Kline "[http://www.ncnr.nist.gov/programs/sans/pdf/publications/0569.pdf Reduction and Analysis of SANS and USANS Data using Igor Pro]", ''J. Appl. Cryst.'' 2006, 39, 6, 895. [http://dx.doi.org/10.1107/S0021889806035059 doi:10.1107/S0021889806035059]
* Erika M. Saffer, Melissa A. Lackey, David M. Griffin, Suhasini Kishore, Gregory N. Tewb and Surita R. Bhatia [http://pubs.rsc.org/en/Content/ArticleLanding/2014/SM/c3sm52395k#!divAbstract SANS study of highly resilient poly(ethylene glycol) hydrogels] ''Soft Matter'' '''2014''', 10,1905-1916. [http://dx.doi.org/10.1039/C3SM52395K doi: 10.1039/C3SM52395K]

← Older revision		Revision as of 15:25, 4 May 2016
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	[[Image:Gel scattering example.png\|thumb\|center\|300px]]		[[Image:Gel scattering example.png\|thumb\|center\|300px]]
		+
		+	==Kratky plot==
		+	In a [[Kratky plot]] (<math>\scriptstyle q^2I(q) </math> vs. <math>\scriptstyle q</math>), the equation becomes:
		+
		+	:<math>
		+	q^2 I(q) = \frac{A}{q^{n-2}} + \frac{C q^2}{1 + (q \xi)^m} + B q^2
		+	</math>
		+

	==See Also==		==See Also==

← Older revision		Revision as of 18:26, 27 October 2015
Line 7:		Line 7:
	where ''B'' is a constant [[background]]. The first term represents the [[Porod scattering]] from clusters, while the second term is a Lorentzian function ascribed to the scattering of the polymer chains themselves. In the context of a gel, <math>\scriptstyle \xi</math> represents the average mesh size. The parameters ''A'', ''C'', ''n'', and ''m'' may be used as fitting parameters.		where ''B'' is a constant [[background]]. The first term represents the [[Porod scattering]] from clusters, while the second term is a Lorentzian function ascribed to the scattering of the polymer chains themselves. In the context of a gel, <math>\scriptstyle \xi</math> represents the average mesh size. The parameters ''A'', ''C'', ''n'', and ''m'' may be used as fitting parameters.

		+	[[Image:Gel scattering example.png\|thumb\|center\|300px]]

	==See Also==		==See Also==

@@ Line 13: / Line 13: @@
 * S.R. Kline "[http://www.ncnr.nist.gov/programs/sans/pdf/publications/0569.pdf Reduction and Analysis of SANS and USANS Data using Igor Pro]", ''J. Appl. Cryst.'' 2006, 39, 6, 895. [http://dx.doi.org/10.1107/S0021889806035059 doi:10.1107/S0021889806035059]
 * Takuro Matsunaga, Takamasa Sakai, Yuki Akagi, Ung-il Chung and Mitsuhiro Shibayama [http://pubs.acs.org/doi/abs/10.1021/ma901013q SANS and SLS Studies on Tetra-Arm PEG Gels in As-Prepared and Swollen States] ''Macromolecules'' '''2009''', 42 (16), 6245–6252. [http://dx.doi.org/10.1021/ma901013q doi: 10.1021/ma901013q]
 * Erika M. Saffer, Melissa A. Lackey, David M. Griffin, Suhasini Kishore, Gregory N. Tewb and Surita R. Bhatia [http://pubs.rsc.org/en/Content/ArticleLanding/2014/SM/c3sm52395k#!divAbstract SANS study of highly resilient poly(ethylene glycol) hydrogels]  ''Soft Matter'' '''2014''', 10,1905-1916. [http://dx.doi.org/10.1039/C3SM52395K doi: 10.1039/C3SM52395K]

@@ Line 5: / Line 5: @@
 I(q) = \frac{A}{q^n} + \frac{C}{1 + (q \xi)^m} + B
 </math>
-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, <math>\scriptstyle \xi</math> represents the average mesh size. The parameters ''A'', ''C'', ''n'', and ''m'' may be used as fitting parameters.
+where ''B'' is a constant [[background]]. The first term represents the [[Porod scattering]] from clusters, while the second term is a Lorentzian function ascribed to the scattering of the polymer chains themselves. In the context of a gel, <math>\scriptstyle \xi</math> represents the average mesh size. The parameters ''A'', ''C'', ''n'', and ''m'' may be used as fitting parameters.

@@ Line 1: / Line 1: @@
 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]] data from such systems:
+Hammouda ''et al.'' proposed the following functional form to describe [[scattering]] [[Scattering intensity|intensity]] from such systems:
 :<math>
 I(q) = \frac{A}{q^n} + \frac{C}{1 + (q \xi)^m} + B