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2014-03-25T00:19:58Z

References

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	'~~''Chromatographic response function''', often abbreviated to '''CRF''', is a coefficient which measures the quality of the separation in the result of a [[chromatography]]~~.		I'm Luther but I never really liked that name. Her buddies say it's not great for her but what she loves doing is flower arranging and she is trying to make it a profession. He presently life in Arizona and his mothers and fathers live nearby. I am a manufacturing and distribution officer.<br><br>Also visit my webpage - [http://Marbellaclassified.com/2014/09/10/boost-your-auto-repair-knowledge-using-this-advice/ auto warranty]

	The CRF concept have been created during the development of separation optimization, to compare the quality of many simulated or real chromatographic separations. Many CRFs have been proposed and discussed.

	In [[high performance liquid chromatography]] the CRF is calculated from various parameters of the peaks of solutes (like width, retention time, symmetry etc.) are considered into the calculation. In [[Thin layer chromatography\|TLC]] the CRFs are based on the placement of the spots, measured as [[Retention factor\|RF]] values.

	~~== CRFs examples in thin layer chromatography ==~~

	~~The CRFs in thin layer chromatography characterize the~~ '~~'equal-spreading'' of the spots. The ideal case, when the RF of the spots are uniformly distributed in <0,1> range (~~for ~~example 0.25,0.5 and 0.75 for three solutes) should be characterized as the best situation possible.~~

	~~The simplest criteria are <math>\Delta R_F</math> and <math>\Delta R_F</math> product (Wang et al., 1996). They are the smallest difference between sorted RF values, or product of such differences.~~

	~~Another function~~ is ~~the multispot response function (MRF) as developed by De Spiegeleer et al.{{Citation needed\|date=September 2009}} It is based also of differences product. This function always lies between 0~~ and ~~1. When two RF values are equal, it~~ is ~~equal~~ to ~~0, when all RF values are equal-spread,~~ it ~~is equal to 1~~. ~~The L~~ and ~~U values - upper~~ and ~~lower limit of RF - give possibility to avoid the band region~~.

	<~~math~~>
	~~MRF = \frac {(U~~ - ~~hR_{Fn})(hR_{F1} - L)\prod^{n-1}_{i=1}(hR_{Fi+1} - hR_{Fi})} {~~[~~(U - L)~~/~~(n+1)]^{n+1}}~~
	</~~math>~~

	~~The last example of coefficient sensitive to minimal distance between spots is [[Retention distance]] (Komsta et al~~.~~, 2007)~~

	~~<math>~~
	~~R_D = \Bigg[(n+1)^{(n+1)} \prod^n_{i=0}{(R_{F(i+1)}-R_{Fi})\Bigg]^{\frac{1}{n}}}~~
	</~~math>~~

	~~The second group are criteria insensitive for minimal difference between RF values (if two compounds are not separated, such CRF functions will not indicate it). They are equal to zero in equal~~-~~spread state increase when situation is getting worse.~~

	~~There are:~~

	~~Separation response (Bayne et al., 1987)~~

	~~<math>~~
	~~D = \sqrt{\sum^n_{i=1}\left(R_{Fi}~~ - ~~\frac{i~~-~~1}{n~~-~~1}\right)}~~
	~~</math>~~

	~~Performance index (Gocan et al., 1991)~~

	~~<math>~~
	~~I_p = \sqrt{\frac{\sum(\Delta hR_{Fi}~~ - ~~\Delta hR_{Ft})^2}{n(n+1)}}~~
	~~</math>~~

	~~Informational entropy (Gocan et al., 1991, second reference)~~

	~~<math>~~
	~~s_m = \sqrt{\frac{\sum(\Delta hR_{Fi}~~ - ~~\Delta hR_{Ft})^2}{n+1}}~~
	~~</math>~~

	~~[[Retention uniformity]] (Komsta et al., 2007)~~

	~~<math>~~
	~~R_{U} = 1 - \sqrt{\frac{6(n+1)}{n(2n+1)}\sum_{i=1}^{n}{\left(R_{Fi}~~-~~\frac{i}{n+1}\right)^2}}~~
	</~~math>~~

	In all above formulas, ''n'' is the number of compounds separated, ''R<sub>f (1...n)</sub>'' are the [[Retention factor]] of the compounds sorted in non-descending order, ''R<sub>f0</sub>'' = 0 and ''R<sub>f(n+1)</sub>'' = 1.

