Experimental Validation of the Van Deemter Equation

The equations discussed in the previous chapter, that described the variance per unit length of a solute band after passing through an LC column, were all significantly different. It is, therefore, necessary to identify the specific equation that most accurately describes the dispersion that takes place, so that it can be employed with confidence in the design of optimized columns. The different equations were tested against an extensive set of accurately measured experimental data by Katz et at (1) and, in order to identify the most pertinent equation, their data and some of their conclusions will be considered in this chapter. 

Reiterating the equations that were examined, they are as follows, 

When a satisfactory fit of the experimental data to a particular equation, is obtained the constants, (A), (B), (C) etc. must then be replaced by the explicit functions derived from the respective theory and which incorporate the respective physical properties of solute, solvent and stationary phase. Those physical properties of solute, solvent and stationary phase must then be varied in a systematic manner to change the magnitude of the constants (A), (B),(C) etc. The changes predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered the true equation that descr ibes band dispersion in a packed column. 

The identification of the pertinent HETP equation must, therefore, be arrived at from the results of a sequential series of experiments. Firstly, all the equations must be fitted to a series of (H) and (u) data sets and those equations that give positive and real values for the constants of the equations identified. The explicit form of those equations that satisfy the preliminary data, must then be tested against a series of data sets that have been obtained from different chromatographic systems. Such systems might involve columns packed with different size particles or employ mobile phases or solutes having different but known physical properties. 

et at(1) measured the efficiency of two different solutes (benzyl acetate and hexamethyl benzene) on a silica column 25 cm long and 9mm I D. packed with Partisi 10 (actual mean particle diameter 8.5 1) employing six 

The chromatography literature contains a vast amount of dispersion data for all types of chromatography and, in particular, much of the data pertains directly to GC and LC. Unfortunately, almost all the data is unsuitable for validating one particular dispersion equation as opposed to another. There are a number of reasons for this firstly, the necessary supporting data (e.g., diffusivity data for the solutes in the solvents employed as the mobile phase, accurate distribution and/or capacity factor constants (k )) are not available secondly, the accuracy and precision of much of the data are inadequate, largely due to the use of inappropriate apparatus with high extracolumn dispersion. 

The need for extra physical chemical data to test the equations arises from their close 

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To identify the pertinent HETP equation that describes dispersion in a packed bed, the following logical procedure will require to be carried out. 

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The Van Deemter equation (1) was the first rate equation to be developed and this took place as long ago as 1956. However, it is only relatively recently that the equation has been validated by careful experimental measurement (2). As a result, the Van Deemter equation has been shown to be the most appropriate equation for the accurate prediction of dispersion in liquid chromatography columns, The Van Deemter equation is particularly pertinent at mobile phase velocities around the optimum velocity (a concept that will shortly be explained). Furthermore, as all LC columns should be operated at, or close to, the optimum velocity for maximum efficiency, the Van Deemter equation is particularly important in column design. Other rate equations that have been developed for liquid chromatography will be discussed in the next chapter and compared with the Van Deemter equation... 

The first experimental results published by Keulemans and Kwantes [4] confirmed the applicability of the equation to gas chromatography, but it soon became apparent that the equation introduced by van Deemter et al. is only of limited validity for liquid chromatography. 

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