Plate height and

There is some disagreement on the correct equation for describing the relationship between plate height and mobile-phase velocity. In addition to the van Deemter equation (equation 12.28), another equation is that proposed by Hawkes... 

Now, the column length (L) can be defined as the product of the minimum plate height and the number of theoretical plates required to complete the separation as specified by the Purnell equation. 

Figure 7.5 Left, variation of the average plate height of fine-and coeurse-particle layers as a function of the solvent aigration distance and method of developaent. Right, relationship between the optiauB plate height and solvent migration distance for forced-flow development.

The plate height, and thus the total number of theoretical or effective plates, depends on the average linear carrier gas velocity (van Deemter relationship) and, for a particular carrier gas, the efficiency will maximize at a particular flow rate. Only at the optimum carrier gas flow rate are n, N, and HETP Independent of the column length. The efficiency will also depend on the column diameter (see section 1.7.1) where typical values for n, N, and HETP for different column types can also be found. Values for n, N, and HETP are reasonably independent of temperature but may vary with the substance used for their determination, particularly if the test substance and statioKary phase are not compatible. 

The following values for plate height and gas velocity were obtained for -hexane on a 2-metre Apiezon-L column ... 

Plot a graph of //versus Ti and calculate the optimum gas velocity, the corresponding minimum plate height and the maximum plate number. 

FIGURE 12.2 Van Deemter plot illustrating evolution of particle sizes and resulting changes of relationship of plate height and linear velocity. Source From Swartz, M., J. Liq. Chromatogr. Rel. Technol., 2005, 28, 1253. With permission from Taylor Francis Group.)... 

The band broadening may be characterised by a plate height, and its causes provide a basis for understanding why modem chromatography is such an efficient separation technique. 

This equation indicates that the particle size, dp, is the main contributor to the H value. The smaller the particles, the higher the theoretical plate number. The optimum condition is obtained by the relationship between the theoretical plate height and the flow velocity. 

For validation of columns that will be used for an official assay and to provide an unambiguous standard for qualifying future media lots, it is useful to employ more measurable comparative criteria than a simple overlay. Resolution, plate heights, and peak symmetry, as calculated by the classical formulae, should match very closely among test and reference columns (Figure 6.1, Figure 6.2). 

These results are in agreement with the results of the calculations made above if we take into account the values of the reduced plate height and velocity. From that we can safely predict that using wider columns it is possible to achieve about 1,000,000 plates with a 20-m-long column packed with 10-/xm particles, operated under 250 atm, with an analysis time of 18 h. 

FIGURE 9.2 Theoretical plate-height curves for 5 pm particles, illustrating the effect of temperature on plate height and linear velocity. (Reprinted from Lestremau, F. et al., J. Chromatogr., 1138, 120, 2007. Copyright 2007. With permission from Elsevier.)... 

The van Deemter plots in Figure 25-3 show that small particles reduce plate height and that plate height is not very sensitive to increased flow rate when the particles are small. At the optimum flow rate (the minimum in Figure 25-3). the number of theoretical plates in a column of length L (cm) is approximately3... 

Capillary electrophoresis provides unprecedented resolution. When we conduct chromatography in a packed column, peaks are broadened by three mechanisms in the van Deemter equation (23-33) multiple flow paths, longitudinal diffusion, and finite rate of mass transfer. An open tubular column eliminates multiple paths and thereby reduces plate height and improves resolution. Capillary electrophoresis reduces plate height further by knocking out the mass transfer term that comes from the finite time needed for solute to equilibrate... 

There is much interest in high-efficiency- and high-speed separation media for liquid chromatography. The plate numbers available in practice have been in the range of 10,000-30,000 in HPLC for 20 years or so, but these are low compared to well over 100,000 theoretical plates in capillary gas chromatography or in capillary electrophoresis. This is caused by the limitation in the use of small-sized particles for HPLC, where a particle-packed column is commonly used under a pressure-drop of up to 40 MPa. An increase in column efficiency by using small particles, which is the approach taken in the past, is accompanied by an increase in the pressure-drop, as expected from Eqns. 5.2 and 5.3, below. Eqns. 5.1-3 describe the efficiency (plate height) and flow resistance of a column packed with particles [1-3], where N stands for the... 

To better understand the heightened resolving power of 2D systems, we need some measure by which 2D and ID separations can be compared. Not all criteria of separation power lend themselves to ready comparison. The resolution of a specific pair is not a suitable criterion because this resolution varies widely for different separation mechanisms irrespective of ID or 2D configurations. Plate height and plate number are not directly comparable because these are defined only for a single dimension. While H or N values can be found for each axis, it is not immediately obvious how to combine them for both axes in order to compare the overall separation effectiveness with that of a ID system. 

We would like to know the plate height and the number of theoretical plates generated in Sc separations. Equation 5.38 gives plate height as H = 2Dt/W. By writing DT = 0D and W= U, this becomes... 

In the text it is stated that a molecular weight M of MO6 is necessary for effective operation in sedimentation FFF. We can examine this matter by further considering the system described in 9.6 above. If the two molecules (Af = 106, M = 107) are spherical globules, estimate the plate height and the number of plates in a channel 50.0 cm long. The flow velocity (u) is 1.25 cm/s. 

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