Effect of column i.d. on efficiency

[MG]

adam said in the column scalability thread:

In reality, there have been papers published that show that one can get better efficiency with smaller ID columns. That's a whole other topic (if you want to start a new thread on it, I can throw in what I know - though I'm not the world's leading authority on it).

OK, I am starting a new thread. Can I get better resolution with smaller i.d. columns?

[Uwe Neue]

Well nothing is happening until you get to a ratio of column diameter to particle diameter of about 10 or so. Then there are some improvements possible. However, in the standard range of column diameter to particle diameter, there is no reason why there should be any effects.

[Klaus]

(I might be wrong but) I disagree with Uwe.
As far as I know the resolution gets better, when you decrease the I.D. of the column. There is less eddy-diffusion and thus the whole Van-Deemter curve shifts downwards - less bandbroadening and better resolution.
Uwe: I never heared about that particle size/I.D.-ratio. Could you explain more backround?

[adam]

MG

It has been awhile since I looked at the literature, but the best paper I'v seen on this topic was By Kennedy and Jorgenson way back in 1989 (Anal. Chem. Vol 61 page 1128). They basically gave the following reasons why better efficiency can be obtained with smaller ID packed columns:

- Normally in a packed column, we have 2 regions: the part near the wall which is less dense because the wall effects packing, and the rest of the column which is more dense. From this we can get flow inhomogeneities (less backpressure in the less dense region hence higher flow rates). And also differences in phase ratio (more mobile phase in the less dense region). Smaller ID columns minimize these concerns because we can have a more uniform packing density. But Uwe is right, we must be in the correct range with respect to the ratio of column diameter to particle diameter.

- Secondly, to the extent that these inhomogeneities still exist, their effect will be statistically averaged out, since the smaller ID allows the analytes to spend time in different regions of the column (radially). Also because one can use longer columns (see below) that further allows more time for this averaging effect. The authors refer to this as "diffusional relaxation".

- The reduced backpressure that results from the less dense packing structure allows longer columns to be used.

- Less Eddy Diffusions is obtained (as mentioned by Klaus).

- Finally, the presence of the walls, largely prevents channeling from occurring.

The one point that I find confusing is that the less dense packing should have a cost in terms of mobile phase mass transfer? I don't think that was mentioned in the paper.

Hope that helps.
Adam

[MG]

I took a course in CZE a few years back, and recall that one reason for high efficiencies in CZE as compared to LC, is that we don't have laminar flow in CZE. In other words, the flow rate in CZE is the same at the walls as it is in the center if the capillary. Adam, this sounds similar to what you are saying about very small i.d. LC columns.

[adam]

Actually, I think they are 2 different issues (both of which effect band broadening). What I had referred to above were differences in flow rate due to packing density in different parts of the column. This is nowhere to be found in the classic van deemter equation (nor any other equation I don't believe).

What you're refering to is basically the mobile phase mass transfer term of the van deemter (or Golay equation for OT columns). This is much easier to visualize with an open-tubular column. The fluid near the wall will move more slowly due to a frictional drag, compared to the fluid in the center. I'm sure you've seen in texts where they talk about the 'parabolic flow profile'. The same thing happens with packed columns, it's just that we have numerous winding channels of changing diameter.

For reasons I don't think I could do much justice to off the top of my head, we get a much flatter flow profile with electrophoresis, or for that matter, electrokinetic chromatography.

[marc]

Interesting topic. The Jorgensen and Kennedy papers are interesting. I believe Milos Novotny was the first to show and discuss the advantage of really small ID columns at Riva in '87 and in a AChem paper in '88. In Jim's latest work he shows ID up to 150 um and you can see reduced plate heights going from just over 1 to just over 2. By the time you get up to 300 um there is little advantage, in A term, over 4.6 mm columns. The 4.6 mm columns are so robust and easy to pack that 300 um might seem of little value for isocratic work. The huge advantage of 300 um columns is in fast gradient analysis. At 4 ul/min and mixing in a 30 um tube prior to the column, mixing is nearly instantaneous so gradients can be run in tens of seconds throughout the mobile phase range. At mL's/min mixing just is not nearly as fast or reproducible as diffusional mixing in a 30 um tube.

