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

Abstract

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.

Phase stability in scandia‐zirconia nanocrystals

“…In Figure A, water coverage is plotted as a function of relative pressure. The shape of the curve consists of three stages, consistently with recent literature reports for other oxides . Initially, there is a rapid increase in the adsorbed water at small relative pressures (<0.02) associated to the high reactivity of the anhydrous surface.…”

“…The enthalpy of water adsorption as a function of water coverage is presented in Figure B. All curves show a typical behavior with highly exothermic adsorption at low coverages, and a systematic decrease followed by leveling . The enthalpy becomes less exothermic with increase of water layers until saturation of the nanoparticles, where enthalpy reaches −44 kJ/mol (dotted line), which is the enthalpy of liquefaction of water.…”

“…The surface energy (SE) for each sample was determined using a custom written MATLAB 2010a function recently reported based on the Gibbs adsorption analysis—relating the SE with the heat of adsorption and respective adsorbed quantities . To that end, the water adsorption curves were fitted using a modified Langmuir‐BET adsorption curve:where θ c and θ p are the chemisorption and physisorption monolayer coverage, respectively, and b and c are unit‐less fit parameters, and k is the relative pressure ( p/p 0 ).…”

Surface Segregation on Manganese Doped Ceria Nanoparticles and Relationship with Nanostability

“…For instance, by using a nitric acid washing method, the amount of the surface excess of Mg ion when doping tin dioxide was quantitatively determined and a relationship between this amount, the surface energy and the particle size was established by Gouvea et al 10 . This is because the surface energies are extremely small quantities, and though many methods have been proposed in the literature [16][17] , only recently practical experimental techniques have been reported to assess the surface energies of oxides with high accuracy 16,[18][19] . Similar phenomenon was found in Gd However, direct evidence of this decrease in the surface energy associated with the surface excess is rarely found in the literature.…”

“…Meanwhile, the microcalorimeter was used to acquire the heat of water adsorption, which after proper calibration (with gallium melting) and combination with the adsorbed water quantities was used to calculate the enthalpy of adsorption per mol (details of this experimental setup can be found elsewhere [18][19]27 ). In order to measure the water content of the samples as well as to design a proper degassing temperature (needed for the water adsorption experiment), thermogravimetric analysis and differential scanning calorimetry (TGA/DSC) was performed simultaneously by using a combined to measure the enthalpy of water molecules adsorption on the surface of particles as a function of coverage.…”