Preparative Chromatography Column Loadability

[unisci]

I am having difficulty finding an equation that will allow me to determine or relate the amount of material I can load on a preparative column. I have two different Dynamic Axial Compression column configurations. Column one has an ID of 76.2 mm, the other is 135mm. If I load these 2 columns with 1 kg of 10µm C18, will I be able to load the 2nd column with more sample than the first?
Mobile phase is 70/30 EtOH/H2O. Flow rate is between 1.0 and 1.5 LPM. Back pressure is not an issue.

This is essentially a question of can I load more sample on a short fat column or a long skinny one? Longitudinal diffusion is counterbalanced with linear velocity. I don't need to optimize HETP, this is prep. Just good enough is what I am looking for.

Any ideas?

[tom jupille]

Given the same mass of packing, the capacities of both columns should be about equal.

[unisci]

Thanks for the response. The idea that you can put more sample on a short fat column than on a long skinny column makes sense because of the larger cross-sectional area. I just don't have the equations to prove it. Or the empirical data to back it up. I do lose linear velocity which is a big concern. If I go too slow the plate height increases vastly and i can't separate anything......

[tom jupille]

Prep separations are generally run under massive overload conditions, so the assumptions involved in plate height calculations via the Van Deemter or Knox equations (most importantly, the assumption that the distribution coefficients are independent of concentration) don't apply. That means that there is no "simple" set of equations that you can plug in; you have to make an assumption about the shape of the distribution isotherm. Even then, it's typically easier to "brute force
model it using sort of Craig-countercurrent model in Excel.

Unless you're really limited in how much sample you have, the easiest approach is empirical: run a series of injections with increasing load (double or triple or more) each time and see how far you can push it before the separation becomes inadequate.

As I indicated above, most of the time the load is determined by the mass (or volume) of packing.