Calculate HETP on a linear gradient

[blaise5669]

Hello,

I am working with a prototype column that is designed to separate large molecules like proteins. I'm curious to know what the number of theoretical plates are, but I don't know where to find an HETP equation for gradient elution (as opposed to isocratic). Any suggestions?

[tom jupille]

It can't be done from a single gradient run. The process involves first calculating the gradient retention factor (k*), which requires retention data from two runs with different gradient steepnesses. N* (the gradient plate number) can then be estimated from t0, k*, and the peak width.

The pertinent equations can be found in the Snyder and Dolan "High-Performance Gradient Elution" book on pages 38 and 372-373. The catch is that they do not lend themselves to easy computation. The various chromatography modeling programs incorporate the calculation, but the math is messy.

A useful approximation is to measure an isocratic plate count for your protein on your column, and then impute that value to the gradient separation.

[Uwe Neue]

What kind of a column is it? RP? There may be some shortcuts...

[blaise5669]

Uwe Neue:
The column is an experimental polymeric (specifically, polypropylene) monolith-type. Right now, I am operating under RP conditions.

tom jupille:
Thanks for the advice- I'll try to get my hands on that book!

[Uwe Neue]

There is a brief description of the method in my book on "HPLC Columns" on the pages 77-79. In principle, the first part is identical to the Snyder method. For large molecules like proteins and reversed-phase chromatography, you may be able to get away with a second trick. Since proteins have a steep change in velocity from column inlet to column outlet, it is often the case that they elute unretained at the column outlet. You can prove that by running an experiment where you run isocratically the solvent composition at which the protein is eluting. If it comes out as an unretained peak, you have proven the point. Now, you take the isocratic retention time of the protein as the retention time, and the peak width from the gradient chromatogram, and calculate the plate count from these two values. N = f*(tr/w)^2, where f depends how you measure the peak width (e.g. 16 for the tangent method etc.) I have done this many times.