Retention distance

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:

where 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.

Additional recommended knowledge

Don't let static charges disrupt your weighing accuracy

What is the Correct Way to Check Repeatability in Balances?

Daily Sensitivity Test

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 delta-Rf, delta-Rf product or MRF (Multispot Response Function). 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 uniformity, R_d is sensitive to R_f values close to 0 or 1, or close to themselves. If two values are not separated, it is equal to 0. 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_D equal to 0, but R_U equal to 0.3609. When some distance from 0 and spots occurs, the value is larger, for example R_f values (0.1,0.2,0.25,0.3) give R_D = 0.4835, R_U = 0.4066.

Calculation

The calculation of the R_D 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_D value.

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

rd <- function (x) 
{
        x <- sort(x)
        n <- length(x)
        d <- diff(c(0,x,1));
        pd <- prod(d);
        rd <- ((n+1)^(n+1)*pd)^(1/n);
        return(rd);
}

The GNU Octave/Matlab implementation:

function res = rd(x)
        x = sort(x);
        n = length(x);
        d = diff([0 x 1]);
        pd = prod(d);
        res = ((n+1).^(n+1).*pd).^(1./n);
endfunction

The Scilab implementation:

function res = rd(x)
        x = gsort(x,"g","i");
        n = length(x);
        d = diff([0 x 1]);
        pd = prod(d);
        res = ((n+1).^(n+1).*pd).^(1./n);
endfunction

See also

• Chromatographic response function

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.