We're having a bit of heated discussion that I was hoping could be solved here. A CE friend believes that the theoretical plates will be higher for a less concentrated analyte (same volume). He states that fick's 2nd law dictates more rapid change in the concentration gradient for the same time period for the more concentrated sample. I really haven't seen this in my LC. My plates remain generally statistically the same (given that I don't overload). When I look at van Deemter, there's nothing about concentration in terms of plate height. It seems to me that for a given analyte, diffusion is a constant, and therefore FWHM should be the same regardless of concentration.
Thanks for any input.
Jim

Maybe he is right, when you see the equation for theoretical plates:

N = 5.54(Rt/W)^2

where N = theoretical plates
Rt= retention time for a given analyte
W = peak width at 50% of the peak height

when you decrease your concentration, your peak width decrease too, but the retention time will still be the same, so the theoretical plates will increase. But the peakwidth @ 50% should not change a lot, so statistically you might be right.

Maybe both of you guys are right.

The general derivation of the plate theory does not give any effects of concentration, as long as one is working in the linear range of the adsorption isotherm or partitioning system. The peaks are self similar, independent of the concentration. This is why one gets the same plate count, independent on the concentration - unless you inject so much that you get out of the linear regime.
In CE the plate count is for the most part determined by axial diffusion. Axial diffusion does not depend on the concentration, unless one applies really large concentrations. The same story should apply there.
In summary, under normal circumstances, there is no effect of concentration on plates. The primay reason is that we are dealing hydrodynamics, which are not affected by concentration.

In a theoretical sense, I think your friend is right. Surely there is a greater flux down a steep concentration gradient than a shallower gradient. However, I think you are right and will never see it in practice. Longitudinal molecular diffusion or mobile phase mass transfer is summed in the B term of the Knox equation. With HPLC we normally operate at flow rates well above those that would generate the maximum number of plates. At these flow velocities multipath effects, sample mass transfer kinetics, and hydrodynamics have a greater effect on plate count than molecular diffusion. However, if you operated a very low flow rates where molecular diffusion became dominate, it wouldn't surprise me if you saw differences based on large changes in sample concentration.

Things are simpler than most of you think. Here is the simple version: take Einstein' diffusion equation: s^2 = 2*D*t. In words, the variance of a diffusing peak is proportional to its diffusion coefficient and the time it diffused. No effect of concentration in this equation!
Same thing, if you look at the van Deemter equation. No effect of concentration! How one gets there, one will see in textbooks that take you from Fick's law to the Einstein equation.

Onother version (derivable from the one A.nonymous gave) of the th. plate equation shows nicely what Uwe is saying:

N = 6.28(t*h/A)^2

t is ret. time, h is peak hight, A is area of the peak. The gut feeling that w1/2 goes up with amount is, therefore, not correct (if you work within theory, here: the range where h varies linearily with amount inj.).

It seems that the baseline width (wb) version of the equation:

N = 16(t/wb)^2


should then be avoided, because integrators are not adjusted for each amount injected, so that a higher inj. amount certainly records a higher wb. (One does not at all stay within theory)

Thanks for your help.
I think the discrepancy is in the ability of the detector to see the "wings" of the peak at low concentration. Therefore when the software calculates the N for a concentrated sample, it takes into account the full peak, but for a low concentration, it can't calculate the true width.
been very informative
Jim

The way the detector sees the peak depends on the settings on how it should start seeing the peak. If you set it at a fixed value way above the baseline noise, it will cut off the bottom of the peak, and as the peak gets smaller, the amount of bottom that gets cut off becomes larger. Goes to show that detectors can't think...