Fundamental Equation of Dual-Mode Gradient Elution in Liquid Chromatography Involving Simultaneous Changes in Flow Rate and Mobile-Phase Composition

The rigorous derivation of the fundamental equation of the dual-mode gradient elution in liquid chromatography involving any type of simultaneous changes in flow rate and mobile-phase composition is developed following Drake's approach. The equation is a generalization of the already known fundamental equations of single gradient when either the mobile-phase composition or the flow rate is constant. The theory was tested in the retention prediction from isocratic data of 18 o-phthalaldehyde derivatives of amino acids in eluting systems modified by acetonitrile or methanol. The retention prediction obtained for all solutes under all dual-mode gradient conditions was excellent. The average percentage error between experimental and predicted retention times ranged from 0.9 to 2.5%. Two approximations that simplify the calculations considerably without increasing the above error were also proposed.