By Anonymous on Sunday, March 21, 2004 - 01:16 pm:

Here's a question for the theorists. Plate count is defined by the ratio of retention time to peak width (where the ratio is squared and multiplied by a factor of 16). By including retention time in the defenition, the effects of peak broadening as the material spends more time on column is normalized: because the peak broadens by the same factor that the retention time increases.

OK. All well and good. But there is nothing in the defenition of plate count that accounts for the quantity of material on column. It is well known that as you inject more material, the size of the peak increases. It gets both taller and fatter. Hence, the peak width will increase. It doesn't seem that the way plate count is defined allows any way to normalize for this.

Any thoughts?

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By DR on Monday, March 22, 2004 - 06:22 am:

Once you get to a certain point, additional material on column results in fronting. In turn, this fronting effectively shortens the RT and broadens the peak. These effects, in turn, cut into your plate count.

If you really want to throw a wernch into the theory, do nothing but halve your extra column volume and see what that does to your plate count.

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By Uwe Neue on Monday, March 22, 2004 - 03:31 pm:

There is the column plate count itself, which is for the most part (not completely) independent of retention. Then there is overload. Among overload, you have either mass overload (injecting too much mass of analyte) or volume overload (large injection volume). Both things make peask wider.

For a more complete discussion, I recommend my book - HPLC Columns.

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By Anonymous on Tuesday, March 23, 2004 - 03:38 pm:

Uwe

I do have your book (and I often refer to it). But this issue I have never seen discussed in any text. The question is not the effect of retention on plate count, but the effect of concentration on plate count. And I am not referring to the phenomenon of column overload. That is a separate issue alltogether.

The basic situation is as follows: if you inject 5 uL of a standard and, subsequently, inject 10 uL of the same standard (with both concentrations well below the point of column overload) you will get different peak widths - and hence different plate count values - for the 2 injections. But if there is no way to normalize for the effect of concentration, that would make the plate count parameter absolutely meaningless!!

Further insight would be appreciated. I must be missing something, but I can't figure out what.

Much Thanks

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By tom jupille on Tuesday, March 23, 2004 - 04:37 pm:

Actually, you *should* get the same peak width for both a 5 microliter and a 10 microliter injection; if you're not, then there is a problem with your chromatography. Possible issues:

- if you are using a very small column, of if you are doing size exclusion, then (as Uwe suggested), your observed width may be dominated by the injection volume rather than by peak broadening in the column.

- if your sample is dissolved in something much stronger than the mobile phase (e.g., pure organic solvent in a reversed-phase system), then you may be seeing abnormal peak broadening as the sample equilibrates with the mobile phase at the head of the column.

Other than that, in my experience, peak width (e.g., width at half-height) is independent of injection volume.

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By Uwe Neue on Wednesday, March 24, 2004 - 03:09 pm:

I agree with Tom:
If you do not overload the column or inject the sample in a strange solvent and so on, the peak shape at a 5 microliter injection and a 10 microliter injection are self-similar, and should completely overlay, if scaled by the height. Then the plate count is the same.

If you rely on your computer to calculate the plates, you must be careful, how he does it. Computers do not know what baselines are....

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By Anonymous on Wednesday, March 24, 2004 - 04:38 pm:

Interesting. All these years I always thought peaks got both taller and fatter as the concentration increased. But come to think of it, I guess its true that the kinetic factors that cause band spreading are not a function of concentration and, therefore, neither should peak width or plate height be a function of concentration (in the absence of secondary factors - as you pointed out).

Thanks, Uwe and Tom, for your thoughtful responses.

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By Anonymous on Thursday, March 25, 2004 - 02:17 am:

I think maybe in the past you have used chart recorders. When the peak goes off scale, it looks fatter. You are not able to observe its width at half height under these cicumstances. You have to remember also that you need to draw tangents to the peak to measure its width at base. The wings of the peak may make it look fatter when more sample is there.

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By Jon H on Friday, March 26, 2004 - 03:11 pm:

Hi.

I'm confused. If you inject a 1 uL sample,
then the next run inject 1000 uL of the same
sample (Assuming the column can handle it
and the response is linear), would you
really expect the peak widths to be
the same? I recognize that with a well-
retained compound on a gradient run, this
can be the case. Say, though, you run
isocratically and the analyte moves at a
constant rate through the column without
a pause. At common flow rates, the 1-mL
sample is already a minute wide when it
enters the column, while the 1-uL sample
peak is 1000 times more narrow.

What happens in the column to negate the
different sample plug sizes in the tubing?

Thanks in advance

Jon

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By Uwe Neue on Friday, March 26, 2004 - 04:05 pm:

Jon: this situation is called volume overload. Assume that you do the following: you inject always the same mass of sample, but in an ever increasing volume. This is done in a very straightfroward way: you dilute the sample by a factor of 2, and then inject 2x the volume (assuming that you got a variable-volume injector that lets you do this). You initially get your nice normal peaks, but as the volume becomes as large or larger than the original peak volume, you peak becomes wider, flatter and gets a flat top. All of this assumes that your sample is made up in mobile phase, and the dilution is made with mobile phase.

