# Introduction to the Rate Theory

The separation of a solute pair in a chromatographic system depends on moving the peaks apart in the column and constricting their dispersion so that the two solutes are eluted discretely. The factors that control retention have been discussed in The Mechanism of Chromatographic Retention and in this book the processes of peak dispersion will be considered together with the means by which peak dispersion can be minimized.

Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly at the maximum of a peak. To circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (1) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a 'dwell time' for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. This approach has been discussed in Plate Theory and Extensions .

Employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others  can be developed that describe the various properties of a chromatogram. Such equations have permitted the calculation of efficiency, the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector.

The Plate Theory, however, does 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 discussed, but most were very similar in form to that of Van Deemter et al. It is interesting to note, however, that, even after thirty five years of chromatography development, the equation that best describes band dispersion in practice is still the Van Deemter equation. This is particularly true for columns operated around the mobile phase optimum velocity where the maximum  column efficiency is obtained.