effect of internal diameter of column??

[danko]

Thank you for your discussion

You were welcome.

I understand your point and yet: Performance is usually benchmarked using N (plate count) and that’s what I addressed in my first post/answer. I never mentioned alpha which of curse has nothing to do with column dimensions nor particle size.
Resolution (Rs) is another thing. As we all know N is included the Rs equation and rightly so. Because slimmer peaks give more space for other peaks to elute separately. This is especially important when dealing with closely eluting peaks in a “crowdedâ€

[HW Mueller]

Danko, the retention time is in the denominator of the N equation. Since the increase in flow rate decreases the retention time it tends to cancel any decrease in the numerator.
I am sorry, I don´t follow your other descriptions either. I have not seen much if anything mathematical on eddies, but that much more on diffusion. I don´t understand all of this either, but Fick´s laws are obviously based on "random walk". I don´t see how the possibility to randomly walk further in the columns transverse direction has anything to do with random walk in the longitutional direction. Certainly, diffusion is a factor in band broadening, the diffusion laws didn´t indicate to me that column diameter have an effect on longitutional diffusion. I am wide open for correction on this thinking as well as for an explanation as to why people who keep things comparable do not see a difference in efficiency.

[mardexis]

If you can eliminate extra-column dispersion and you can pack columns to near theoretical efficiency then you will see plate counts improve with decreasing column diameter with almost all of the improvement in the capillary range.

If there are transcolumn effects (slightly different flow paths across the column diamter) then you can imagine that sample molecules will have a chance to 'sample' different flow paths by lateral diffusion and reduce transcolumn effects over the region sampled over some characteristic time. Lets say 100 seconds. Most things are on column for at least two minutes. Over 100 seconds the molecules will 'sample' about 300 microns by diffusion. Thus a 300 micron column will exhibit less "A" term broadening than a larger ID column. Columns with ID less than 300 um will get even better. Unless your chromatography is taking hours you will not see much effect in column ID's larger than 300 um.

And, if plate counts go up then peak widths go down and sensitivity improves.

All this being said I would say that most purchase capillary columns are poorly packed compared to conventional columns and very few of the vendors equipment can eliminate extracolumn broadening for capillary columns. I can't even run 2.1 mm ID well on all of my HPLC's so I stick to 4.6.

Marc

[unmgvar]

i will join Tom, Kostas and Uwe regarding this topic.

by moving from on column ID to another be it higher or lower, keeping all other column parameters constant; parameters have to be scaled such as flow rate in order to keep linear velocity constant. rule of thumb is the ration of dividing the squares of the IDs.
this ratio will give us the aproximate change in sensitivity that we can expect (the closer we are to it depends on the effects from the overall system).
column effeciency and resolution on the other hand does not change one bit if all other parameters are left constant . what needs to be considered are the system parameters which will generally make things worst if not adapted to meet the different ID used.
the change in colunm ID directly affect another very important parameter of the column which is its volume.

if we take for example the example given by bryan.
the peak broadening due to extra column volume effects is something that is happening outside of the column. it is a well known phenomena. that is why system capillaries, gradient delay volumes and flow cells are changed to smaller ID and volume. this is a must in order to keep in proportion to the new column ID and volume.

when moved to an adapted micro/nano system, peaks show no change in peak width.

[danko]

by moving from on column ID to another be it higher or lower, keeping all other column parameters constant; parameters have to be scaled such as flow rate in order to keep linear velocity constant. rule of thumb is the ration of dividing the squares of the IDs.

You are forgetting to think about what happens after the column and more precisely in the flow cell. Although the flow rate is scaled to achieve equal linear velocity in the different columns, the flow cell is not scaled – it remains constant. That’s why the higher the flow rate the smaller is the peak width. And that is the reason for not observing the peak broadening.

Or do you find it easier to believe that some of the analyte disappears when switching from say 2.1 mm to 3 mm column (lower peak)? Or vice versa - some stuff is being generated somewhere in the system, when switching from 3 to 2.1 mm column (higher peak). Remember you’re loading the same amount regardless of the column diameter.

[mardexis]

Jorgenson et. al; Anal. Chem. 2004, 76, 5777-5786

[danko]

Hi Mardexix,

“A picture is worth a thousand wordsâ€

[unmgvar]

i did talk about the flow cell.
flow cells are scaled, otherwise they permit mixing, diffusion, peak broadning and loss of resolution when going to smaller ID colunms.

from what i have seen:
waters: 6ul for the acquity detector.
dionex micro 1.4 ul 7 mm, semi micro 2.5 ul 7mm
agilent: micro 2 ul 3mm, semi micro 5ul 6mm

Although the flow rate is scaled to achieve equal linear velocity in the different columns, the flow cell is not scaled – it remains constant. That’s why the higher the flow rate the smaller is the peak width. And that is the reason for not observing the peak broadening.

Danko,
this has me confused. you say that the flow is scaled to keep linear velocity constant and then you speak of using higher flow rates?
we are talking of all column parameters constant except for the column ID

[Uwe Neue]

Dancho,

In your post on May 28 10:38 (and again on May 29 12:51), you are putting a bunch of different concepts into a blender, and then after proper mixing, you take out some pieces again and try to fit them back together again. This does not work.

Indeed, when you scale a separation to a larger column, keeping particle size and column length constant, you should scale two things with the column volume: the flow rate and the injection volume. Then the retention times will remain constant, and the peak height will remain constant. You get the exact same chromatogram (if the columns have been packed to the same quality and the extra-column bandspreading is negligible). If you inject half the scaled amount onto the fatter column (as you have proposed), you will get a peak that is half the size of the one you would have gotten with proper scaling. It is also half the size of the one you got on the smaller column.

