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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:

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

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.

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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

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.

Category: Chromatography