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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 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

, 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 and, in particular,

somewhat similar in form to that of Giddings and a separate term describing the resistance to mass transfer in the mobile phase contained between the particles. The form of their equation was as follows:-                                        (47) It is seen that the first term differs from that in the Giddings equation, in that it now contains the mobile phase velocity to the power of one half. Nevertheless, again when u1/2 >> E, the first term reduces to a constant similar to the Van Deemter equation. The additional term for the resistance to mass transfer in the mobile phase is an attempt to take into account the 'turbulent mixing' that takes place between the particles. Huber's equation implies (but, in fact, was not explicitly stated by the authors) that the mixing effect between

15.  R. P. W. Scott, Nature  (London), 183(1959)1753. 16. J. C. Giddings, "The Dynamics of Chromatography ", Marcel       Dekker, New York  (1965)265. 17. J. C. Giddings,  J. Chromatogr. Sci , 12(1974)1753. 18. A. Klinkenberg, in "Gas Chromatography 1960 (Ed. R. P. W.       Scott), Butterworths  Scientific Publications, London (1960)194. 19. A. A. Zhukhovitski and Turkel'taub, Dokl. Acad. Nauk. USSR.,      143(1961)646. 20. C. N. Reilley, C. P.

62 Figure 20. Graph of A Term against Solute Diffusivity for Benzyl Acetate Figure 20 demonstrates that the magnitude of the (A) term appears, within experimental error, independent of the diffusivity of the solute in the mobile phase. Closer examination, however, indicates that there might be a slight residual dependence of (A) on diffusivity. This probably indicates that the velocity range over which the data was taken was not sufficiently high enough to ensure that the first term of the Giddings equation was reduced to a constant value as it is in the simple Van Deemter equation. This can be examined further by considering the detailed expression for the first term of the Giddings equation. The expanded expression for the first term in the Giddings equation is as follows

Figure 22 discloses, in more detail, the factors that control the 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.