Plate height

The other measure for the band broadening as mentioned in Section 1.3 is the plate height H  

The plate height is also called the height equivalent to a theoretical plate (HETP). 

In both the well-packed HPLC columns and the capillary GC, plate heights of 5-10 xm and 0.2-0.25 mm, respectively, should be obtained. 

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Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

Now t[i is a minimum when k = 2, that is, when = 3t . There is little increase in analysis time when k lies between 1 and 10. A twofold increase in the mobile-phase velocity roughly halves the analysis time (actually it is the ratio Wu which influences the analysis time). The ratio Wu can be obtained from the experimental plate height/velocity graph. 

High-Performance liquid Chromatography. Typical performances for various experimental conditions are given in Table 11.15. The data assume these reduced parameters h = 3, V = 4.5. The reduced plate height is... 

In these expressions, dp is the particle diameter of the stationary phase that constitutes one plate height. D is the diffusion coefficient of the solute in the mobile phase. 

V = 4.5. These are optimum values from a graph of reduced plate height versus reduced... 

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... 

Another approach to improving resolution is to use thin films of stationary phase. Capillary columns used in gas chromatography and the bonded phases commonly used in HPLC provide a significant decrease in plate height due to the reduction of the Hs term in equation 12.27. 

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... 

Hsieh and Jorgenson prepared 12-33- 4m HPFC columns packed with 5.44-pm spherical stationary phase particles. To evaluate these columns they measured reduced plate height, h,... 

In 1972-1973 Knox et al. [3, 4, 5] examined, in considerable detail, a number of different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The reduced plate height (h) and reduced velocity (v) were introduced by Giddings [6,7] in 1965 in an attempt to form a rational basis... 

It is seen that the reduced plate height is dimensionless. 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

Figure 2. Graph of Log of Reduced Plate Height against Log of Reduced Velocity for Poorly and Well Packed Columns...

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

The resistance to the mass transfer term for the stationary phase will now be considered in isolation. The experimentally observed plate height (variance per unit length) resulting from a particular dispersion process [e.g., (hs), the resistance to... 

Thus, if high efficiency columns are to be used, with their inherent small plate heights, then connecting tubes must either be eliminated altogether, or reduced to the... 

Further, by substituting for (uopt.) in equation (3), it can be seen that the minimum plate height (Hmin.) is given by,... 

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. 

The expression that gives the minimum plate height is given by equation (29), chapter 12, and is reiterated here. 

It must be emphasized that equation (4) only applies to the separation and conditions defined in Table 1. The effect of the magnitude of the separation ratio on the minimum plate height is shown in Figure 4. 

Figure 4. Graph of Minimum Plate Height against Separation Ratio of the Critical Pair...

The optimum velocity changes linearly from about 1 cm/sec. to 800 cm/sec. and the minimum plate height from 200 pm to about 10 pm over the same separation ratio... 

Employing the value (N) obtained for the plate efficiency, again, in an analogous manner to GC and LC the plate height of a TLC plate (Htlc) is given by... 

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