This is very simple. There is no need to think about the detector cell. There is no need to think about eddy diffusion or van-Deemter A-terms, which have nothing to do with any of the things under consideration.

[Uwe Neue]

Marc,

The effects of improvement in column performance with decreasing diameter don’t kick in until the radial dispersion leads to a proper mixing. In addition, once the ratio of column diameter to particle diameter becomes less than 10, you gain in permeability due to the looser packing.

However, the amount of eddy diffusion is a question of the column packing technology. Modern columns have A-terms in the order of 1 to 1.5 particle diameters. The best that I have ever seen was an A-term of about 0.5 particle diameters on a radially compressed column (with a diameter of 8 mm!). I bet that this can be reduced even further with the right technology. Golay once said that he does not see any good reason for the existence of a van-Deemter A-term.

[danko]

Hi Uwe,

There is no need to think about eddy diffusion or van-Deemter A-terms, which have nothing to do with any of the things under consideration.

The column diameter has indeed something to do with van Deemter’s A-term. Larger diameter – more alternative paths for the molecules to follow – more dilution i.e. band spreading. It is as simple as that!

There is no need to think about the detector cell.

This was only an explanation of the fact that very few chromatographers understand the reason for the roughly constant peak widths they observe when columns and flow rates are scaled. The thing is, they use the same system i.e. detector i.e. flow cell and when they double the flow rate in order to keep the linear velocity in the columns constant (e.g. from 0.2 mL/min for a 2 mm column to 0.4 mL/min for 3 mm column) they forget that the mobile phase velocity after the column is again the double, even though it was normalized in the 2 different diameter columns. It results in roughly the same peak widths even though the mobile phase velocities (corresponding to 0.2 and 0.4 mL/min) in the flow cell were different (factor 2). As you can see the equal plate count numbers for these 2 columns are only apparent and the effect is caused by the time that took the analyte to travel through the flow cell (i.e. it took the half of the time for the analyte to travel through the flow cell when the flow rate was 0.4 mL/min, 3 mm column, compared to the time that took when the flow rate was 0.2 mL/min, 2 mm column). And the wrong conclusion was: No plate count changes when scaling the column diameter up or down. Yes wrong indeed, because the real peak width in the case of the 3 mm column would’ve been twice as large as it was in the case of the 2 mm column had the mobile phase’ velocity after the column been equal for the to configurations.

If you inject half the scaled amount onto the fatter column (as you have proposed), you will get a peak that is half the size of the one you would have gotten with proper scaling. It is also half the size of the one you got on the smaller column.

I never proposed different amounts (please read my posts more thoroughly). On the contrary I proposed the same sample amount loaded on both columns (of course reasonable amount, in order not to overload any of the columns). Didn’t I suggest 5 μg on both columns (just an imaginary number, in order to underline that the load should be the same)?
OK. If you do that, you’ll end up with roughly the same peak widths both with the 2 and the 3 mm columns. The peak heights however will be quite different – the 3 mm column configuration will result in half the peak height compared to the 2 mm column configuration.
And now I’m asking you: Did the half of the analyte disappear somewhere in the system? Or did the peak width double, but you didn’t notice that, because the flow rate was doubled?

Golay once said that he does not see any good reason for the existence of a van-Deemter A-term

The plots Mardrexis posted suggest otherwise! In addition to that you can confirm all that, if you conduct the experiment I suggested above. But I’m convinced that you’d see it without the experimenting, if only you gave it a shot – mentally.

Best Regards

[HW Mueller]

Danko, how does dilution cause band spreading? How does transverse diffusion influence lateral diffusion?
mardexis´ graphs do not show completely on my monitor, so I can´t tell what is compared.

What is the evidence for eddies anyway? We just came to the conclusion that there is no turbulent flow in columns, can one have eddies without it?

[danko]

Hi Hans,

Easy questions. Thank you!

how does dilution cause band spreading?

Concentrated band = narrow peak. Diluted band = broad peak.

mardexis´ graphs do not show completely on my monitor, so I can´t tell what is compared.

The data represents HETP for 7 different column diameters (from 10 to 150 mm). The lowest HETP is achieved with 10 mm column, the next lowest with 15 and so on. Perfectly confirming the theoretical expectations.

What is the evidence for eddies anyway?

No eddies! As I mentioned earlier (please read my previous posts more thoroughly) van Deemter’s A-term represents – despite the name - the diffusion due to the alternative paths molecules follow down the column. I don’t suppose you believe that the molecules line up in a queue waiting for each other to follow the same path.

We just came to the conclusion that there is no turbulent flow in columns.

We didn’t. As I pointed out there could be generated turbulent flow in a column, depending on the particle size and the flow rate (mobile phase velocity). Large particles + high velocity will generate turbulence. I sent you a reference, as far as I remember correctly. But in this case/discussion no eddies are considered.

Best Regards

[Uwe Neue]

Dancho,

Wow... May I recommend to you to read a book on HPLC Columns? There is one available with this title, published by Wiley-VCH. It has a pretty good section on theory. Once you have read and understood this, then we can discuss the A-term again.

As I stated before, there is no reason to think about the detector.

PS.: I read your post carefully. You have the difficulties reading. You indeed proposed to inject half the scaled amount on the fatter column. When you inject 5 microgram on both columns, you are not injecting 10 micrograms on the 2x fatter column, right?

If I inject 10 micrograms on the fatter column, and 5 micorgrams on the thinner column, I will get the exact same chromatogram, no larger peak, no smaller peak, just the same peak.

[Uwe Neue]

Mardexis
The plot by Jorgenson is complicated due to the thermal effects in columns packed with 1.0 micron particles. There are many items in your plot which are not relevant for larger particles and large diameter columns.