Theoretical prediction of single-site enthalpies of surface protonation for oxides and silicates in water

Surface protonation is the most fundamental adsorption process of geochemical interest. Yet remarkably little is known about protonation of mineral surfaces at temperatures greater than 25°C. Experimentally derived standard enthalpies of surface protonation, ΔHr,1°, ΔHr,2°, and ΔHr,ZPC°, correspond to the reactions >SOH+H+=>SOH2+ >SO−+H+=>SOH >SO−+2H+=>SOH2+ respectively, and provide a starting point for evaluating the role of surface protonation in geochemical processes at elevated temperatures. However, the experimental data for oxides do not have a theoretical explanation, and data are completely lacking for silicates other than SiO2. In the present study, the combination of crystal chemical and Born solvation theory provides a theoretical basis for explaining the variation of the enthalpies of protonation of oxides. Experimental values of ΔHr,1°, ΔHr,2°, and ΔHr,ZPC° consistent with the triple layer model can be expressed in terms of the inverse of the dielectric constant (1/ε) and the Pauling bond strength per angstrom (s/rM-OH) of each mineral by equations such as ΔHr,ZPC°=ΔΩr,Z[(1/ε)−(T/ε)2(∂ε/∂T)]−B′Z(s/rM-OH)+H′Z. The Born solvation coefficient ΔΩr,Z was taken from a prior analysis of surface equilibrium constants. The coefficients BZ′ and HZ′ were derived by regression of experimental enthalpies for rutile, γ-alumina, magnetite, hematite, and silica. This approach permits widespread prediction of the enthalpies of surface protonation. Predicted standard enthalpies of surface protonation for oxides and silicates extend over the ranges (in kcal.mole−1): ΔHr,1° ≈ −3 to −15; ΔHr,2° ≈ −0.5 to −18; ΔHr,ZPC° ≈ −4 to −33. Minerals with the largest values of s/rM-OH (e.g., quartz and kaolinite) are predicted to have weakly negative enthalpies and a weak temperature dependence for their protonation equilibrium constants. Conversely, minerals with the smallest values of s/rM-OH (e.g., garnets and olivines) should have strong negative enthalpies and a strong temperature dependence for their protonation equilibrium constants.