The Van Deemter Equation The Van Deemter equation (9) was derived as long ago as 1956 and was the first rate equation to be developed. There are, however, a number of alternative rate equations that have been reported, but when subjected to experimental test, the Van Deemter equation has been shown to be the most appropriate equation for the accurate prediction of dispersion in chromatographic systems. The Van Deemter equation is particularly pertinent at mobile phase velocities around the optimum velocity (a concept that will shortly be explained). Consequently, as all columns should be operated at, or close to, the optimum velocity for maximum efficiency, the Van Deemter equation is particularly important in column design. Restating the Van Deemter equation,           

long and have an inordenantly long analysis time. In addition, the practical limitations of present day chromatography equipment render the realization of even a modest performance from LC capillary columns extremely difficult to realize experimentally.   Experimental Validation of the Van Deemter Equation The different equations were tested against an extensive set of accurately measured experimental data reported by Katz et al. (24) and, in order to identify the most pertinent equation, their data and some of their conclusions will be considered in this chapter. The equations that were examined, are as follows,                                      The Van Deemter equation.                     &

.) than any inadequacies of the Van Deemter equation. Nevertheless, it was the poor agreement between theory and experiment at the time, that provoked a number of workers in the field to develop alternative HETP equations. This work was carried out in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data. The Giddings Equation In 1961, Giddings (16) developed an HETP equation of which the Van Deemter equation was shown to be a special case. Giddings work was not provoked by poor agreement between theory and experiment but because he was dissatisfied with the Van Deemter equation inasmuch that it predicted a finite contribution to dispersion, independent of the solute diffusivity, in the limit of zero mobile phase velocity. This concept, not surprisingly, appeared to him unreasonable and unacceptable. Giddings developed the following equation to avoid this irregularity.   

) the van Deemter equation is simpler and give equally accurate and precise calculated data. In GC columns, the compressibility of the mobile phase must be taken into account and the exit mobile phase velocity (not the mean velocity) employed in the dispersion function. In addition, the diffusivity of the solute must be taken at atmospheric pressure. Only the Van Deemter equation, the Giddings equation and the Knox equation fit experimental (H) versus (u) data accurately and only the Van Deemter equation and the Giddings equation correctly account for other physical properties of the chromatographic system. The Van Deemter equation appears to be a special case of the Giddings equation, which simplifies to the Van Deemter equation when the mobile phase velocity is close to, or around, the optimum mobile phase velocity. The form of the Van Deemter equation and, in particular, the individual functions contained in it, are well substantiated by experiment. The Knox equation is

Van Deemter as the C term in the Van Deemter equation would now only describe the resistance to mass transfer in the mobile phase contained in the pores of the particles, and thus, would constitute an additional resistance to mass transfer in the stationary (static mobile) phase. This concept has some indirect experimental support in the development of the form of f1(k') from experimental data which will be discussed later. The form of f1(k') is shown to be closer to the original form given by Van Deemter for f2(k') that is appropriate for the resistance to mass transfer in the stationary phase. It is not known for certain, but it is possible and likely, that this was the reason why Van Deemter et al. did not include a resistance to mass transfer term for the mobile phase in their original form of the equation. The Huber Equation The next HETP equation to be developed was that of Huber and Hulsman in 1967 (17). These authors introduced a modified multipath term somewhat similar

of the (A) term and the effect of particle diameter on the mobile phase velocity at which the Giddings equation simplifies to the Van Deemter equation. For very small particles (e.g. 3 m) the Giddings equation simplifies to the Van Deemter at a velocity of about 0.2 cm/sec but for the larger particles (e.g., 10 m) it occurs at about 1 cm/sec. However, at the optimum velocity, irrespective of the particle diameter, the contribution from the coupling term is very small and so the Van Deemter equation can be used with confidence in column design.   J.Chromatogr.,270(1983)62.  Figure 23. Graph of the (B) Term against Diffusivity In summary, the Data of Katz et al. shows some slight dependence of the (A) term on Dm, (which can be explained on the basis of the calculations given above). However, as a result of the curve fitting procedure to the equation   it is shown not to be dependent on (u) and thus, supports the Van Deemter equation as opposed to the Knox