Informational orthogonality of two-dimensional chromatographic separations

A qualitative informational similarity technique has been used to describe the informational orthogonality of projected two-dimensional (2-D) chromatographic separations of complex mixtures from their one-dimensional 1-D separations. The reversed-phase liquid chromatography (RPLC), supercritical fluid chromatography (SFC), gas-liquid chromatography (GLC), and micellar electrokinetic capillary chromatography (MECC) retention behavior of up to 46 solutes of varying molecular properties was studied by 2-D range-scaled retention time plots and information entropy calculations. One hundred five combinations of technique/stationary phase pairs were used to simulate the 2-D chromatographic analyses. The informational entropy of one and two dimensions, the mutual information, the synentropy or "cross information", and the informational similarity were calculated to describe the informational orthogonality. In addition, pattern descriptors were used to qualitatively describe the 2-D peak distribution. With the solutes tested, informational orthogonality, zero informational similarity, was observed with MECC-SDS/SFC-C1, MECC-SDS/SFC-Carbowax, MECC-TTAB/SFC-Carbowax, HPLC-C18/GLC-DB-5, HPLC-PBD/SFC-phenyl, SFC-Carbowax/GLC-DB5, and HPLC-phenyl/SFC-phenyl 2-D chromatographic systems. Conversely, with the solutes tested, informational nonorthogonal behavior described by range-scaled retention time plots to moderate to severe band overlap and data clustering was observed with 2-D chromatographic systems with high informational similarity and moderate to high degrees of synentropy. These results should prove useful for predicting complementary 2-D techniques as well as for choosing a second separation technique for confirmation of separation or peak purity.