Efficiency of an Unretained Peak

[M_Farooq]

The efficiency of an unretained peak is the highest efficiency a column can deliver (at least in theory), because it has no interaction with the stationary phase. Has anyone seen a lower efficiency of an unretained peak than the retained peak in the normal phase? The unretained marker is the typical marker used in normal phase (tri-tertbutylbenzene), but toluene, benzene also show the same effect. The column is extremely well packed (reduced plate height < 2 for retained compound) and the extra-column effects are negligible. Is there any possible explanation of this observation?

[tom jupille]

Is there any possible explanation of this observation?

I can provide a "hand-wave": your column has just enough small pores that there is a bit of size-exclusion going on, making some of your sample molecules elute a bit early and thus broadening the peak.

[M_Farooq]

Is there any possible explanation of this observation?

I can provide a "hand-wave": your column has just enough small pores that there is a bit of size-exclusion going on, making some of your sample molecules elute a bit early and thus broadening the peak.

It may be possible but even smaller molecules like benzene/toluene are doing the same thing. Are you aware of any other well behaving dead time markers in normal phase, whose efficiency can be measured?

[tom jupille]

Well, I *said* it was only hand waving!

Maybe something like dichloromethane?

And, just for the record, are you sure the extra-column contribution is *really* negligible (e.g., by plotting sigma^2 vs. tR^2 and extrapolating back to 0)?

[Jiri Urban]

As Tom suggests - I would "blame" contribution of extra-column volume

[Hollow]

What about injection volume and solvent?
My thoughts go in these directions: as the void marker doesn't interact with the stationary phase, there is also no possibility for it to get "compressed" at the top of the column before starting to elute.
So the peak volume is at least the injection volume plus the part of the Eddy and other dispersion effects. I could imagine, that a well retained compound could be compressed to a smaller band than that of the injection volume before it starts to elute (in opposit to volume overload effects with strong injection solvents).

Does the observed "efficiency" correlate with the injection volume?

Btw: what do you want to express with that number? As it doesn't interact with the stationary phase it's just a measure of the Eddy and other dispersion effects and tells nothing about the performance of the separation possibilities of the column? Maybe it tells something about the particle size distribution but there are other techniques to measure that.

[M_Farooq]

What about injection volume and solvent?
what do you want to express with that number? As it doesn't interact with the stationary phase it's just a measure of the Eddy and other dispersion effects and tells nothing about the performance of the separation possibilities of the column? Maybe it tells something about the particle size distribution but there are other techniques to measure that.

I agree that the unretained compound cannot "freeze" as it hits the packed bed like retained compounds. The injection volume is kept to a minimum and the sample is made in the mobile phase. The puzzling thing is that another column (different chemistry but same particle morphology and same dimensions) gives the highest efficiency of an unretained marker, as it should. On the other hand the column under discussion, is extremely well packed (for retained peaks) yet it gives lower efficiency for unretained compounds tested so far. The interest in unretained peaks originates from the fact that after packing the column, it is a good idea to test the efficiency of an unretained marker. It gives me an idea of the packed bed quality and the slurry packing technique. An unretained peak, in principle, should have the highest efficiency that a column can deliver. The only suspect was extra-column and one can correct it by subtracting the extracolumn variance , yet the unretained peak is clearly lower in efficiency than retained peaks by 2 to 3 thousand plates. Not sure why tri-tert butylbenzene is behaving like an exception in normal phase.

[M_Farooq]

For the interest of the general readers, a theoretical chromatographer told me that is possible to see lower efficiency for an unretained marker, if the column is too well packed. There are no published examples per se, but this was also seen by him with one special morphology of the monolith. The reason is that the unretained marker can have a larger B term (of the van Deemter) than the retained ones, since nothing can stop a molecule from longitudinal diffusion. To validate it, one can design a set of beautiful diffusion experiments. Note that is a very rare case, because the plate theory predicts that something with k= 0, has the maximum plate count; this is always (~99.9%) the case for a well designed instrument.

[TychoMaudd]

If you are measuring efficiency by plate count, you have to take into account that the injection volume will contribute to peak width. Since in a real HPLC, your sample is spread over a volume, you have a minimum peak width determined by your flow rate and injection volume*. If there was no band broadening, you'd have peaks of all the same width, and since plate count is dependent on retention time, you'll see higher and higher plate counts for each successive peak. Since there is band broadening in an HPLC, instead you'll find that as retention time increases, plate count will increase until the theoretical maximum for the column is reached under your chromatographic conditions (assuming well behaved analytes). So you would expect that for an unretained compound your plate count would be the lowest, however if you're measuring peak width, it should be the narrowest peak.

