Chromatographic response function

Last updated April 12, 2024

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

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 $\Delta R_{F}$ and $\Delta R_{F}$ 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.{Analytical Chemistry (1987):59(1),62-64} 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.

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

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

$R_{D}={\Bigg [}(n+1)^{(n+1)}\prod _{i=0}^{n}{(R_{F(i+1)}-R_{Fi}){\Bigg ]}^{\frac {1}{n}}}$

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)

$D={\sqrt {\sum _{i=1}^{n}\left(R_{Fi}-{\frac {i-1}{n-1}}\right)}}$

Performance index (Gocan et al., 1991)

$I_{p}={\sqrt {\frac {\sum (\Delta hR_{Fi}-\Delta hR_{Ft})^{2}}{n(n+1)}}}$

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

$s_{m}={\sqrt {\frac {\sum (\Delta hR_{Fi}-\Delta hR_{Ft})^{2}}{n+1}}}$

Retention uniformity (Komsta et al., 2007)

$R_{U}=1-{\sqrt {{\frac {6(n+1)}{n(2n+1)}}\sum _{i=1}^{n}{\left(R_{Fi}-{\frac {i}{n+1}}\right)^{2}}}}$

In all above formulas, n is the number of compounds separated, R_{f (1...n)} are the Retention factor of the compounds sorted in non-descending order, R_f0 = 0 and R_f(n+1) = 1.

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Retention uniformity, or R_U, is a concept in thin layer chromatography. It is designed for the quantitative measurement of equal-spreading of the spots on the chromatographic plate and is one of the Chromatographic response functions.

Retention distance, or R_D, is a concept in thin layer chromatography, designed for quantitative measurement of equal-spreading of the spots on the chromatographic plate and one of the Chromatographic response functions. It is calculated from the following formula:

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References

Q.S. Wang, B.W. Yan, J. Planar Chromatogr. 9 (1996) 192.
B.J.M. de Spiegeleer, P.H.M. de Moerloose, G.A.S. Sleghers, 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.

Chromatographic response function

Contents

Examples in thin layer chromatography

Related Research Articles

References

See also