Plate height phases

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. 

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. 

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,... 

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... 

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... 

FIGURE 10.1 I Effect of linear velocity on plate height for proteins. Column SynChropak GPC 500, 250 X 4.6 mm i.d. Mobile phase 0.1 M potassium phosphate, pH 7. (Reprinted from Ref. 4 by courtesy of Marcel Dekker, Inc.)... 

D. P. Poe and D. E. Marthe, Plate height theory for compressible mobile phase fluids and its application to gas, liquid and supercritical fluid cliromatography , 7. Chromatogr. 517 3-29(1990). 

The contribution to the plate height from molecular diffusion in the mobile phase arises from the natural tendency of the solute band to diffuse away from the zone center as it moves through the column [59,60,63,64]. Its value is proportional to the diffusion coefficient and the. time the sample spends in the column. Its contribution to the total plate height is given by... 

Mass transfer resistance in the mobile phase is more difficult to calculate because it requires an exact knowledge of the flow profile of the mobile phase. This is only known exactly for open tubular columns for which the contribution of mass transfer resistance in the mobile phase to the total plate height can be described by equation (1.27)... 

The A term represents the contribution from eddy diffusion, the B term the contribution from longitudinal diffusion, and the C terms the contributions from mass transfer in the mobile and stationary phases to the total column plate height. By differentiating equation (1.31) with respect to the mobile phase velocity and setting the result equal to zero, the optimum values of mobile phase velocity (u ) and plate height (HETP ) can be obtained. 

Figure 1.14 Plot of plate height (mb) as a function of the nobile phase velocity ( 1/ain) for a series of colunns of 0.46 cm I.O. packed with a spherical porous n-octadecylsllanized silica of different particle diameters. For the 8 and 5 micrometer diameter particles the column length was 25 cm, for the 3 micrometer diameter particles IS cm and for 2 micrometer dieuaeter particles 4 cm. (Reproduced with permission from ref. 3. Copyright Elsevier Scientific Publishing Co.)...

The possibility of obtaining significant improvements in performance by using semi-packed and open tubular columns is clearly illustrated by the values for the separation impedance in Table 1.17. Variation of the reduced plate height with the reduced velocity for an open tubular column is given by equation (1.82), assuming that the resistance to mass transfer in the stationary phase can be neglected... 

The general approach for kinetic optiaization of open i tubular columns has been to adopt the familiar Golay equation T (equation 1.34) and to assuae that the aobile phase can be approximated by an incompressible fluid with ideal gas properties, (44-50). Circumstances that are approximate at best but serve adequately to demonstrate some of the fundamental characteristics of open tubular columns operated at low fluid densities. The column plate height equation can be written in the form given in M equation (6.1)... 

In liquid chronatography where diffusion coefficients are saall, the contribution of to the plate height is ften negligible. Diffusion coefficients are much larger in gases and hence is More inportant, particularly at low Mobile phase velocities. 

RELATIVE CONTRIBUTION (PERCENTAGE BASIS) OF MASS TRANSFER RESISTANCE IN THE MOBILE AMD STATIONARY PHASE TO COLUMN PLATE HEIGHT FOR A SERIES OF 0.32 mm I.D. OPEN TUBULAR COLUMNS USING UMDECAME AT 130 C AS THE TEST SOLUTE... 

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