Novotny's paper of '88 is the first reference I can find. Did Giddings or Knox or someone else predict that small capillary columns would have better efficiencies because of smaller A terms? Anyone??

Isocratic===> 1 to 4.6 mm ID
Gradient===> .3 or 0.5 mm ID
>15KPSI===> 1 mm ID or smaller

[Uwe Neue]

Small i.d. columns have been around in gas chromatography for a long time. In LC, I believe it was Endele who worked with a very small ratio of column diamter to particle diameter first, around 1972/1973, but the fact that at these ratios the structure is looser must have been around already before that, i.e. from GC.

Marc is correct: the rule of thumb is that once you get to a column to particle diameter ratio over about 30, the thing is a standard packed bed, and there is no difference in column performance, if the column is packed properly. Of course, for columns with a low aspect ratio (L/d), one runs into a lack of radial exchange, which can cause problems if the column packing is non-uniform. Giddings talked about the interchange of various non-uniformities in his coupling theory in the Dynamics of Chromatography from 1966.

Bottom line: a properly packed column works the same way, once the column to particle diameter becomes large enough.

The A-term of the van Deemter equation represents the non-uniformities in the packed bed. This includes the lack of uniformity between the wall and the center of the bed. Interestingly, Golay mentioned at some point that in an ideally constructed packed bed, this non-uniformity term should go away. I agree with this, because we reduced the non-uniformity term to about half a particl diameter with radially compressed columns. (For reference, a decent uncompressed column has a van-Deemter A-term of about 2.)

In electrokinetic chromatography, the fluid is transported forward by movement along the surface of the particles (or the wall in open tubes). If you visualize the open tube as an example, there is no frition between the different fluid layers, and thus the flow is a plug flow. In pressure-driven flow in an open tube on the other hand, the velocity is 0 at the wall and maximum far away from the wall. This difference is the basic reason for the higher performance of electrochromatography.

[HW Mueller]

So why doesn´t one use knitted (etc.) tubes to prevent the laminar flow (faster flow in the center...)?

[Ben Buglio]

On this same topic there is the work of RPW Scott who derived an equation (Liquid Chromatographic Column Theory, p197-198)) showing that the optimum column radius is directly proportional to the separation factor- 1 and to a small degree, pressure. His prediction was that for difficult separations a long narrow diameter column packed w relatively large particles would be best whereas for simple separations (a=1.12 or better) short wide columns packed a very small particles would be best.

[Uwe Neue]

Hans,

I have not yet found a colony of ants that are willing to knit 1-micron channnels.

[adam]

An interesting point was raised above regarding the fact that faster gradients can be used with smaller ID columns.

Can anyone suggest any rules of thumb with respect to the maximum gradient speed (increase in % B solvent / minute) with respect to columns of different diameters.

Thanks

[Uwe Neue]

One can run fast gradients on standard HPLC equipment, provided one uses tools that get around the gradient delay volume. We have run gradients in a 1 minute time frame over a solvent composition of 0 to 100% at high flow rate, and recently we went down to gradients under 15 seconds using a UPLC instrument. All of this work was done with 2 mm columns.

Fast gradient require high linear velocities to be effective. This requires high flow rates and high pressures, but the equipment can handle this. The problem is not with the mixing, at least not within the conditions that we have played with.

[tom jupille]

Assuming the hardware constraints discussed by Uwe, it's more a matter of the column volume than diameter:

rate (%/min) approx = 4 * F / Vm

where F is the flow (mL/min) and Vm is the column internal volume (you can assume Vm approx = 0.5 * L * dc^2)

This is assuming a "reasonable" k* value (5) and small molecules (S = 5). If you're willing to run at a lower k* (2.5), you could double that rate.

[DR]

But as soon as you minimize the column volume, flow cell volume, extra column effects etc. etc. the question becomes "Do you have any capacity (and sensitivity or dynamic range) left?"