If you dilute the sample with the more retentive solvent (water in RP), you can go on nearly forever diluting your sample with water, and you'll still get the same peak...

(Before somebody corrects me: I said NEARLY forever...)

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By Jon H on Monday, March 29, 2004 - 01:23 pm:

Thanks for the reply, but I'm still not
quite with you.

Is there, then, an injection volume for a
given system above which volume overload
begins to affect peak shape? Why doesn't
this occur to some degree at all volumes?

Maybe most injection volumes are insignificant
compared to peak volume gained by diffusion and dispersion?

I am curious about this because my lab does
large volume injections.

thanks for your patience

Jon

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By DR on Monday, March 29, 2004 - 01:32 pm:

As long as a relatively weak solvent is used, the sample is caught on the column head until it gets pushed along by the mobile phase. In the weak solvent, it gets 'focused' on the column head, kind of like cold trapping an analyte on a GC - a large injection volume of a high boiling analyte can be put on a GC column if it is diluted in a low boiling solvent and injected very slowly. Once the injection is complete and the solvent gone, the temp is raised enough to volatilize the high boiling analyte - you can get a very sharp peak doing this despite the large injection volume. This all assumes that the mass of analyte is not enough to overload the column.

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By Jon H on Monday, March 29, 2004 - 02:28 pm:

DR-

Thanks for the explanation.
The idea of focusing makes sense in the case of a
gradient run, but in an isocratic run, wouldn't
the focusing be reversed at the column outlet?
Assuming all analyte molecules behave independently
on the column, if it takes 1 minute to load them,
it should also take 1 minute (plus some time for
dispersive effects) to unload them at the other
end, regardless of their speed moving through the column.

I agree, though, that the focusing effect seen
in gradient runs is elegant.

Jon

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By Uwe Neue on Monday, March 29, 2004 - 03:55 pm:

DR gave a nice explanation of the focusing effect on the top of the column. The sample focuses, because it is in a weaker solvent than the mobile phase, meaning that its retention is very large. In the moment the sample solvent is replaced by the mobile phase, the sample migrates through the column as normal. Now, as it leaves the column, it has no reason to spread out, since it is still in the mobile phase.

If you want to, the molecules have by then forgotten the injection solvent :-)

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By Jon H on Tuesday, March 30, 2004 - 07:48 am:

Got it. Thanks, all!

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By tom jupille on Tuesday, March 30, 2004 - 11:52 am:

One further comment on volume overload. Assuming an isocratic separation, with a dilution (sample) solvent identical to the mobile phase:

The sample injection volume *does* contribute to observed peak width under all circumstances. However, independent contributions to band broadening are "root mean square" additive (the observed width is the square root of the sum of the squares of the contributions). As a "back-of-the-envelope" calculation, this means that you wouldn't notice any effect from injection volumes smaller than about 1/5 of the volume of your peak (that would result in about a 2% increase in observed peak width). Even an injection of half the peak volume would only increase the observed width by about 11%

If you have a 10 x 0.46-mm column with 10,000 plates, a peak at k' = 2 should have a "theoretical" baseline width around 120 microliters, so volume overload would begin to set in somewhere around 20 - 50 microliters injection volume. Proportionally more for bigger columns.

Note that this ignores peak tailing issues, non-ideal peak shapes, other causes of band-broadenting, etc.

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By Anonymous on Wednesday, March 31, 2004 - 05:11 pm:

Tom

Maybee you could elaborate on what you mean when you say that "the injection volume does effect peak width under all circumstances". I think I would disagree with that point. In cases where the extra-column effects are negligable, the peak width would be determined only by the "van Deemter broadening" that occurs as the components move through the column. Ideally, we should be operating most of the time in such a way that these extra column effects are not substantial (though I know this is often not the case in the real world and will become more problematic if smaller diameter columns become popular).

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By tom jupille on Wednesday, March 31, 2004 - 06:25 pm:

It's a matter of semantics. We're saying the same thing: injection volume *does* contribute to observed peak width in all cases, but in the case of a properly set-up system, that contribution (as well as all other extra-column contributions) is negligible ("negligible" is not the same as "non-existent"). :-)

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By Anonymous on Wednesday, March 31, 2004 - 07:50 pm:

Got it.

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By Anonymous on Thursday, April 1, 2004 - 05:47 pm:

Tom (are you still out there)

I want to pick up on what you said above about the contributions to peakwidth being root-mean-square additive. I've seen that several times in textbooks and papers, but I have always had difficulty understanding it conceptually. In other words I can't visualize why the relationshiop would work that way. Can you (or anyone else who wants to jump in) offer any guidance as to why this behavior is root-mean-square additive. I think there is some connection to statistics, but I can't really get any farther than that.

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By Uwe Neue on Friday, April 2, 2004 - 03:13 pm:

It is indeed founded in statistics. If you have independent interacting random events that each have a standard deviation, then the variances (the squares of the standard deviations) add up.

