Theoretical plates & column efficiency

[hmlurd]

Hi all!

I'm using EP formula to calculate theoretical plates number: N=5.54(Rt/W0.5)^2 and I have a few basic questions:

1) What peak(s) I must use to do the calculation? First, middle, last... (I'm using RP-HPLC gradient separation)

2) All peaks must give the same N number?

In my calcutations I have different N values depending on the peak used. Values ranges from 50,000 to 265,000!), I think that are too high!

My column is 250 mm x 4.6 mm x 5 um and the last peak Rt is about 49 min.

Any idea?

Thank you all.

[zokitano]

I suppose that you need to do those calculation for the system suitability.

1) So, the method should specify the minimum N for certain compound (to meet the system suitability).
Number of theoretical plates(N) differs from peak to peak, because different peaks have different retention times and peakwidth at 5% of the peak height.

2) That's why all peaks wouldn't have the same value of N, because column efficiency is (often) different for different compounds (peaks) that are taken into consideration

At the end, the higher values of N for certain compound, the better column efficiency for that compound. (that's something that methods should tend to achieve)

Best regards

[philippem]

Hi you ,

First of all , one does not calculate the plate number when doing gradient analysis. Of course you can do it , but you will get results which are as such meaningless and difficult to use in order to compare the quality of the column. Thats the reason why you get such results ( from 50,000 till 265,000). Peak width is smaller at the end of the chromatogram , due to the gradient and therefor you get higher values !

The plate number is a measure how well the chromatography is performed in your column,so its depending on the analyte, chromatographic conditions and stationary phase!

Platenumber calculations are done in isocratic mode ( same solvent compostion during analysis) and at constant flow, temperature. So you can compare different columns or conditions moe easily.

Even in isocratic mode the plate number is/can be depending on the retention time ( or k 'value) , so calculate N on peaks with at least k' of 3 [ k' = (TR component -tdead volume)/t dead volume].
Plate number can be reported per column ( lentgh) or per meter, be aware of that !
Your column( 250 mm filled with 5 um ) would result in a plate number of around 25,000/column I guess.

Values can be depending on type of analyte, but usually one takes a PAH to calculate the plate number ( in optimal conditions, that what all manufacturers are doing). If you calculate the plate number with the parameters of your analyte of interest the values could be different ( = less) .!

[zokitano]

I forgot to mention:

Platenumber calculations are done in isocratic mode ( same solvent compostion during analysis) and at constant flow, temperature. So you can compare different columns or conditions moe easily.

Also, sorry for the mistake:

1) So, the method should specify the minimum N for certain compound (to meet the system suitability).
Number of theoretical plates(N) differs from peak to peak, because different peaks have different retention times and peakwidth at 5% of the peak height.

corrected: 1) So, the method should specify the minimum N for certain compound (to meet the system suitability).
Number of theoretical plates(N) differs from peak to peak, because different peaks have different retention times and peakwidth at 50% of the peak height. (N=5.54(tr/W0.5)^2)

[hmlurd]

Thank you for your answers.

Really I don't need to meet EP specifications. I need the N calculation for accept new replacement columns and to estimate the loss of efficiency during column life.

Maybe I could use a "dedicated" isocratic method to do this, instead of use the separation method. Nevertheless I'll verify if N astronomical values obtained with gradient separation are useful for this purpose. I had to send back some columns (same reference, different batch) because can't resolve critical pairs, in spite of vendors tests seems to be correct.

Best regards.

[hmlurd]

Another question:

Plate number can be reported per column ( lentgh) or per meter, be aware of that !

From the formula aforementioned: Is not N adimensional? How can be expressed with units?

[zokitano]

Yes, N is a nondimensional quantity, and N in the previous formula (N=5.54*(Rt/W0.5)^2) refers to a number of theoretical plates per column.

The number of theoretical plates per meter [unit: 1/m] can be calculated by following equation:

Number of theoretical plates per meter = (N/L)*100

where, N= number of theoretical plates per column and
L= length of the column [in cm]

Best regards

[HW Mueller]

Here is another quote, from J-C Janson and J-A Jönsson, page 49, in J-C Janson and L Ryden, eds., Protein Purification, VCH, NY, 1989:

"To a first approximation all (symmetrical) peaks in a chromatogram show roughly the same plate number."

and,

"It should be emphasized that they (they refers to equations for N) are only valid in isocratic chromatography and when the peak is reasonably symmetrical."

[tom jupille]

"To a first approximation all (symmetrical) peaks in a chromatogram show roughly the same plate number."

That's true in principle and to a first approximation; it's closer to true for proteins than for small molecules, and it was more true two decades ago than it is now. In practice, it ignores "extra-column" contributions to band broadening. These are proportionally more significant for narrow peaks than for wide peaks (small molecules tend to give narrower peaks than proteins, early peaks tend to be narrower than later peaks, and "newer" smaller columns packed with smaller particles tend to give narrower peaks than older, longer, larger-particle columns).

hmlurd, if what you are trying to do is to monitor column lifetime and performance for your own records, the simplest approach would be to simply track the width and retention of a specified peak under defined conditions. Combining them into a "pseudo" plate number calculation would merely add error (and possibly mask problems if both retention and efficiency changed).

[Uwe Neue]

I agree with Tom. Do not bother with the wrong and artificial plate count measurement. Measure peak width, and retention times of your peaks. It allows you to check separately, what is happening as the column ages, and what the differences are between different columns. As the column ages, the retention might decrease (from loss of bonded phase) or the peaks may get wider (due column contamination, for example). Having the different numbers on peak width and retention, you can immediately make a guess at the major factor that affects your column lifetime. The same can be said for the difference between two new columns. If the retention times wiggle around, it could be a difference in the packing material or your method. If the peak widths are different, if could be column packing/plate count or related effects.

[hmlurd]

Zokitano: Thank you for the explanation. Calculate N per column or meter is really trivial, I didn't see the point before.

Uwe and Tom: Taking into account your ideas and suggestions, I think I'll simply make a record of peak widths and retention times (and thus resolutions) to check column lifetimes and differences between columns.

Thank you all

[HW Mueller]

Actually, my quotes were intended to indicate two things:
a) That N can vary due to deviations from Gaussian distribution, not because of the t term in the plate number equation given above, and
b) if peaks are not Gaussian these formulars don´t apply anyway.

[tom jupille]

HW, both are good points. In principle, you could get around the second by using the more general N = (tR/σ)^2. I would work for any shape peak, assuming a data system that can accurately calculate σ. In that case, though, the term "plates" would be divorced from any physical analogy (such as number of stages of equilibration) and would simply be a dimensionless measure of relative peak width.

[Mark Tracy]

Chromeleon can calculate the 0th, 1st and 2nd statistical moments that correspond to area, mean and variance of the peak. Note that if the peak is assymetric, tR != mean

[tom jupille]

Note that if the peak is assymetric, tR != mean

Thanks, Mark. I had lost sight of that. The "generalized" N is actually the first moment squared divided by the second moment. That would even work for a square peak (which would not have a unique value of tR).