THERORETICAL PLATE COUNT

[Harry]

Hi Chromatographers,
I am a reputed dealer of HPLC columns in Asia Pacific. One of our customer complaint about much lesser theoretical plates in column we have supplied (Phenyl 250x4.6, 5µ, 100A). As per the customer they compared the results with the chromatogram given with column. They have used the same test analytes with the similar conditions given in chromatogram. Meanwhile please give me the following clarifications.


1. Do theoretical plates have any relation with Flow Cell ? As per customer, with similar problem in Merck column, Merck gave the factor of 1.8 to be multiplied with that of the theoretical plate count of customer. This is due to the difference in flow cell being used by customer. I am failed to understand this. Please clarify regarding any relation to flow cell and also about this factor of 1.8 stated above.



2. There are different formulas for calculating plate numbers i.e. N = (tR/σ)2 , N = 16(tR/wb)2 and N = 5.54(tR/w0.5)2 . As I understand In the ideal case (a perfectly Gaussian peak), all three forumulas will give the same value for N. In the real world, peak shape is seldom ideal, and plate numbers based on different formulas can vary tremendously. The greater the deviation from ideality, the greater the variation in plate number. In general, measurements made closer to the top of the peak will generate larger plate numbers than will measurements made near the bottom.

When describing column performance, it is important to specify not only the plate number but also the formula used. Is this true? Please correct me if I am wrong.

Does different software calculate the plate count with different formulae?

Will there be difference in plate count calculated by different formulae even if the chromatographic conditions are perfectly identical?

3. Does plate count mentioned by different manufacturers are Plate Count PER COLUMN or Plate Count PER METER.

WHAT INFORMATION IS REQUIRED FROM THE CUSTOMER TO UNDERSTAND THE PROBLEM BETTER.

A bit lengthy question? But I hope You guys will help me out.

[AA]

I can not really directly answer the questions, but I can tell you this. Plate count is directly related to both the column and the system. Many (all?) manufacturers use optimized, non commercial system to evaluate plate counts. They do this to try and show the effienciey of the column only, as oppsed to the system and column together. It is very unusual that a customer will get the same plate count as the even following the method conditions listed in the quality document included with the column.

[Harry]

Dear AA,
Thanks for reply. But is there any specific relation between plate count and flow cell. What is this factor 1.8 mentioned in my last mail?
Plate counts mentioned by manufacturers are per column or per mtr?

[philippem]

Harry,

By doing Chromatography one dilute the peaks. All interferences which contributes to peak broadening wil lead to a lower plate number.
When you have two systems with different flow cells ( volume) , you will get an different plate numbers. The system with a small detector flow cell will generate higher plate number, asumming of course that all other parameters are the same! The factor 1.8 can be caused by the detector volume contribution
As the previous person mentionned , a suppler will test his columns in optimum situation, this means all connections as low volume as possible, low detector flow cell and short connecting lines. The supplier wans to test the column, not the equipment.

Usually the plate number, in HPLC, is given per column, but the supplier should mention it on his test chromatogram to avoid confusion. A 25 cm *4.6 mm column filled with 5 micron reversed phase particles should generate around 20 000 plates/column

I always use this formulae: N = 5.54(tR/w0.5)2

succes

Philippe

[Mark Tracy]

The factor of 1.8 is empirical. Merck knows the performance of their factory test system, and the performance of the customer's system (assuming correct installation), and 1.8 is the performance ratio. Every configuration will have a different ratio.

The theoretical plate count will be degraded by factors external to the column. They include diameter of the connecting capillaries, care with which you make fitting connections, detector cell design, sample injection volume, sample injection solvent, data collection settings, and so forth.

Our factory test systems are standard Dionex components, but carefully selected and installed. Not all models perform equally well.

Plate counts are sometimes reported per column and sometimes reported per meter. Read the test report carefully. Even Dionex is not consistent in this practice.

[tom jupille]

This will echo some of the previous responses, but just to be thorough:

1. Do theoretical plates have any relation with Flow Cell ? As per customer, with similar problem in Merck column, Merck gave the factor of 1.8 to be multiplied with that of the theoretical plate count of customer. This is due to the difference in flow cell being used by customer. I am failed to understand this. Please clarify regarding any relation to flow cell and also about this factor of 1.8 stated above.

The observed plate count reflect the total amount of band broadening that occurs in the entire system. This includes the column, injector, detector, connecting tubing, fittings, etc. So yes, the detector will have en effect. Using a constant "fudge factor", however, is misleading. Assuming independent sources of band broadening, the observed variance will be the sum of the component variances: σ²(obs) = σ²(col) + σ²(inj) + σ²(det) + . . . For an ideal peak shape, σ = 1/4 X baseline width. Multiplying observed plate count by a constant factor is valid only for a specific plate count.

