Extrathermodynamic Study of Surface Diffusion in Reversed-Phase Liquid Chromatography with Silica Gels Bonded with Alkyl Ligands of Different Chain Lengths

Abstract

Surface diffusion on adsorbents made of silica gels bonded to C1, C4, C8, and C18 alkyl ligands 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 values of the surface diffusion coefficient (D(s)), normalized by the density of the alkyl ligands, were analyzed with the modified Arrhenius equation, following the four approaches proposed in earlier research. This showed that an actual EEC resulting from substantial physicochemical effects occurs for surface diffusion and suggested a mechanistic similarity of molecular migration by surface diffusion, irrespective of the alkyl chain length. Second, a new model based on EEC was derived to explain the LFER between the logarithms of D(s) measured under different RPLC conditions. This showed that the changes of free energy, enthalpy, and entropy of surface diffusion are linearly correlated with the carbon number in the alkyl ligands of the bonded phases and that the contribution of the C18 ligand to the changes of the thermodynamic parameters corresponds to that of the C10 ligand. The new LFER model correlates the slope and intercept of the LFER 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, the new model was used to estimate D(s) under various RPLC conditions. The values of D(s) that were estimated from only two original experimental D(s) data were in agreement with corresponding experimental D(s) values, with relative errors of approximately 20%, irrespective of some RPLC conditions.