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Effect of Mobile Phase Compressibility On the HETP Equation for a Packed GC Column  As the pressure falls along the column length, the velocity changes and, as the solute diffusivity depends on the pressure, the diffusivity of the solute will also change. The multi-path term, which contains no velocity or gas pressure dependent parameters, will be unaffected and the expression that describes it the same. The other terms in the  HETP equation, however, all contain parameters that are affected by gas pressure (solute diffusivity and mobile phase velocity) and, therefore, need to be modified to accommodate the compressibility of the mobile phase.    Reiterating the HETP equation for a packed column,                      where  f1(k")  =      and      

Figure 9. HETP Curves for the Same Column and Solute Using the Average Mobile Phase Velocity and the Exit Velocity   The two curves are clearly quite different and, if the results are to be fitted to the HETP equation, only the data obtained using the exit velocity  will give meaningful values for the exclusive dispersion processes. This problem is further emphasized in the graphs shown in figure 10. In figure 10, the individual contributions from the different dispersion processes are obtained by deconvoluting the HETP curve obtained using the average velocity data

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 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

;                             Therefore,                         The ratio, (), (the column length divided by the number of theoretical plates in the column) has, for obvious reasons, become termed the Height Equivalent to the Theoretical Plate (HETP) and has been given the symbol (H). However, it is seen that (H) is numerically equal to, , which is, in fact, the variance per unit length of the column. Thus, the function, , is the variance that the Rate Theory will provide an explicit equation to define and can be experimentally calculated for any column from its length and column efficiency. It follows that the equations that give a value for, (H), the variance per unit length of the column, have been termed HETP equations

30) Equation (30) gives the variance per unit length of a GC column in terms of the outlet pressure (atmospheric); the outlet velocity; and physical and physicochemical properties of the column, packing, and phases and is independent of the inlet pressure. However, equation (28) is the recommended form for HETP measurements as the inlet pressure of a column is usually known, (and consequently (g), the inlet/outlet pressure ratio is also known) and the equation is less complex and easier to use. The important aspect of this development is that the resistance to mass transfer in the stationary phase is seen to be a function of the inlet-outlet pressure ratio (g). Regrettably, the average velocity is the variable that is almost universally used in constructing HETP curves in both GC and LC. This

where, A=2ldp, B=2gDm and   Equation (33) is a hyperbolic function which has a minimum value of (H) for a particular value of (u). Thus, a maximum efficiency will obtained at a particular linear mobile phase velocity. An example of an HETP curve obtained in practice showing this hyperbolic relationship is given in figure 11.     Figure 11. HETP Curve for Hexamethylbenzene