An improved subtraction model applied in supercritical fluid chromatography to characterise polar stationary phases

Herein, an improved subtraction model was proposed to characterise the polar stationary phases in supercritical fluid chromatography (SFC). Fifteen stationary phases were selected, including two types of aromatic columns, Waters Torus and Viridis series columns, as well as silica and amino columns. Ethylbenzene and Torus 1-AA were defined as the reference solute and column, respectively. Identifying the interaction with the maximum contribution to retention in SFC separation and using it as the initial term is a key step in modelling. The dipole, or induced dipole interaction (θ^'P), replaced the hydrophobic interaction (η^'H) as the starting term. The improved model was expressed as logα=η^'H+β^'A+α^'B+κ^'C+θ^'P+ε^'E+σ^'S, where the term ε^'E indicated that anion exchange interaction was intentionally supplemented. A 7-step modelling process, including bidirectional fitting and residual analysis, was proposed. The obtained column parameters had reasonable physical significance, with the adjusted determination coefficient (R²_adj) greater than 0.999 and the standard error (SE) less than 0.029. Methodological validation was further performed using the other four columns and 12 solutes that were not involved in the modelling. The result revealed good predictions of solutes' retention, as demonstrated by R²_adj from 0.9923 to 0.9979 and SE from 0.0636 to 0.1088. This study indicated the feasibility of using the improved subtraction model to characterise polar stationary phases in SFC, with the most crucial being the determination of an initial term, followed by the addition of a new descriptor and the selection of an appropriate reference column. The study expanded the application scope of the subtraction model in SFC, which will help gain an in-depth understanding of the SFC separation mechanism.