*Edit: Even with a perfect delta function, you'd still have a minimum peak width for all peaks due to extra-column broadening.

[M Farooq]

If you are measuring efficiency by plate count, you have to take into account that the injection volume will contribute to peak width. Since in a real HPLC, your sample is spread over a volume, you have a minimum peak width determined by your flow rate and injection volume*. If there was no band broadening, you'd have peaks of all the same width, and since plate count is dependent on retention time, you'll see higher and higher plate counts for each successive peak. So you would expect that for an unretained compound your plate count would be the lowest, however if you're measuring peak width, it should be the narrowest peak.

*Edit: Even with a perfect delta function, you'd still have a minimum peak width for all peaks due to extra-column broadening.

I am afraid that we might disagree here that for the unretained compound the column efficiency is the lowest. In fact, we empirically see very high plate counts on well packed column and an optimized instrument for an unretained peak (e.g. 20,000 plates on a 10 cm column). Lets start with the simplest process by injecting an analyte without a column. No doubt the band is very narrow with a tail (since laminar flow produces a tailed peak) and the efficiency is extremely low. One can see about 30-40 plates for a peak without a column because the time is very short. Now introduce an extremely well-packed column and inject an unretained compound. The packed bed will "flatten" the parabolic flow profile to some extent (the local velocity is chaotic but overall the average velocity in the center of the bed is higher). As a result the peak shape can be near Gaussian and extremely high efficiency (larger time, smaller peak variance). Do you agree with these ideas?

[TychoMaudd]

The increase in efficiency in that case is the longer retention time since the time spent on the column is adding less dispersion than laminar flow through tubing. Any effect that a well packed bed has on an unretained compound will also effect a retained compound. The idea behind what I'm trying to explain is that dispersion caused by the column is proportional to tR and since N=16(tR/Wb)^2 any increase in peak width caused by the column will not have an effect on plate count (ie. the number of plates is a property of the column, not retention time for similar, well behaved compounds). But the contributions to peak width caused by extra column dispersion and injection volume is constant. So the shorter the retention time of the compound, the greater the effect the extra-column dispersion and injection volume have on the overall width of the peak. This causes a non-retained peak to have a lower plate count than a retained peak.

You can see the effect that I am talking about by injecting a series of analogous compounds (we use xanthines in our lab) with various retention factors. The efficiency for a non retained peak will be lowest, and as retention increases, efficiency increases asymptotically as the dispersion from the column overwhelms extra-column dispersion. You can actually use this to calculate the extra-column dispersion of a chromatographic system.

[M Farooq]

You can see the effect that I am talking about by injecting a series of analogous compounds (we use xanthines in our lab) with various retention factors. The efficiency for a non retained peak will be lowest, and as retention increases, efficiency increases asymptotically as the dispersion from the column overwhelms extra-column dispersion. You can actually use this to calculate the extra-column dispersion of a chromatographic system.

Thanks for your insight. I am really interested in the way you calculate the extra-column effect. Do you have a reference and what is the criterion of choosing the compounds in different chromatographic modes for a series of analogous compounds.
Do you also find the extra-column calculated by connecting dead volume unions useful or not?

[danko]

M Farooq wrote:
[*]The puzzling thing is that another column (different chemistry but same particle morphology and same dimensions) gives the highest efficiency of an unretained marker, as it should.[*]

Non specific retention. In this case some hydrophobic interactions between marker and stationary phase.

Best Regards

[HPLCaddict]

Thanks for your insight. I am really interested in the way you calculate the extra-column effect. Do you have a reference and what is the criterion of choosing the compounds in different chromatographic modes for a series of analogous compounds.
Do you also find the extra-column calculated by connecting dead volume unions useful or not?

Have a look at this article:
"Accurate measurements of the true column efficiency and of the instrument band broadening contributions in the presence of a chromatographic column", Journal of Chromatography A, 1327 (2014) 49– 56
by the late Georges Guichon.

[M Farooq]

Thanks for your insight. I am really interested in the way you calculate the extra-column effect. Do you have a reference and what is the criterion of choosing the compounds in different chromatographic modes for a series of analogous compounds.
Do you also find the extra-column calculated by connecting dead volume unions useful or not?

Have a look at this article:
"Accurate measurements of the true column efficiency and of the instrument band broadening contributions in the presence of a chromatographic column", Journal of Chromatography A, 1327 (2014) 49– 56
by the late Georges Guichon.

Thanks. I think this is a reliable way of measuring extra-column dispersion because at higher pressure compression effects make the mobile phase dense, which in turn decreases the diffusion coefficient. In a union connection without a column, the diffusion coefficient must be different.