Chromatographic theory capacity factor

So far the Plate Theory has been used to determine the equation for the retention volume of a solute, calculate the capacity factor of a solute and identify the dead volume of the column and how it should be calculated. However, the equation for the elution curve of a solute that arises directly from the Plate Theory can do far more than that to explain the characteristics of a chromatogram. The equation will now be used in a variety of ways to expand our knowledge of the chromatographic process. 

It is possible to correct this ultra-simple approach with a Plate Theory model for the variation of peak width with retention time (volume), conveniently expressed via the capacity factor k. The derivation and final result are complex (Scott, http //www.chromatography-online.org/) and are not reproduced here. Instead, Figure 3.5 shows representative plots of Cp vs k for several values of N, calculated from this more realistic model. The values of N and k are of course those for the last-eluting peak, but this last peak will be different for different chromatographic detectors with different sensitivities. It is clear from Figure 3.5 that any chromatographic conditions that limit the k value for the last-detected peak will thus limit the peak capacity, particularly at lower values of k. ... 

Fritz and Scott (23) derived simple statistical expressions for calculating the mean and variance of chromatographic peaks that are still on a column (called position peaks) and these same peaks as they emerge from the column (called exit peaks). The classical plate theory is derived by use of simple concepts from probability theory and statistics. In this treatment, each sample chemical substance molecule is examined separately, whereas its movement through the colunm is described as a stochastic process. Equations are given for both discrete- and continuous-flow models. They are derived by calculating the mean and variance of a chromatographic peak as a function of the capacity factor k. 

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