Theoretical plate height

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... 

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 22.9 Reduced plate height versus reduced velocity. Measured data V, toluene O, PS 2200 , PS 43,900 A, PS 77S.000. Theoretical lines solid lines, Giddings, infinite diameter column dotted line, Knox, infinite diameter column dashed line Knox walled column. (Reprinted from J. Chromatogr., 634, IS4, Copyright 1993, with permission from Elsevier Science.)... 

The reduced plate height, h, is defined as the number of particles to a theoretical plate and is given by... 

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. 

In modern TLC the distribution of sample within a spot is essentially Gaussian and the number of theoretical plates (n, ) and the plate height (H,, ) observed can be conveniently expressed ]sy equation (7.7) and (7.8)... 

The Poppe plot is a log-log plot of H/uq = t(JN versus the number of plates with different particle sizes and with lines drawn at constant void time, t(). H is the plate height, Vis the number of plates, and u() is the fluid velocity (assumed equal to the void velocity). The quantity H/u() is called the plate time, which is the time for a theoretical plate to develop and is indicative of the speed of the separation, with units of seconds. In the Poppe plot, a number of parameters including the maximum allowable pressure drop, particle diameter, viscosity, flow resistance, and diffusion coefficient are held constant. 

HETP = height equivalent to a theoretical plate. It is derived from the plate theory of distillation which is a confusing concept having no basis in fact in the context of modem chromatographic separations. Nevertheless the terms plate number and plate height are still very widely used. 

The theoretical plate height (H) related to the separation capacity of the system can be described by... 

A more simple equation has also been proposed for the calculation of theoretical plate height ... 

A second reason why very high resolution can be obtained in chromatography is that very large numbers of theoretical plates are readily achieved. If the column is well packed with particles having a narrow spread of sizes, the plate height is about twice the particle diameter 9, n A typical large-scale GC or LC column will contain of 103-104 plates. 

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. 

I. Height Equivalent of a Theoretical Plate or Plate Height (HETP or H)... 

Teflon tubes and obtained separations with plate heights less than 10 pm. They also provided a theoretical basis for migration dispersion in free zone electrophoresis. 

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