1. Chromatographic performance
Ulrich Bergmann
2009

2. Summary of the previous part
Chromatography relies on (equilibrium) distribution of compounds between 2 phases.
Kinetics of the equilibration process (mass transport/diffustion) between phases is critical.
Likewise, the (same) diffusion process will cause band broadening
Optimization will look for a compromise
That maximizes the mass transport
Minimizes longitudinal diffusion
And ”irregular” flow (Eddy diffusion)
Main parameters to optimize are
Flow rate
Particle size and shape of the immobile phase
temperature

3. What is the performance and how to measure it?
A good column produces sharp peaks
bad one ?
Of course it’s the same peak
good one?

4. Obviously, some real measure for chromatographic performance is needed
If you want to produce a nice looking chromatogram, extend x range and compress y range
Obviously, some real measure for chromatographic performance is needed

5. Performance Means separation power
For the craig apparatus it’s simple: The number of equilibrations runs the show. This is the number of extraction glasses and corresponds to the plates of the destillation column.
For chromatography columns that concept is called ”theoretical plate” and it’s number describes the performance of the column.

6. How to determine the theoretical plates?
In chromatography, the number of equilibration steps is unkown and depends on external conditions.
So we need an expression to describe column performance that is easy to measure and corresponds to the real plates in the craig apparatus.
We put something into the chromatography, elute, and see what comes out.

7. Peaks The peak shape will be used to define the theoretical plates
The concept is simple: assumption is, that the peak has a normal distribution (Gauss curve), and the width of that is the quality measure:
Sharp peaks:
many theoretical plates
Good separation power
Broad peaks:
Few theoretical plates
Bad chromatography

8. Homework question?
Why is the concept based on the normal distribution?
We have seen in the Craig apparatus that there is a binomial distribution?

9. However, peak shape is not all
Again the craig machine
Sharp peaks with 20
plates

10. The same system with the same 20 plates and we have lousy peaks

11. How to get an ”independend” scale
Relate peak width to the retention time (or elution volume)

12. Stronger interaction with the mobile phase will increase elution volume and peak width
Early peaks are sharper than late ones
Our quality parameter should take that into account
N = 5.55 (tr/w1/2)2
Or depending on where we want to measure the peak:
N = 16 (tr/w)2 at bottom w
W1/2

13. Plate height
We can calculate the height for each plate by dividing the colulmn length by the plate number.
H=L/N
H is a better measure for column quality, since it is not dependend on the lenght of the column

14. Theoretical plates depend on the chromatography conditions
And can be compared only with
The same compound injected at same concentration and volume
Same flow rate, temperature, eluent system, chromatography system.
No good for gradient elutions.

15. t0, tR and u
If you run a compound that doesn’t interact with the stationary phase you get the dead time (breakthrough time) t0.
For some applications, it’s useful to define a linear velocity u
U= L/ t0 where L is the column length

16. From: http://www.chromedia.org/dchro/gfx/ZmgmagnHcB.jpeg

17. Checking column packing
If you calculate the theoretical plates for a not retained compound, you have a measure for the quality of the column packing
sharper the peaks can’t be, but they can get broader if something is wrong with the column packing or system flow path.

18. An expression for the interaction
Compounds that don’t interact with the stationary phase can produce sharp peaks (high N, small H), but they can’t be spearated from each other.
Retention time could be a measure for interaction, but it is dependend on flow and column dimension
We define the:

19. Retention (or capacity) factor k
k=(tR -t0 )/ t0 = t’R/ t0
Desirable are k values between 1 and 10, low values mean poor separation capacity, high ones are ”boring”.
To measure separation between two compounds we define:

20. Separation factor (relative retention)
a= k2/k1 =
t’2/t’1
= D2/D1
With D distribution coefficient

21. Resolution
For separation, the retention between two peaks has to be bigger than the peak width.
If you want to work with peak width at half height (w1/2),
The factor 2 is replaced with 1.18

22. And what resolution can we expect from the theoretical plates?k1 1 4 R=
(a-1) √N (
K1+ k2 )
1 + 2
(a-1) k2 1 4 R= √N (
K1+ k2 ) a
1 + 2

23. How many theoretical plates are needed
Resolution
1.005
780000
1.05
8100
18000
1.25
320
860
1.50
120
260 2 40 90

24. In pictures
From:
Resolution of 1.5 is sufficient/required for baseline separations

25. Higher resolution is needed to analyze compounds present in ratios different from 1:1

26. So far we are dealing with ideal conditions
In reality, peaks are not following the gauss distribution,
Most remarkably is the tailing (or heading) of peaks, and that effect is described by
The tailing or the asymmetry factor which can be defined in different ways.
Both figures from:

27. Last and least the extended vanDeemter equation
From wikipedia
All clear?