Plate counts, calculation

FIGURE 13.24 A mixture of hydrocarbons and some polyethylene standards at I45°C. Column backpressure was approximately 5500 psi. Plate counts calculated on the hexane and heptane peaks yield 204,000 plates. 

Kirkland, J. J., Yau, W. W., Stoklosa, H. J., and Dilks Jr., C. H., Sampling and extra-column effects in high-performance liquid chromatography influence of peak skew on plate count calculations, /. Chromatogr. Sci., 15, 303, 1977. 

SUMMARY OF RESULTS FOR TFE RUGGEDNESS OF THE METHOD ON THE PLATE COUNT CALCULATED FOR ASPIRIN... 

This equation has recently been shown to be the most accurate manual method of plate count calculation (10). 

PSS uses the following formulae (22,23) to calculate plate count, asymmetry, and resolution. PSS uses test conditions that conform to the ISO/EN 13885 and DIN 55672 requirements for SEC sample testing. 

There are different ways to calculate the theoretical plate count of a column. PSS SEC column plate counts are measured using the so-called half-height method. Figure 9.9 shows a graphic representation of this test. 

The following formula is used to calculate the plate count ... 

Using other methods for the calculation of plate count can result in different numbers, depending on peak shape. It should also be kept in mind that many other operational parameters, such as eluent viscosity, column temperature, flow rate, and injection volume, will influence the results of the plate count determination. 

For SEC separations of polymers, column efficiency is better characterized by specific resolution, R,p, and efficiency, T, than by theoretical plate count. Peak resolution, R is calculated according to (7) ... 

FIGURE 13.21 A series of polymer additives using the infrared detector at 5.78 micron. Efficiencies were calculated using the last peak, Tinuvin P, and a plate count of 290,000 was achieved. 

FIGURE 13.25 Using chloroform as the solvent, a mixture of polystyrene standards were nicely separated on the 3-m set of columns. Run times here were 160 min. Plate count for toluene was calculated at 240,000 plates. The 500 MW Standard is separated nicely into its oligomers. 

Having chosen the test mixture and mobile diase composition, the chromatogram is run, usually at a fairly fast chart speed to reduce errors associated with the measurement of peak widths, etc.. Figure 4.10. The parameters calculated from the chromatogram are the retention volume and capacity factor of each component, the plate count for the unretained peak and at least one of the retained peaks, the peak asymmetry factor for each component, and the separation factor for at least one pair of solutes. The pressure drop for the column at the optimum test flow rate should also be noted. This data is then used to determine two types of performance criteria. These are kinetic parameters, which indicate how well the column is physically packed, and thermodynamic parameters, which indicate whether the column packing material meets the manufacturer s specifications. Examples of such thermodynamic parameters are whether the percentage oi bonded... 

The efficiency, or plate count of a column N is often calculated as 5.54 (tr/a)2, where tr is the retention time of a standard and a is the peak width in time units at half-height.1 2 5 This approach assumes that peaks are Gaussian a number of other methods of plate calculation are in common use. Values measured for column efficiency depend on the standard used for measurement, the method of calculation, and the sources of extra-column band broadening in the test instrument. Therefore, efficiency measurements are used principally to compare the performance of a column over time or to compare the performance of different columns mounted on the same HPLC system. 

Much of this work was carried out using a special distilling column called a bubble-plate column (Fig. 141). Each plate really does act like a distilling flask with a very efficient column, and one distillation is really carried out on one physical plate. To calculate the number of plates (separation steps, or distillations) for a bubble-plate column, you just count them ... 

Efficiency or plate count (N)—an assessment of column performance. N should be fairly constant for a particular column and can be calculated from the retention time and the peak widths. Selectivity (a)—the ratio of retention k ) of two adjacent peaks. Sample capacity— the maximum mass of sample that can be loaded on the column without destroying peak resolution. Capacity factor k )—a measure of solute retention obtained by dividing the net retention time by the void time. 

