Equivalence of the Different <i>C</i>_m- and <i>C</i>_s-Term Expressions Used in Liquid Chromatography and a Geometrical Model Uniting Them

Abstract

It is shown that all C m and C s expressions ever established in the literature are intrinsically fully identical and can be derived from a simple parallel plug flow model. Analytically solving this model yields C m- and C s-term expressions that exactly correspond to the expressions obtained via either the method of moments (general rate model) or via Giddings' nonequilibrium theory. This holds for open-tubular as well as packed and monolithic columns. From this equivalence, a set of convenient "translation" expressions could be established, enabling a swift transition between the different C m- and C s-term expressions that currently coexist in literature. The link with the parallel plug flow model provides a good physical insight into the assumptions underlying the general rate model (e.g., a plug flow in the flow-through pores) and in the physical meaning of the different parameters involved in it. The parallel plug flow model also allows us to illustrate the difference between the zone and the phase retention factor and between the intraparticle diffusion coefficient and the effective diffusion coefficient used in the general rate model. These differences are subtle, but as they can have a large impact, they constitute important potential sources of confusion currently obscuring the modeling of HPLC columns.