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.

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.