Theoretical plate column efficiency

Thus, the minimum value of (a) for any pair of solutes can be calculated for any given column. The minimum values of (a) required for a pair of solutes that will be separated on a column having 25,000 theoretical plates (the efficiency of the standard ASTEC column 25 cm long, 4.6 mm in diameter and packed with spherical particles 5 p in diameter) is shown plotted against the (k ) of the first eluted solute is shown in figure 5. 

The relative "goodness" of a column is expressed in terms of efficiency, n/L, as plates per foot. A 6-foot column having 2000 plates would only be half as efficient as a 3-foot column with the same number of plates. Although the total number of plates, n, influences the degree to which peaks will be resolved, column efficiency is a measure of how well the column has been prepared and operated. A performance of 1000 plates per foot can be obtained but 500 is reasonable anything less is indicative of a problem. Column efficiency is also expressed as h, which is the length of column (expressed in millimeters) equivalent to one theoretical plate. This efficiency is related to column variables by the van Deemter equation ... 

In HPLC, the flow rate has a profound influence on the separation, because retention times and separation performance (theoretical plate number, efficiency) of a column depend on it. A decreased flow rate results in later elution of the peaks and in increased distance between them and vice versa. The relationship between flow and column efficiency is described by the Van Deemter curve (see Fig. 42-1). 

A theoretical model for the calculation of the number of theoretical plates using the Newton-Raphson method is presented by Kaibel et al. (31). However, it does not incorporate a constraint on T so that temperature becomes an independent variable. Such an assumption is obviously highly questionable. Nevertheless, this difficulty can be overcome by incorporating such a constraint into the equations. The problem of different plate efficiencies for concentration and reaction equilibrium is, however, considerably more difficult to handle. It would appear that the best approach will be to abandon completely the concept of theoretical plates and efficiencies and develop instead a plate-to-plate calculation method based on real plates. Here the extension of the differential equations for packed columns into difference equations and their subsequent modification to apply to each individual plate offers the best chance of success. 

In the case of a plate column the performance of a real plate is related to the performance of a theoretical one by the plate efficiency. In the case of a packed column the height equivalent to a theoretical plate HETP) gives a measure of the contacting efficiency of the packing. 

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where... 

A column s efficiency improves with an increase in the number of theoretical plates or a decrease in the height of a theoretical plate. 

Equations 12.21 and 12.22 contain terms corresponding to column efficiency, column selectivity, and capacity factor. These terms can be varied, more or less independently, to obtain the desired resolution and analysis time for a pair of solutes. The first term, which is a function of the number of theoretical plates or the height of a theoretical plate, accounts for the effect of column efficiency. The second term is a function of a and accounts for the influence of column selectivity. Finally, the third term in both equations is a function of b, and accounts for the effect of solute B s capacity factor. Manipulating these parameters to improve resolution is the subject of the remainder of this section. 

To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in equation 12.27 or equation 12.28. The easiest way to accomplish this is by adjusting the velocity of the mobile phase. At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. As shown in Figure 12.15 (which is interpreted in terms of equation 12.28), the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of u. 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

Microcolumns use less solvent and, because the sample is diluted to a lesser extent, produce larger signals at the detector. These columns are made from fused silica capillaries with internal diameters of 44—200 pm and lengths of up to several meters. Microcolumns packed with 3-5-pm particles have been prepared with column efficiencies of up to 250,000 theoretical plates. 

Open tubular microcolumns also have been developed, with internal diameters of 1-50 pm and lengths of approximately 1 m. These columns, which contain no packing material, may be capable of obtaining column efficiencies of up to 1 million theoretical plates.The development of open tubular columns, however, has been limited by the difficulty of preparing columns with internal diameters less than 10 pm. 

The required number of actual plates, A/p, is larger than the number of theoretical plates, because it would take an infinite contacting time at each stage to estabhsh equihbrium. The ratio is called the overall column efficiency. This parameter is difficult to predict from theoretical... 

This is the one case where the overall column efficiency can be related analytically to the Murphree plate efficiency, so that the actual number of plates is calculable by dividing the number of theoretical plates through equation 86 ... 

The simplest efficiency is the overaH column efficiency which is the number of theoretical plates in a column divided by the number of actual plates ... 

An alternative to determining packed height is through the use of an empirical term, height equivalent to a theoretical plate (HETP). This term can be measured in a fashion similar to that used for the overall plate efficiency of a column (eq. 44) ... 

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