Theoretical plates & column efficiency

[HW Mueller]

Now I am really confused. The derivatization of the plate number equation, as I understood it, originates from the factor µ^2/s^2 in the equation describing a gaussian curve. Someone called this ratio (µ is the mean, s should be sigma the SD) N, the plate number. To make this useful for chromatography the first step is to point out that in a chrom. peak (Gaussian) the µ is tR, that is, N = (tR/s)^2. This is easily converted to the formular given earlier, or still others, all are just derivatives of this factor in the equation for the Gaussian distribution. Now there are some attempts in the literature to adapt these formulars to non-Gaussian (tailing, etc.) peaks. Some additional terms appeaer in these equations. OK, my problem: The ratios µ^2/s^2, (tr/s)^2, and the earlier 5.54(Rt/w0.5)^2 are identical statements. Also, I have trouble seeing tR (Rt) of a tailing peak as being the mean of that peak.
Anybody see where I am mentally stuck?

[danko]

Hans, you’re absolutely right!
Maybe one should calculate the mean, using the peak start and the peak end?
But then again, the value wouldn’t represent the time where the highest concentration elutes, unless the peak is gaussian

Best Regards

[tom jupille]

Also, I have trouble seeing tR (Rt) of a tailing peak as being the mean of that peak.
Anybody see where I am mentally stuck?

You're not stuck. You are correct. tR is the mode (highest value) of the peak. It equals µ only for a symmetrical peak

The ratios µ^2/s^2, (tr/s)^2, and the earlier 5.54(Rt/w0.5)^2 are identical statements

For Gaussian peaks, yes. Not for tailing peaks.

The advantage to the moments calculations is that they are based on general statistics rather than arbitrary definitions of things like baseline width. The disadvantages are that they usually can't be done with pencil and paper, and they don't lend themselves to an intuitive "mental picture". As a matter of practice, if the purpose is to track column performance, it doesn't really matter much which (if any) you use, so long as you are consistent.

[Uwe Neue]

Hans,

The calculations of mean m and standard deviation s can apply to anything, whether the peak is Gaussian, square, triangular, or even a double peak. If I define the plate count as m^2/s^2, I can calculate plates for any peak, no matter how ugly it is. This is good for the theoreticians...

For us practitioners, we do not deal with really ugly peaks, and if we want to count the plates, we want a reproducible number. To get the true mean and standard deviation from a tailing peak over a noisy baseline is art, and not a measurement technique. For us, it is best to measure the peak width at a prescribed height and call this the plate count. Keeps us happy, even if it is not perfectly correct...

[HW Mueller]

OK, I have no problem with keeping things "relative". Just thought that some "absolutisms" had been suggested.