Water Adsorption Microcalorimetry Model: Deciphering Surface Energies and Water Chemical Potentials of Nanocrystalline Oxides

The surface energy of a nanomaterial is a primary characterization parameter that has important implications on the material’s properties and applications including: catalysis, prediction of polymorphic stability, optimization of consolidation processes, and general colloidal science issues. However, currently, there is a dearth of techniques and theory to accurately measure surface energies for nanocrystalline solids and oxides. Therefore, we present a water adsorption microcalorimetry model using a novel second order surface energy differential equation to calculate the surface energy of anhydrous and hydrated (at any given level) nanocrystalline oxides. The experimental setup, used to feed data to the model, uses a water adsorption apparatus to measure the adsorbed water content on the specimen’s surface as a function of pressure (∼2 μmol dose) coupled with a microcalorimeter that can measure changes in the differential heat of water adsorption during the dosing. Using the experimental data and derived model, we can regression-fit the adsorbed water and differential heat of water adsorption data over the entire pressure range, vacuum to saturation, to calculate the surface energy via numerical integration of the second-order differential equation with the appropriate boundary conditions. We have tested the method using two technologically relevant nanoparticles, yttria doped zirconia (10YSZ) and γ-alumina. As key results, the calculated anhydrous surface energies for 10YSZ and γ-alumina are thus 1.54 ± 0.08 and 1.57 ± 0.04 J·m –2, respectively, and correlate well with other theoretical and experimental data. The model also provides relevant information on the changes of interaction energies between water molecules and the oxide surface.