Extrathermodynamic interpretation of retention equilibria in reversed-phase liquid chromatography using octadecylsilyl-silica gels bonded to C1 and C18 ligands of different densities

The retention behavior on silica gels bonded to C18 and C1 alkyl ligands of different densities was studied in reversed-phase liquid chromatography (RPLC) from the viewpoints of two extrathermodynamic relationships, enthalpy–entropy compensation (EEC) and linear free energy relationship (LFER). First, the four tests proposed by Krug et al. were applied to the values of the retention equilibrium constants (K) normalized by the alkyl ligand density. These tests showed that a real EEC of the retention equilibrium originates from substantial physico-chemical effects. Second, we derived a new model based on the EEC to explain the LFER between the retention equilibria under different RPLC conditions. The new model indicates how the slope and intercept of the LFER are correlated to the compensation temperatures derived from the EEC analyses and to several parameters characterizing the molecular contributions to the changes in enthalpy and entropy. Finally, we calculated K under various RPLC conditions from only one original experimental K datum by assuming that the contributions of the C18 and C1 ligands to K are additive and that their contributions are proportional to the density of each ligand. The estimated K values are in agreement with the corresponding experimental data, demonstrating that our model is useful to explain the variations of K due to changes in the RPLC conditions.