Hi I have a method for a 4.6 x 100mm column and I would like to switch to a 2.1 x 100 mm column. For the 4.6 mm column I go from 50% A to 0% A in 7 minutes, how should I change this for the smaller column to have a comparable gradient?

Scale your flow rate down to give the same linear velocity, leave your gradient slope the same.

The scale factor (assuming that both columns have the same length) is calculated as;

(radius column B)^2/(radius column A)^2

so in your case, where A=4.6 and B=2.1, the scale factor is 0.208 (to 3 dp). So, if your flow rate for the 4.6mm column was 1mL/min, use a flow rate of 0.2mL/min with the 2.1mm column to achieve similar retention times.

Hope that helps :o)

Ann, Anonymous: your formula using the column internal radius squared would suffice for isocratic operation, no problems. But for gradient you'd need to adjust the gradient profile as well, to account for plumbing dead volume, etc. We find we usually need to have the % organic increase start at an earlier time or higher % organic, or both.

Anon 2

Thank you, that's handy to know, I only have experience of scaling down isocratic methods.

Some instruments allow you to program a gradient delay volume so you do not have to tweek gradient profiles when you do a scaledown like this. I know Waters Alliance and Shimadzu LC2010 do this for sure but I can not be sure about others. On the same topic, sometimes you lose a bit of resolution when you scale down so you may have to make small adjustments after all.

To A.Nonymous 2:
I strongly recommend not to fool around with the gradient profile. If you want to get the same retention pattern, the gradient volume is changed with the column volume. If you use two columns of the same length, this means that you change the flow rate with the square of the column diameter.
Of course, you are correct in that the purging of the gradient delay volume of the instrument will take longer at the slower flow rate. As was pointed out in the last post, modern systems allow you to take care of this problem by a trick that is called delayed injection. With this, your entire gradient profile can be made to be absolutely identical on a large i.d. column and a small i.d. column. It also does not increase your run time, since you can use the time at the end of the gradient for reequilibration to the next run. The only thing that is happening is a delay in the point in time where you trigger your injection. The gradient profile and reequilibration profile remain identical.
It is also correct that this may be splitting hairs, if you have miles of space between the different peaks that you are separating. But if you are looking at an impurity profile or something similar with a lot of different compounds of interest, the scaling must be done by column volume.