Retention uniformity

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Retention uniformity, or R_U, 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:

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

where n is the number of compounds separated, R_{f (1...n)} are the Retention factor of the compounds sorted in non-descending order.

1 Theoretical considerations
2 Calculation
3 See also
4 References

[edit] Theoretical considerations

The coefficient lies always in range <0,1> and 0 indicates worst case of separation (all R_f values equal to 0 or 1), value 1 indicates ideal equal-spreading of the spots, for example (0.25,0.5,0.75) for three solutes, or (0.2,0.4,0.6,0.8) for four solutes.

This coefficient was proposed as an alternative to earlier approaches, such as D (separation response), I_p (performance index) or S_m (informational entropy). Besides its stable range, the advantage is a stable distribution as a random variable, regardless of compounds investigated.

In contrast to the similar concept called Retention distance, R_u is insensitive to R_f values close to 0 or 1, or close to themselves. If two values are not separated, it still indicates some uniformity of chromatographic system. For example the R_f values (0,0.2,0.2,0.3) (two compounds not separated at 0.2 and one at the start ) result in R_U</sub _{equal to 0.3609.}

_{[edit] Calculation}

_{The calculation of the R_U requires some operations and is quite difficult to perform in spreadsheets. The following implementations may help. They take the vector of R_f values, returning the single R_U value.}

The R (programming language)/S-PLUS implementation:

ru <- function (x) 
{
        x <- sort(x)
        n <- length(x)
        i <- (1:n)/(n+1)
        s <- sum((x-i)^2)
        ru <- 1-sqrt( (6*(n+1)) / (n*(2*n+1)) * s );
        return(ru);

}

The GNU Octave/Matlab implementation:

function res = ru(x)
        x = sort(x);
        n = length(x);
        i = (1:n)./(n+1);
        s = sum((x-i).^2);
        res = 1-sqrt((6.*(n+1))./(n.*(2.*n+1)).*s);
endfunction

The Scilab implementation:

function res = ru(x)
        x = gsort(x,"g","i");
        n = length(x);
        i = (1:n)./(n+1);
        s = sum((x-i).^2);
        res = 1-sqrt((6.*(n+1))./(n.*(2.*n+1)).*s);
endfunction

[edit] See also

Chromatographic response function

[edit] References

Komsta Ł., Markowski W., Misztal G., A proposal for new R_F equal-spread criteria with stable distribution parameters as a random variable. J. Planar Chromatogr. 2007 (20) 27-37.