Clarification of band broadening parameters

[U0mrj1K]

Dear reader,

I have a question relating to a sentence I have recently read in Synder, Kirkland and Dolan's (2010) book entitled: Introduction to Modern Liquid Chromatography, 3rd ed., page 42.

The sentence followed the equation: W^2 = ([16/L]*tr^2)*H; where W^2 represents the sum of the intra-column contributions to band broadening (Eddy diffusion/longitudinal diffusion/resistance to mass transfer in both mobile and stationary phases), tr is retention time, L is column length and H is the height equivalent to a theoretical plate.

I quote:

where values of H = L/N for different solutes are approximately independent of retention time tr for a given column of length L and the same experimental conditions.

Am I right in thinking that values for H can be regarded as approximately independent of tr, because the contribution by the longitudinal diffusion is (relatively) small under "normal" HPLC conditions? I think I'm confused as to why the authors have decided to state that tr has seemingly no effect on H, when my understanding was, that it does.

All the best,
U0mrj1K

[tom jupille]

It helps me to look at it this way: differences in retention time are due to differences in the time a molecule spends on/in the stationary phase.

Because all molecules spend the same total amount of time in the mobile phase, they all "see" the same flow path variations, so the "A term" in the Knox equation is also approximately independent of the retention time.

Because all molecules spend the same total amount of time in the mobile phase and so undergo the same amount of longitudinal ("molecular diffusion") band broadening, the "B term" in the Knox equation is approximately independent of retention time.

Because it's the residence time on the stationary phase that matters, all molecules make roughly the same number of transitions between the phases, so the "C term" is approximately independent of retention time.

Actually, if you look closely at the process, all bands *on the column* have approximately the same "physical" width when they get to the end of the column. The increase in peak width with retention time comes entirely from the fact that strongly retained peaks take longer to wash out to the detector.

[U0mrj1K]

Okay, that reply does help to make sense of the authors' comments, however, I remain a little confused.

On the basis of what you've described, if each of the A, B and C terms of the Knox equation have very little impact upon the retention time, why then would we wish to optimise our flow rate (which will impact tr) to minimise HETP? Afterall, by optimising our flow rate, are we not minimising A, B and C such that the HETP is as small as possible, or at least at a value that is small enough to offer high N values in a reasonable analysis time - i.e reasonable tr values?

All the best,
U0mrj1K

[tom jupille]

why then would we wish to optimise our flow rate (which will impact tr) to minimise HETP

As a practical matter, we don't. In our Advanced HPLC Method Development course, we suggest setting the flow rate for small-molecule analytes as high as possible subject to instrument constraints (things like pressure or baseline noise).

The only people who go for the optimum flow rate are theoreticians studying how chromatography works or column manufacturers seeking to evaluate the quality of their handiwork. With "modern" columns (anything from about 3.5 microns down), the Knox curves are fairly flat so that there is little loss in efficiency (and less loss in resolution) associated with higher-than-optimum flow. In effect (as you point out) optimizing flow provides a small improvement in resolution at a large cost in run time.

For macromolecules (e.g., proteins or peptides) that's not necessarily true; the big guys are subject to slower mass transfer kinetics so the C term is larger and there is more to be gained by optimizing flow.

[U0mrj1K]

Tom, thank you for your comments. I think they have partly helped to clear my confusion.

I guess my previous thoughts were leading me to believe that terms B and C of the Knox equation were some how affecting the overall retention/selectivity towards a molecule (as would say stationary phase choice and %B used in RP-HPLC). Obviously that was the wrong thought process (perhaps I can blame a Friday brain-fog?) as terms B and C are simply descriptions of band broadening events that, through changes in flow rate, have a greater or lesser effect upon the spread of a solute. I guess if they gave rise to a sufficiently broadened solute band (due to suboptimal flow rate choice), then there might be a slight difference in the system calculated tr at the peak apex (assuming that's how the algorithms work).

From a LC-GC article I read earlier today relating to shifts in tr between labs (using the same method but different instruments), it seems I should focus more time in to worrying over preparation of solvents at the correct %B and in ensuring the online mixing ratios are correct.

I'm currently working with a peptide molecule and so will go easy with flow rate when separating this 'big guy' from his equally large brothers and sisters.

Thanks,
U0mrj1K