Analytic solution for volume-overloaded gradient elution chromatography

Abstract

An analytic solution to a partial differential equation model for gradient elution chromatography is obtained. The model is restricted to linear isotherms and treats mass transfer effects with the linear driving force approximation. The solution is obtained for periodic, rectangular feed pulses, with an arbitrary gradient shape and type, and is given in the form of a convergent series that allows a direct calculation of the effluent profile and of the average product concentration. Calculations for small feed pulses, show that the solution gives the retention time and peak spreading predicted by the linear solvent strength theory for reversed phase chromatography, in the limit of Gaussian peaks. For larger feed pulses the solution predicts asymmetric peaks with concentrations exceeding that of the feed sample. The theory developed is succesfully used to predict volume overload effects in gradient elution from isocratic elution data for an experimental system.