On the Stochastic Theory of Chromatography

Abstract

Chromatography has been represented as a Poisson process and expressions have been derived for the elution curves of various types of chromatographic systems, such as a column with several kinds of sites, and a column with one kind of site but with various realistic input distributions. The previous stochastic treatments of chromatography have solved exactly only the case of a column with one kind of site with a delta-function input distribution. These various cases have been solved by means of the complex-variable theory of Laplace transforms. The exact expressions are usually complicated and of not much numerical utility. A technique is described by means of which any case can be well approximated by a consideration of only the first few central moments. This has proved to be of great practical use since there exists a theorem of mathematical statistics which allows one to determine moments of complex problems when those of simpler problems are known. This makes it possible to derive easily used expressions for the various elution curves.