Combined column–mobile phase mixture statistical design optimization of high-performance liquid chromatographic analysis of multicomponent systems

A statistical approach for the simultaneous optimization of the mobile and stationary phases used in reversed-phase liquid chromatography is presented. Mixture designs using aqueous mixtures of acetonitrile (ACN), methanol (MeOH) and tetrahydrofuran (THF) organic modifiers were performed simultaneously with column type optimization, according to a split-plot design, to achieve the best separation of compounds in two sample sets: one containing 10 neutral compounds with similar retention factors and another containing 11 pesticides. Combined models were obtained by multiplying a linear model for column type, C8 or C18, by quadratic or special cubic mixture models. Instead of using an objective response function, combined models were built for elementary chromatographic criteria (retention factors, resolution and relative retention) of each solute or pair of solutes and, after their validation, the global separation was accomplished by means of Derringer's desirability functions. For neutral compounds a 37:12:8:43 (v/v/v/v) percentage mixture of ACN:MeOH:THF:H2O with the C18 column and for pesticides a 15:15:70 (v/v/v) ACN:THF:H2O mixture with the C8 column provide excellent resolution of all peaks.