Dispersion in Chromatography Columns - Experimental Validation of the Van Deemter Equation > Page 77

It is seen that the 1 micron column can provided an efficiency of over two hundred thousand plates whereas the column 100 micron column can provide an efficiency of over two billion theoretical plates (assuming an inlet pressure of 1000 p.s.i). However, it must be emphasized that the high efficiency column will be extremely 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.

                                 The Giddings equation.

                 The Huber equation.

                                 The Knox equation.

                The Horvath equation.


At first sight, it might appear adequate to apply the above equations to a number of experimental data sets of (H) and (u) and to identify that equation that provides the best fit. Unfortunately, this is of little use as, due to their nature, all five equations would provide an excellent fit to any given experimentally derived data set, provided the data was obtained with sufficient precision. However, all the individual terms in each equation purport to describe a specific dispersive effect. That being so, if the dispersion effect described is to be physically significant over the mobile phase velocity range examined, all the constants for the above equations derived from a curve fitting procedure must be positive and real. Any equation, that did not consistently provide positive and real values for all the constants, would obviously not be an appropriate and explicit equation to describe the dispersion effects occurring over the range of velocities examined. However, any equation that does provide a good fit  to a series of experimentally determined data sets and meet the requirement that all constants were positive and real would still not uniquely identify the correct equation for column design.