Dispersion in Chromatography Columns - The Summation of Variances > Page 2

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 its nearest neighbor determines whether two solutes are resolved or not. The ultimate band width as sensed by the detector is the result of a number of individual dispersion processes taking place in the chromatographic system, some of which take place in the column itself and some in the sample valve, connecting tubes and detector (see Extra Column Dispersion ). In order to determine the ultimate dispersion of the solute band it is necessary to be able to calculate the final peak variance. This is achieved by taking into account all the individual dispersion processes that take place in a chromatographic system. It is not possible to sum the band widths (standard deviation or (s)) resulting from each individual dispersion process to obtain the final band width, but it is possible to sum all the respective variances. However, the summation of all the variances resulting from each process is only possible if each process is non-interacting and random in nature. That is to say, the extent to which one dispersion process progresses is independent of the development and progress of any other dispersion process.