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little to explain how the efficiency of a column may be changed or, what causes peak dispersion in a column in the first place. It does not tell us how dispersion is related to column geometry, properties of the packing, mobile phase flow-rate, or the physical properties of the distribution system. Nevertheless, it was not so much the limitations of the Plate Theory that provoked Van Deemter et al  (2) (who were chemical engineers and mathematicians) to develop, what is now termed the Rate Theory for chromatographic dispersion, but more to explore an alternative mathematical approach to explain the chromatographic process. Virtually all basic chromatography theory evolved over the twenty five years between 1940 and 1965 and it was in the middle of this period that Van Deemter and his colleagues presented their Rate Theory concept in (1956). Since that time, other Rate Theories have been presented, together with accompanying dispersion equations and in due course each will be

The chromatogram that depicts the elution of a solute is a graph relating the concentration of the solute in the mobile phase leaving the column to elapsed time. However, at a constant flow rate, the chromatogram will also relate the solute concentration to the volume of mobile phase passed through the column. In figure 1, is shown the elution of a single peak. The expression, f(v), is the elution curve equation and this will be derived using the plate theory. Figure 1. The Elution Curve of a Single Peak   Once the nature of f(v) identified, then by differentiating f(v) and equating to zero, the position of the peak maximum can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention. The Plate Theory The plate theory needs to assume that the solute, during its passage through the column, is always in equilibrium with the

The purpose of the Rate Theory is to help understand the processes that cause dispersion in a chromatographic column and to identify those properties of the chromatographic system that control it. Such information will allow the best column to be designed to effect a given separation in the most efficient way. However, before discussing the Rate Theory some  basic concepts must be introduced and illustrated. The Summation of Variances The width of the band of an eluted solute relative to its proximity to

;                   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

; , where (n) is the variance of the Gaussian curve. Now, (n) is the volume variance of the Gaussian curve (i.e., ), then, by comparison, (2Dmt) will be the length variance  of the concentration curve where (t) is the elapsed time. Consequently, if a differential equation of the form  is derived that describes some form of dispersion that arises from a random diffusion process, then the solution will be a Gaussian function and, more important from the point of view of the Rate Theory, the Gaussian curve will have a variance given by (2Dmt

be identified, and an expression for the variance arising from each dispersion process evaluated, then the variance of the final band can be calculated from the sum of all the individual variances. This is how the Rate Theory provides an equation for the final variance of the peak leaving the column. The Alternative Axes of a Chromatogram An elution curve of a chromatogram can be expressed using parameters other than the volume flow of mobile phase as the independent variable. The Plate theory provides an equation that expresses the retention and standard deviation of a peak in terms volume flow of mobile phase. However, instead of using milliliters of mobile phase, as the independent variable, solute concentration in the mobile phase can be related, time, or distance  traveled by the solute band along the column and proportionally the same chromatogram will be obtained. This is illustrated in figure (1