Van Deempter

J. J. Van Deempter, Chem. Eng. Sci., 13, 143 (1961) M. Leva, Fluidization, McGraw-Hill Book Company, New York, 1959 F. A. Zenz and D. F. Othmer, Fluidization and Fluid-Particle Systems, Reinhold Publishing Corporation, New York, 1960 O. Levenspiel and D. Kunii, Fluidization Engineering, John Wiley Sons, Inc., New York, 1969. 

The first notable point Is that the minimum plate heights are the same. This Is reasonable and predictable since the minimum plate height (HETP j n) In a van Deempter curve for a packed column Is a function of the packing particle diameter (dp) and the analyte capacity factor (k ) ... 

Assuming the simplest case of no eddy diffusion coupling (the coupling approach (6) describes velocity Inequalities from lateral diffusion and classical eddy diffusion) so that the "A term Is Independent of the linear velocity (u) and also assuming no resistance to mass transfer In the thin liquid film (2) of the stationary phase, the van Deempter relationship for a packed column Is... 

Van Deempter curves for packed column HPLC ( 1), packed column SFC ( 2), capillary column SFC ( 3, 6, 7). and capillary column GC ( 4, 5). Curves 1 and 2, experimental data (5) Curves 3-7. calculated (see text). 

For a capillary column, the "A" term is zero and the column inner radius, r, replaces the particle diameter in the van Deempter equation, resulting in what is known as the Golay equation, so that... 

Curve 7. The values to calculate this curve were taken from capillary SFC work by Peaden et al (14) who presented van Deempter curves obtained with pyrene in n-pentane at 210°C and 29 atm for several capillary column diameters. A value for D12 for pyrene in n-pentane was calculated from one of those curves (for a 300 pm... 

For open-tubular columns, dp is replaced by d. ) The reduced form of the van Deempter equation is... 

As we will see in Chapter 20, capillary columns are the most widely used in gas chromatography because of their high efficiency due to large numbers of plates. These columns have no packing, and so the eddy diffusion term in the van Deempter equation disappears. For open tubular columns, the modification of the van Deempter equation, called the Golay equation, applies ... 

LC must contain a correction for When a van Deempter plot is applied to HPLC, there is a curvature away from the mass transfer in both the mobile and theoretical curve at high velocities. Huber pointed out that in relating plate height... 

Knox developed an empirical equation for liquid chromatography that contains a term useful for correcting the deviation from the van Deempter equation. 

Fig. ie.s. van Deempter plots for different particle sizes in HPLC. The smaller particle sizes are more efficient, especially at higher flow rates. Column i.d. 4.6 mm mobile phase 65% acetonitiile/35% water, sample f-butylbenzene. [From M. W. Dong and M. R. Gant, LC.GC, 2 (1984) 294. Reprinted with permission.]... 

A generalized plot of the Van Deempter Equation is illustrated in Fig. 11.3. Each of the terms is plotted individually (A = 0 here, as this figure illustrates a plot for an open tubular column) and their sum is shown as the dashed line with a distorted U-shape. The important feature of the plot is that each chromatographic system will have a minimum value for 7/ as a... 

Figure 11.3 Van Deempter plot for open tubular column as sum of three terms B and C [as Sum of Cm (mobile phase) and Cs (stationary phase)] with A term = 0.

Figure 11.4 Mechanism of origin of multipath term A of Van Deempter equation.

In Sections 11.7 -11.9 we have seen how interacting parameters of column efficiency and linear flow velocity (the Van Deempter Equation), selectivity, and capacity factor (related to the distribution of analytes between phases under operating conditions)... 

What do the Van Deempter equations look like for packed column chromatography, capillary chromatography, and capillary electrophoresis (hint in the last of these there is no stationary phase) ... 

Draw a Van Deempter curve for each of the three techniques in Problem... 

If the dimensions of stationary phase coating thickness and diffusion distance to the film from the gas phase have been optimized, for further improvement of GC resolution, it becomes necessary to increase the length of the column. This is seen from the simple relation of Eq. (11.7), which indicates that for an optimal minimized value of H (the height equivalent to a theoretical plate) the number of plates, N, is proportional to the length of the column. From Eqs. (11.8) and (11.9) we note that the resolution is proportional to the square root of N. For columns packed with particles of optimal size, and operated at the optimal linear flow rate at the minimum of the Van Deempter curve (Fig. 11.3), the typical maximum pressure of 100 psi achievable from a regulated gas cylinder requires that most packed columns be less than 4-7 m long. More typically they are only 1 -2 m in length. These considerations hmit the resolution achievable in packed column GC. 

Figure 12.7 Van Deempter plots for three GC carrier gases N2, He, H2 H (height equivalent to theoretical plate) vs. u (linear flow velocity, cm/s).

The composition of the stationary phase (strongly effects on both absolute and relative retention) and the mobile phase gas (less strongly effects on resolution via differences in the parameters which control the Van Deempter constants, but essentially no effect on retention)... 

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