Van Deemter plot

A van Deemter plot for a given particle size dp and diffusion coefficient Du shows the relation of the theoretical peak height H to the linear velocity u that can be expressed as column length L... 

FIGURE 3.3 Van Deemter plot of columns with different particle sizes. (Courtesy of Agilent Technologies, Inc.)... 

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.)... 

Fig. 14.2. van Deemter plot showing contributions of eddy diffusion, molecular diffusion and mass transfer to the rate of band broadening. Picture courtesy of Prof. Harold McNair. 

Explain how you would use a van Deemter plot, as shown in Fig. 14.2 to determine the optimum flow rate for a separation. What are the key variables When using theoretical plate measures for comparing columns, what experimental conditions must be controlled ... 

The effect of pore size on CEC separation was also studied in detail [70-75]. Figure 9 shows the van Deemter plots for a series of 7-pm ODS particles with pore size ranging from 10 to 400 nm. The best efficiency achieved with the large pore packing led to a conclusion that intraparticle flow contributes to the mass transfer in a way similar to that of perfusion chromatography and considerably improves column efficiency. The effect of pore size is also involved in the CEC separations of synthetic polymers in size-exclusion mode [76]. 

Figure 1.9— Van Deemter plot for gas phase chromatography showing domains for A, B and C. A similar equation exists in which H is plotted as a function of column temperature for each parameter H = A + B/T + CT.

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... 

A van Deemter plot for the separation of neutral dyes by micellar electrokinetic chromatography follows.61... 

Effective Diffusivity. The effective diffusivity for N2/He at 25° C was calculated from the slope of the straight-line portion obtained in the high velocity region of a van Deemter plot [height of an equivalent plate vs. interstitial velocity 14, 15)]. A binary diffusion coefficient for N2-He of 0.717 cm2/sec was computed from Ref. 21, and the partition coefficient was taken as the reciprocal of the particle porosity (Table III) on the assumption that the adsorption of N2 at 25° C can be neglected. The calculated diffusivities are listed in Table III. 

GC analysis was also carried out on a Si-glass chip using an off-chip flame ionization detector (FID). Figure 6.2 shows the Golay plots (cf. Van Deemter plots) of the n-C9 peak when both the native and oxidized Si surfaces were used. H, is lower in native Si because of the less polar stationary phase. Figure 6.2... 

FIGURE 6.10 Van Deemter plots for capillary electrophoresis ( ) and microchip electrophoresis (o), where plate height (H) of TRITC-labeled bovine serum albumin is plotted vs. migration velocity (v) [174]. Reprinted with permission from the American Chemical Society. 

Vervoort, N., Clicq, D., Baron, G.V., Desmet, G., Experimental Van Deemter plots of shear-driven liquid chromatographic separations in disposable microchannels.. /. Chromatogr. A, 2003, 987, 39M8. 

Figure 1.12 Hypothetical van Deemter plot showing the relationship between efficiency and average linear velocity of the mobile phase.

The plate theory assumes that an instantaneous equilibrium is set up for the solute between the stationary and mobile phases, and it does not consider the effects of diffusional effects on column performance. The rate theory avoids the assumption of an instantaneous equilibrium and addresses the diffusional factors that contribute to band broadening in the column, namely, eddy diffusion, longitudinal diffusion, and resistance to mass transfer in the stationary phase and the mobile phase. The experimental conditions required to obtain the most efficient system can be determined by constructing a van Deemter plot. 

The performance of the monolithic silica in a capillary seems to be dominated by the size of the large through-pores and slow EOF. In the van Deemter plot for open-tube capillary chromatography, a plate height (H) partly depends on the square of dc as in Eqn. 5.4 (Ds, diffusion coefficient in the stationary phase dc, inner diameter of the capillary df, thickness of the stationary layer) [30], This also explains the reduction in the number of theoretical plates with a solute having the longer retention. 

Fig. 5.5. Van Deemter plots obtained for Cib monolithic silica in a capillary in CEC (open symbols) and HPLC (solid symbols) with thiourea (A) and hexylbenzene (0,9) as a solute. Mobile phase acetonitrile-water (HPLC), acetonitrile-Tris.HCl buffer, 50 mM pH 8 (CEC), (a), 80 20 (b), 90 10. Column size 50 pm I.D. x 33.5 cm (effective length 25 cm).

For purpose of illustration, the green line represents the results of a typical van Deemter plot. In Zone 1 the low flow rate allows extensive longitudinal diffusion, which ultimately will result in diffusion against the direction of flow. At high flow rates shown in Zone 2, the decreased efficiency is a result of comparatively slow mass transfer. 

In practice, the less efficient mass transfer within polymeric stationary phases results in a lower optimum flow rate being obtained following a van Deemter plot. It is essential that the... 

The typical appearance of a van Deemter plot is shown in Figure 5.6. At low flow rates an axial longitudinal diffusion results in band broadening (the analyte can diffuse against the... 

In order to accumulate the data for a van Deemter plot (described above) it is necessary to carry out a series of separations on a preparative column of at least 50 mm diameter. This can be done isocratically or using the gradient and optimum load conditions selected above. However, if the study is done using gradient elution the gradient length should be reduced in proportion to increased flow rate. Suggested linear flow rates for this study are 60, 75, 90, 105, 120 and 135 cm/h. These flow rates correspond to approximately 20, 25, 30, 35, 40 and 45 cm3/min for a 50 mm diameter column. 

For GC, a plot of H versus u gives a curve like the one shown in Figure 2.4 and has become known as a van Deemter plot. 

Figure 2.4. Typical plot of rate equation (van Deemter plot).

As an alternative to the plate theory, the so-called rate theory, came into prominence about the same time. The paper that has had the greatest impact was the one published by the Dutch workers van Deemter, Zui-derweg, and Klinkenberg.6 They described the chromatographic process in terms of kinetics and examined diffusion and mass transfer. The popular van Deemter plot resulted. A few years later, Giddings published another paper on this topic,7 and the rate theory has since become the backbone of chromatographic theory. 

Van Deemter plot. A graph of column efficiency, expressed as HETP versus linear velocity of the mobile phase. This plot indicates the optimum linear velocity (and, thus, flow rate) for a particular column. 

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