	~~== References ==~~

	~~{{No footnotes\|date=September 2008}}~~
	* Q.S. Wang, B.W. Yan, J. Planar Chromatogr. 9 (1996) 192.
	* B.J.M. de Spiegeleer, P.H.M. de Meloose, G.A.S. Seghers, Anal. Chem. 59 (1987) 62.
	* C.K. Bayne, C.Y. Ma, J. Liq. Chromatogr. 10 (1987) 3529.
	* S. Gocan, M. Mihaly, Stud Univ B-B Chemia, 1 (1991) 18.
	* S. Gocan, J. Planar Chromatogr. 4 (1991) 169.
	* Ł. Komsta, W. Markowski, G. Misztal, J. Planar Chromatogr. 20 (2007) 27.

	~~==See also==~~
	* [[Chromatography]]

	~~[[Category:Chromatography]~~]

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2012-07-04T09:44:19Z

stub-sort

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'''Chromatographic response function''', often abbreviated to '''CRF''', is a coefficient which measures the quality of the separation in the result of a [[chromatography]].

The CRF concept have been created during the development of separation optimization, to compare the quality of many simulated or real chromatographic separations. Many CRFs have been proposed and discussed.

In [[high performance liquid chromatography]] the CRF is calculated from various parameters of the peaks of solutes (like width, retention time, symmetry etc.) are considered into the calculation. In [[Thin layer chromatography|TLC]] the CRFs are based on the placement of the spots, measured as [[Retention factor|RF]] values.

== CRFs examples in thin layer chromatography ==

The CRFs in thin layer chromatography characterize the ''equal-spreading'' of the spots. The ideal case, when the RF of the spots are uniformly distributed in <0,1> range (for example 0.25,0.5 and 0.75 for three solutes) should be characterized as the best situation possible.

The simplest criteria are <math>\Delta R_F</math> and <math>\Delta R_F</math> product (Wang et al., 1996). They are the smallest difference between sorted RF values, or product of such differences.

Another function is the multispot response function (MRF) as developed by De Spiegeleer et al.{{Citation needed|date=September 2009}} It is based also of differences product. This function always lies between 0 and 1. When two RF values are equal, it is equal to 0, when all RF values are equal-spread, it is equal to 1. The L and U values - upper and lower limit of RF - give possibility to avoid the band region.

<math>
MRF = \frac {(U - hR_{Fn})(hR_{F1} - L)\prod^{n-1}_{i=1}(hR_{Fi+1} - hR_{Fi})} {[(U - L)/(n+1)]^{n+1}}
</math>

The last example of coefficient sensitive to minimal distance between spots is [[Retention distance]] (Komsta et al., 2007)

<math>
R_D = \Bigg[(n+1)^{(n+1)} \prod^n_{i=0}{(R_{F(i+1)}-R_{Fi})\Bigg]^{\frac{1}{n}}}
</math>

The second group are criteria insensitive for minimal difference between RF values (if two compounds are not separated, such CRF functions will not indicate it). They are equal to zero in equal-spread state increase when situation is getting worse.

There are:

Separation response (Bayne et al., 1987)

<math>
D = \sqrt{\sum^n_{i=1}\left(R_{Fi} - \frac{i-1}{n-1}\right)}
</math>

Performance index (Gocan et al., 1991)

<math>
I_p = \sqrt{\frac{\sum(\Delta hR_{Fi} - \Delta hR_{Ft})^2}{n(n+1)}}
</math>

Informational entropy (Gocan et al., 1991, second reference)

<math>
s_m = \sqrt{\frac{\sum(\Delta hR_{Fi} - \Delta hR_{Ft})^2}{n+1}}
</math>

[[Retention uniformity]] (Komsta et al., 2007)

<math>
R_{U} = 1 - \sqrt{\frac{6(n+1)}{n(2n+1)}\sum_{i=1}^{n}{\left(R_{Fi}-\frac{i}{n+1}\right)^2}}
</math>

In all above formulas, ''n'' is the number of compounds separated, ''Rf (1...n)'' are the [[Retention factor]] of the compounds sorted in non-descending order, ''Rf0'' = 0 and ''Rf(n+1)'' = 1.

== References ==

{{No footnotes|date=September 2008}}
* Q.S. Wang, B.W. Yan, J. Planar Chromatogr. 9 (1996) 192.
* B.J.M. de Spiegeleer, P.H.M. de Meloose, G.A.S. Seghers, Anal. Chem. 59 (1987) 62.
* C.K. Bayne, C.Y. Ma, J. Liq. Chromatogr. 10 (1987) 3529.
* S. Gocan, M. Mihaly, Stud Univ B-B Chemia, 1 (1991) 18.
* S. Gocan, J. Planar Chromatogr. 4 (1991) 169.
* Ł. Komsta, W. Markowski, G. Misztal, J. Planar Chromatogr. 20 (2007) 27.

==See also==
* [[Chromatography]]

[[Category:Chromatography]]

Retention distance - Revision history

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