Chromatographic performance Ulrich Bergmann 2009

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

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?

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

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.

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.

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 http://www.asp.ucar.edu/colloquium/1992/notes/part1/fig3-2.gif

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

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

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

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

Stronger interaction with the mobile phase will increase elution volume and peak width http://www.asp.ucar.edu/colloquium/1992/notes/part1/fig3-2.gif 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

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

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.

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

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

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.

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:

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:

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

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

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

How many theoretical plates are needed Resolution 1.0 1.5 1.005 780000 1750000 1.05 8100 18000 1.25 320 860 1.50 120 260 2 40 90

In pictures From: http://media.wiley.com/CurrentProtocols/ET/et0601/et0601-fig-0002-1-full.gif Resolution of 1.5 is sufficient/required for baseline separations

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

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: http://www.lcresources.com/training/training.html

Last and least the extended vanDeemter equation From wikipedia All clear? http://www.chem.uoa.gr/applets/AppletChrom/Appl_Chrom2.html