If you want to get an estimate of N for the column, you can do it by running a standard that has three well-shaped peaks under isocratic conditions. Plot σ² as a function of tR². The slope should be pretty close to 1/N for the column. The intercept should be approximately equal to the extra-column contribution to band broadening.

When describing column performance, it is important to specify not only the plate number but also the formula used. Is this true? Please correct me if I am wrong.

You are correct.

Does different software calculate the plate count with different formulae?

yes. You need to check with the user documentation to find out which formula is used in a particular system.

Will there be difference in plate count calculated by different formulae even if the chromatographic conditions are perfectly identical?

Yes. Generally, the greater the tailing factor, the greater the variation in plate count by different formulae.

3. Does plate count mentioned by different manufacturers are Plate Count PER COLUMN or Plate Count PER METER.

Generally, marketing/promotional literature will use plates/meter, because this is larger number. Test results are more often reported in plates/column (for the specific column tested) but, as Mark pointed out, there is a lot of inconsistency.

[Uwe Neue]

I would like to add one more thing.
The reason the column manufacturers test their columns under special conditions and on equipment with minimal system bandspreading is not so much that they want to brag about how wonderful their columns are. There is another reason: the largest dependence of the plate count on the column packing conditions is around the minimum of the van Deemter curve. Therefore one gets the best impression on the quality of the results from the packing procedure at this point. This is important for an optimization of the packing procedure as well as for good quality control.

[Harry]

Hi Guys,

Thanks for your clarifications.
If Plate count is dependent on so many factors as mentioned by all of you. Then what is the way to cross check the manufacturer's claim regarding column efficiency as it is impossible to EXACTLY replicate the system conditions used by manufacturer (generally it not disclosed by manufacturer) or analytical conditions which is mentioned in chromatograms supplied with the column?

Dear Uwe Neue, I have purchased your book "HPLC Columns : Theory, Technology, and Practice". I congratulate you for being so informative. I am still going through this book. ITS AN EXCELLENT WORK.

[tom jupille]

Manufacturers' plate count specifications are a lot like automobile manufacturers' fuel economy ratings*:
- they represent the highest value you could ever expect to see under absolutely ideal conditions
- they are higher than you will ever see in real life
- they are only one factor in overall performance.


*For Forum members outside the US: the Environmental Protection Agency reports automobile fuel efficiency ratings (miles/gallon) for "city" and "highway" driving. These are generated under computer-controlled conditions and are invariably higher than "real-world" results.

[Mark Tracy]

You don't need to duplicate the factory test system. You need to assemble and configure your system so as to minimize all the external factors. (That is all I did for our factory test stations.) If the column efficiency is really that important to your work, you need to do this anyway. In these times of shorter, narrower, faster columns, this is something we all need to do.

A few tricks to minimize dispersion: Bypass the heat exchanger in the flowcell, bypass the heat exchanger in the column oven, change all the connecting tubing to 0.12mm i.d., remove excess fittings, obtain the smallest detector flowcell that will work at your flowrate, operate at near room temperature, install the smallest sample loop your injector can use, use manual injection if your autosampler is not well designed, change the valve rotor & stator to the smallest available passageways, use only accurately square-cut tubing, practice making good fitting connections, set the detector rise time/time constant/filter to the smallest value possible, set the detector data rate high enough to get 30 points per peak, try turning off software data smoothing.

Not all these tricks are compatible with real operating analysis, but use the ones that are. For example, when you have to operate far from room temperature, a correctly-sized eluent heat exchanger in the column oven will gain more efficiency than it costs.

[juddc]

Manufacturers' plate count specifications are a lot like automobile manufacturers' fuel economy ratings*:
- they represent the highest value you could ever expect to see under absolutely ideal conditions
- they are higher than you will ever see in real life
- they are only one factor in overall performance.

I can't argue with any of the chromatography advice I've seen here, but my personal automotive experience is at odds with this...In almost every car I've ever owned - large and small - I've been able to routinely meet and sometimes exceed these estimates, even in quite old cars. I do drive relatively quickly, but I generally keep my cars in good tune and run them to high mileages. My most recently sold daily commuter was 17 years old and had nearly 200K miles and usually had fuel mileage dead center of the EPA estimate - about 20 mpg for a fairly heavy old BMW with a big 6 and a typical cruise velocity of 80-90mph with passing speeds well beyond if needed.

Mebbe I'm wierd, mebbe my tires are properly inflated...YMMV, of course

[Uwe Neue]

As Mark has pointed out, to get the correct plate count is also not that big of an exercise. However, if you do not get it, I would first check the instrument and the procedure in all details before complaining to the column manufacturer...