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The coupling of stepwise mobile phase gradient elution and flow programming is proposed as an integrated approach to the general elution problem in reversed-phase liquid chromatography. A model is developed to describe the above separation process performed under simultaneous programming of two separation parameters by extending our previous work on the rigorous derivation of the fundamental equation governing the concentration gradient of organic modifier in the mobile phase, that is, a single gradient elution mode (Anal. Chem. 2005, 77, 5670-5677). The theory was tested in the retention prediction and separation optimization 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. In addition, it has been shown that the combination of mobile phase and flow rate programming modes is particularly favorable, whereas the separations among the analytes were considerably improved by using the acetonitrile eluting system, as compared to those obtained by the methanol system.

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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.