System suitability calculations like k, resolution, and plate count (N). 

Another example is the confusion between the terms efficiency, efficacy, and selectivity of a separation. It is not always mentioned how these responses are obtained. Usually, the efficiency is either expressed as the number of theoretical plates or plate number, N, or as the height equivalent to a theoretical plate or plate height, HETP or With efficacy, usually efficiency, thus plate count, is meant, although it is not always clearly specified. The selectivity, in general, is found by calculating the selectivity or separation factor, a, which is a measure for the... 

A further interesting feature of plate count predictions from the model is that N values can be compared with those quoted by column manufacturers for their prodix ts. In this work the quoted N value was 350 and that calculated was 280 at 1.25 ml/min when using polystyrene standard M = 9000, i.e. one which gives a symmetrical curve. In making sucR comparisons one must bear in mind that the plate theory assumes that N is independent of polymer molecular weight which is not the case with our model. When a standard of n = 37,000 was used the calculated N was 160. 

Figures 2 and 3 present typical results obtained from a low plate count column and a high plate count column. The graphs present the calculated molar concentrations of macromolecular species as a function of their degree of polymerization. The straight lines are the theoretical, kinetic distributions. Inasmuch as convergent solutions are obtained, the algorithm is effective for correction for Imperfect resolution.

The main effects are calculated by adding together all the values of a given parameter obtained at one level and subtracting the sum of the values obtained from the other level and divided by the half the number of experiments. For instance, for the calculation of the main effect on plate count N for factor A, using the Plackett-Burman design shown in Table 5.9, is carried out as follows ... 

Table 5.13 shows the confounding pattern for the Plackett-Burman design shown in Table 5.9. The main effect for this design calculated for the plate count is shown in equation (4). The interaction effect between factor B with factor A is the difference between the main effect when B is at the method level and that when B is at its extreme level.

Using this or similar mixtures, inject a sample into an equilibrated column, elute the resolved bands, and record them on the recorder. Calculate plate counts for the first and last peak using the 5 [Pg.38]

It is important, first, to realize that efficiency is not a function solely of the column. Bad extracolumn parameters, such as detector cell volume or tubing diameters, can make the best column in the world look terrible. Second, efficiency measurements are very poor ways of comparing or purchasing columns unless all other parameters are constant. Many columns are bought and sold because they have a higher plate count than someone else s column. The efficiency calculations could have been made with different equations, on different compounds, on different machines, at different flow rates, all of which will have a profound effect on efficiency. The only valid use of plate counts that I have found is in column comparisons where all other variables are equal, or in following column aging over a period of days or months. 

The most common performance indicator of a column is a dimensionless, theoretical plate count number, N. This number is also referred to as an efficiency value for the column. There is a tendency to equate the column efficiency value with the quality of a column. However, it is important to remember that the column efficiency is only part of the quality of a column. The calculation of theoretical plates is commonly based on a Gaussian model for peak shape because the chromatographic peak is assumed to result from the spreading of a population of sample molecules resulting in a Gaussian distribution of sample concentrations in the mobile and stationary phases. The general formula for calculating column efficiency is... 

Using equations 6-8, 6-9, and 6-10, we can calculate the effect of large volume injections. For example, assume that we have two columns, one column has a plate count of 25,000 and the compound elutes with a 10-mL retention volume, and the spreading is W = 0.8 mL. The second column has 8000 plates, and the column elutes with a 10-mL retention volume, and the spreading is W = 0.45 mL. For these two situations the effect of injection volume size can be shown in Table 6-3. 

Foley and Dorsey have recently derived a simple manual method for the calculation of plate counts that corrects for the asymmetry of skewed peaks (9 ). This equation has been used in all of our micellar efficiency calculations and is ... 

Estimate optimum column length, flow rate, amount loaded and required plate count based on the engineering design calculations or numerical methods. 

---