Improving retention-time prediction in supercritical-fluid chromatography by multivariate modelling

•Density or pressure are important for accurate retention modelling in SFC.•Multivariate retention modelling was performed to describe retention in SFC.•Retention time predictions improved by the addition of a pressure or density term.•The use of density improves retention modelling compared to the use of pressure. The prediction of chromatographic retention under supercritical-fluid chromatography (SFC) conditions was studied, using established and novel theoretical models over ranges of modifier content, pressure and temperature. Whereas retention models used for liquid chromatography often only consider the modifier fraction, retention in SFC depends much more strongly on pressure and temperature. The viability of combining several retention models into surfaces that describe the effects of both modifier fraction and pressure was investigated. The ability of commonly used retention models to describe retention as a function of modifier fraction, expressed either as mass or volume fraction, pressure and density was assessed. Using the multivariate surfaces, retention-time prediction for isocratic separations at constant temperature improved significantly compared to univariate modelling when both pressure and modifier fractions were changed. The “mixed-mode” model with an additional exponential pressure or density parameter was able to predict retention times within 5%, with the majority of the predictions within 2%. The use of mass fraction and density further improves retention modelling compared to volume fraction and pressure. These variables however, do require extra computations.