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system. However, for columns operated in the vicinity of the optimum velocity (where the best performance is to be realized) 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

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

it was found that when experimental data was fitted to the Van Deemter equation there was often very poor agreement between theory and experiment (particularly for data measured at high linear mobile phase velocities). In retrospect, this poor agreement between theory and experiment appeared to be due largely to the presence of experimental artifacts (such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc.) 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

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

Van Deemter equation extremely well. J.Chromatogr.,270(1983)65. Figure 25. Graph of (C) Term against the Reciprocal of the Solute Diffusivity. Katz et al. (12) also examined the effect of particle diameter on the value of the overall resistance to mass transfer constant (C). They employed columns packed with 3.2 m, 4.4 m, 7.8 m, and 17.5 m, and obtained HETP curves for the solute benzyl acetate in 4.3%w/w of ethyl acetate in n-heptane on each column. The data was curve fitted to the Van Deemter equation and the values for the A, B and C terms for all four columns calculated. According to the Van Deemter equation the (C) term should be linearly related to the square of the particle diameter. A graph relating the value of the (C) term with the square of the particle diameter is shown in figure 26

magnitude 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