Column length effect on peak resolution

Discussions about HPLC, CE, TLC, SFC, and other "liquid phase" separation techniques.

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I was reading Snyder's Gradient HPLC book. It says that keeping all conditions the same, the shorter the column length the better separated the peaks(higher resolution). I believe this is correct. However, I am not able to overcome the feeling that if I keep on shortening the column, 50 mm, 20 mm, 10 mm, 1mm...the two peaks were separated by 2 min, 4 min, 6 min, 10 min, 20 min...(all values are not true buy only used to illustrate the concept) Something must be wrong.
Please help to rationalize! I am sure someone already covered this. Please help with reference. Thanks.
Excel
You have to be careful about interpreting "separation" as "resolution"; they are not the same thing. As long as you keep the gradient time and range constant, the elution time of a peak will be *almost* independent of the column length :shock:. The resolution will actually be better for the longer column, but nowhere near proportional to column length.

Imagine a 0-100% gradient in, say, 30 minutes. If a particular peak starts to move off the head of the column at 50%B (the mid-point of the gradient), it will start to move at 15 minutes regardless of the column length; the residence time on the column then makes a relatively small contribution to the actual elution time, so the actual elution time doesn't change proportionally if you change the column length.

As with anything else, you can't push the model too far (e.g., why not use a 1 mm long column).

[Edit] I fired up my old demo copy of DryLab software. Ignoring pesky thing like gradient delay volume and extra-column volume, comparing retention for two peaks in the "pnah" example for a 0-100% gradient in 10 minutes:
- 150 mm column: 9.84 and 10.03 minutes
- 75 mm column: 8.18 and 8.33 minutes
-- Tom Jupille
LC Resources / Separation Science Associates
tjupille@lcresources.com
+ 1 (925) 297-5374
This was a very good explanation, thanks! I had not thought about this but this can be useful to keep in mind that the time penalty for longer column on gradient separation may not be so large.
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