Exact peak compression factor in linear gradient elution: I. Theory

The only existing expression for the peak compression factor in linear gradient elution chromatography assumes that the linear-solvent-strength model (LSSM) applies to the retention of the compound studied, that the column efficiency is independent of the mobile phase composition, and that, during gradient elution, the relative retention factor of a compound inside its band varies linearly with the distance from the band center. Because the retention factors of many analytes in reversed-phase liquid chromatography do not rigorously follow the LSSM, we extend the theoretical approach of Poppe et al. to the prediction of peak compression factors in linear gradient elution chromatography for any retention model, when column efficiency varies with the mobile phase composition. Only the contribution of the chromatographic column to the peak compression was taken into account, the contribution of the dwell volume being neglected. A second restriction is the linearity of the relative retention factor as a function of the position along the band width inside the column. These constraints could be the sources for the difference observed between experimental and theoretical values of peak compression factors. When the retention factor varies steeply with the mobile phase composition, such as with proteins or large peptides in RP-HPLC, it is found that the thermodynamic compression term, which tends to sharpen the peak, is coupled with the column dispersion term, which tends to broaden the peak. This coupling term acts as an apparent dispersion term, contributing to broaden the peak. This result is consistent with the measurements of peak compression factors found in the literature.