Chromatography Forum

Hi,

Why it is advisable to get the Theoretical plate count in isocratic run and not in gradient run? will there be any difference in plate count in these two runs? Manufacturers report plate counts in their test chromatogram in isocratic or gradient?

The usual equations for plate count are derived with the assumption of isocratic conditions. Using these equations with a gradient will give wildly inflated counts. Manufacturers always report plate counts from isocratic tests, first because it is the right thing to do, and second because it is easier.

To expand a bit on Mark's post: the number that you get by applying the isocratic plate calculation to a gradient chromatogram is not only wildly inflated, but totally meaningless. It is not possible to accurately calculate plates from a single gradient run. It can be done using data from two linear gradients, but the math is far from simple.

If anyone wants to wallow in it, there is a good review of "linear solvent strength" gradients by Snyder & Dolan in:

Advances in Chromatography, v38, pp 115-187, Marcel Dekker (1998)

Without disagreeing with Mark and Tom, I use to calculate the number of theoretical plates to each and every method I develop, and repeat thes calculation peridocally as a tool to access when my column is nearly dead.

Of course, if you need to calculate it for other purposes, or under a manufacturer point of view, you should use isocratic runs, as it is much more reproducible.

Rafael, your point is a good one. However, in a gradient separation, the number you get from the isocratic plate number calculation bears no relation to plate number.

Simply tracking the peak width would serve the same purpose, and not cause confusion about plate counts.

A plate count measurement in a gradient does not provide any meaningful or useful information. This has nothing to do with a reproducibility of the measurement.

Here is a way, in which the performance of a (reversed-phase) gradient or the column performance can be monitored in a meaningful way. This is the calculation of the peak capacity. This calculation is done based on the gradient run time tG (which you know because you have programmed it into your instrument) and an average peak width w.

Pc = tG / w

You determine the peak width of the peaks that you select based on standard algorithms, for example tangent method. You should select peaks at the beginning, in the middle and at the end of the chromatogram. The peaks that you select for the calculation should be reasonably clean from interferences, but you need this anyway for a good quantitation.

Gradient plate count? Like determining the horse power of a dragster that has its engine magically replaced with a totally different one every 50 yards down the track.

Theoretical plate number equation is deduced from "plate theory". One of the assumptions the theory is based on is that retention factor k is a constant.

Unless more complicated things happen inside the column, the width of most peaks is about the same when they approach the column exit, independent of the retention factor. Ignoring peak compression in gradient chromatography, the same is also true in gradients - the peaks are of the same width as in isocratic chromatography. If I would be able to measure the peak width inside the column, I would have no problem measuring plate counts, independent if I run gradient chromatography or isocratic chromatography. I would measure the width, divide the column length by this width, square the number, apply a factor that depends on how I measure the width, et voila, I got the plate count.

The problem with gradient elution is that I can not relate easily the width that I see on the computer screen to the width inside the column. Therefore the width that you see on the screen can not be used readily to count the plates.

The only thing that you can be reasonably certain about is the fact that you have more plates in your column than in your kitchen.

The point I wanted to make is: When a peak travels along the column, any parameter which can cause retention factor k to change should be avoided for theoretical plate count e.g. PH, temp, mobile phase. For gradient run, k is unkown although k* can be calculated. "plate theory" is not just for HPLC, theoretical plate number of a GC column is calculated from isothermal run. The idea is to keep k constant when the peak develops along the column. Otherwise it will violate the basic assumption of "plate theory".