On the Fundamental Retention Equation in Gradient Elution Liquid Chromatography

Abstract

Basic integral equations used to predict the solute retention times or volumes in gradient elution liquid chromatography are carefully examined. In order to simplify the integration procedure, one strongly suggests to select a convention independent of the solvent composition for defining the solute capacity factor. Most of these equations make use of the volume V′ of mobile phase which has passed through the peak center (or band maximum) as the integration variable. It is shown that, instead of V′, one can use the volume V flowing from the column in these equations as the integration variable in combination with retention conditions prevailing at the column inlet rather than actually within the column, provided that the gradient is displaced without modification through the column, i.e. without retention of the mobile phase components. The general retention equation is derived for a binary gradient where the strong component of the mobile phase is retained in such conditions that its distribution isotherm is linear, i.e. it has a constant capacity factor, k′_b. This general equation is solved in the specific case of a linear solvent strength gradient. It is shown that the retention of the strong component of the mobile phase leads to an increase of the solute retention time approximately equal to k′_b t₀/2, where t₀ is the elution time of an inert solute.