Comparison of optimization methods in reversed-phase high-performance liquid chromatography using mixture designs and multi-criteria decision making

Abstract The optimization of different mobile phase systems is compared using statistical mixture designs. Isoeluotropic and non-isoeluotropic ternary and quaternary mobile phase mixtures have been optimized with regard to selectivity and analysis time. For a sample consisting of six benzene derivatives, the logarithm of the capacity factor of each solute is modelled in a full quaternary mobile phase system consisting of water and three organic modifiers. From the models, different separation criteria such as the resolution or selectivity of the worst separated pair of peaks, i.e. , the Min Res or Min Alpha, respectively, are calculated. Also, the capacity factor of the last peak, the Max k , can be predicted as a measure of analysis time. Response surfaces that show the different criteria as function of the different mobile phase systems re plotted and evaluated by multi-criteria decision making (MCDM). It is concluded that the optimization of isoeluotropic ternary mobile phase systems consisting of mixtures of two pseudo-components of equal solvent strength is inferior to that of iseluotropic quaternary mobile phase systems consisting of mixtures of three pseudo-components of equal solvent strength or to that of non-isoeluotropic ternary systems consisting of mixtures of water and two organic modifiers. The latter two optimization methods do not guarantee that the global maximum with respect to the Min Res of the full quaternary system consisting of mixtures of water and three organic modifiers will be found. On the one hand, the isoeluotropic quaternary system does not use variation of the water fraction to influence the selectivity. On the other, a mixture of three modifiers and water may provide a wider range of selectivity than mixture of two modifiers and water. Both optimization methods predict and realize a good separation of a test sample in a short analysis time provided that the solvent strength of the isoeluotropic quaternary system is properly chosen.