Protonation enthalpies of metal oxides from high temperature electrophoresis

Surface protonation reactions play an important role in the behavior of mineral and colloidal systems, specifically in hydrothermal aqueous environments. However, studies addressing the reactions at the solid/liquid interface at temperatures above 100°C are scarce. In this study, newly and previously obtained high temperature electrophoresis data (up to 260°C) - zeta potentials and isoelectric points - for metal oxides, including SiO ₂, SnO ₂, ZrO ₂, TiO ₂, and Fe ₃O ₄, were used in thermodynamic analysis to derive the standard enthalpies of their surface protonation. Two different approaches were used for calculating the protonation enthalpy: one is based on thermodynamic description of the 1-pKa model for surface protonation, and another one - on a combination of crystal chemistry and solvation theories which link the relative permittivity of the solid phase and the ratio of the Pauling bond strength and bond length to standard protonation enthalpy. From this analysis, two expressions relating the protonation enthalpy to the relative permittivity of the solid phase were obtained.