Surface diffusion in reversed-phase liquid chromatography using silica gels bonded with C1 and C18 ligands of different densities

Surface diffusion in reversed-phase liquid chromatography (RPLC) using silica gels bonded with C1 and C18 alkyl ligands of different densities was studied from the viewpoints of two extrathermodynamic relationships, i.e., enthalpy-entropy compensation (EEC) and linear free energy relationship (LFER). First, according to the four methods proposed by Krug et al., the values of surface diffusion coefficient (Ds) were analyzed to confirm that an actual EEC resulting from substantial physico-chemical effects takes place for surface diffusion. Then, it was also demonstrated that a LFER is observed between surface diffusion and the retention equilibrium. The establishment of EEC and LFER suggests a mechanistic similarity of molecular migration by surface diffusion, irrespective of the alkyl chain length and the densities of C1 and C18 ligands. Finally, a thermodynamic model for the LFER based on the real EEC was used to estimate Ds values under various RPLC conditions. The Ds values can be estimated with a mean square deviation of about 25–30%. The agreement between the Ds values estimated and those experimentally measured suggests that the total mass flux by surface diffusion consists of the two contributions due to C1 and C18 ligands and that the contribution of each ligand is proportional to the ligand density.