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By Uwe Neue on Friday, April 2, 2004 - 03:14 pm:

PS: it is the same as the variance of sources of error in measurements.

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By HW Mueller on Monday, April 5, 2004 - 04:10 am:

This is an interesting discussion to get back "in" after a vacation.
On Jon H, March 29: Of course, if loading with a non-chromatographing solvent takes x minutes you will have an x minute delay in the retention time. This assumes you compare the injection to one with ideal volume, etc., as discussed above.

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By Anonymous on Monday, April 5, 2004 - 09:03 am:

Uwe

Thanks for the clarification. For some reason it is difficult for me to visualize it, though I know it's true. Most laws of nature are logical and easily understood: once stated. For example "Force = mass x acceleration" makes perfect logical sense. I guess I should have been a physicist :-)

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By Anonymous on Tuesday, May 25, 2004 - 05:20 am:

Is the number of theoretical plates always constant accross a chromatographic run independent of the concentration of the components (assuming no column overloading)? In other words, would it be correct to assume that the ratio of retention time to bandwidth is the same for all peaks, even when comparing a minor component against the main component (% area relative = 0.3%)?

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By Uwe Neue on Tuesday, May 25, 2004 - 02:56 pm:

The plate count depends on the analyte and its interaction with the stationary phase. However, if the molecular weight of the analytes is about the same, and the retention factor is about the same, and the type of interaction between the sample and the stationary phase is about the same, then the plate count will be about the same. Unless there is overload, the concentration has no effect.

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By Anonymous on Wednesday, May 26, 2004 - 10:12 am:

If I have a minor peak adjacent to the main peak (0.3% area relative to main), can I assume the the type of interaction between the sample and the stationary phase is about the same and therefore, the ratio of retention time to bandwidth should also be the same?

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By Anonymous on Wednesday, May 26, 2004 - 03:46 pm:

In my opinion (I am the wise guy who started this thread) it is a reasonably safe assumption. If the two components elute close to one another that suggests they are probably similar in size. From there is follows that the diffusion coefficients would be about the same. If you look at the van Deemter equation, the primary reason that plate count would change from one analyte to the next (with the column, mobile phase, and all the rest being the same) would be the diffusion coefficients of the molecules.

Of course, it is always possible that other factors will complicate things. For example, one of the components may have some functional group that caused tailing with the column; whereas the other component does not have this functional group (these types of things are not addressed by the van Deemter).

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By Alex on Friday, May 28, 2004 - 01:01 am:

No, I disagree.
If two peaks elute closely to each other there are at least two possible explanations:
a) they are closely related, behave similar. Then k' of both components will scale with % organic or temperature and separation will be similar under all conditions.
b) there are not closely related, they just have similar retentiontimes by coincidence. Then, with different %organic or temperature separation is likely to be different.

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By Anonymous on Thursday, June 3, 2004 - 06:05 am:

My question is: would the width of two adjacent peaks necessarily have to obey the theoretical plate equation (i.e., will the ratio of retention time to peak width always be the same for all compounds within the run)? The equation is being proposed by one of our lab groups here to differentiate between a real peak, and an artifact (e.g., bubbles or electrical spikes). Can two adjacent peaks give different theoretical plates, yet be real peaks?

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By Uwe Neue on Thursday, June 3, 2004 - 03:56 pm:

Bubbles or spikes can easily be descriminated from real peaks. No need to count the plates.

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By tom jupille on Thursday, June 3, 2004 - 04:30 pm:

Plate count will often vary somewhat from peak to peak, but (absent overload or tailing problems), the plate count for adjacent peaks should be in the same ballpark. As far as bubbles and spikes are concerned, Uwe is right: they should be so different from nearby peaks as to be obvious by inspection. Ditto for late eluters from previous injections (much wider than nearby peaks).

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By Anonymous on Thursday, June 3, 2004 - 04:47 pm:

I agree with Uwe and Tom. Just one point, this is assuming isocratic methods. For gradient methods the peaks widths tend to be more constant throughout the run and so the ratio of retention time to peak width will not generally be constant.

In my personal opinion I am a little uncomfortable with using this ratio as a formal criteria for identifying an artifact peak. As Tom points out, all of the things we're saying assume no overload/tailing (or other complications). In reality these complications often occur.

For bubbles and electrical spikes - what are sometimes called "transient instrument malfunction" - the foolproof way to demonstrate this is to re-inject the sample. If it is transient instrument malfunction, the extraneous peak should not be present in the re-injection. This is also the generally accepted way of handling these issues in the pharmaceutical industry (if that's where you are).

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By A.Mouse on Thursday, June 3, 2004 - 11:40 pm:

Yes, two adjacent peaks can give a much different plate count, and still are peaks. Think of a situation where you want to do isocratic chromatography, and one of two adjacent peaks is a peptide, and the other is a small molecule. The width of both peaks is much different, and the plates will be much different. An even simpler case would be if you have a packing that gives tailing for bases, and one peak is a normal compound, and the other one is a basic compound.
Bottom line: different peaks can have much different plate counts.