Metal nanoparticles supported on oxide surfaces form the basis for many industrial catalysts and promise to play an ever-increasing role in future energy and environmental technologies. The chemical potential (μ) of the metal atoms in these particles depends strongly on particle size and support and is an important factor that determines their catalytic properties, including their binding strengths to adsorbed reaction intermediates and their long-term stability against sintering. We present here a method for estimating this chemical potential as a function of particle size for different metal/oxide combinations. We show that this chemical potential for late transition metals is well approximated for a particle of diameter D by μ, where γ m is the surface energy of the bulk metal, E adh is the adhesion energy at the bulk metal/oxide interface, and D o is ∼1.5 nm, and V m is the molar volume of the bulk metal. We further show that E adh increases with (1) increasing heat of formation of the most stable oxide of the metal from metal gas atoms plus O 2 (gas) per mole of metal atoms, (2) decreasing enthalpy of reduction of the oxide to its next lower oxidation state plus O 2 (gas), per mole of oxygen atoms, and (3) increasing density of surface oxygen atoms on the oxide surface. The linear scaling of E adh with these properties allows estimations of E adh for a variety of metal/oxide combinations. Using this E adh estimate in the above equation with known values for γ m allows estimates of metal chemical potential versus particle size for late transition metals on various oxide supports. This will improve our ability to understand structure−property relations in catalysis and design better catalysts.

The apparent activation energy of chemical reactions has played a central role in the field of chemical kinetics and has served as an important tool for analyzing and understanding reaction rates, mechanistic details of complex reaction mechanisms, elementary-step energetics, catalytic activity, and reaction selectivity. We derive here a general expression that shows that the apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all of the species (intermediates, transition states, and products) in the reaction mechanism, each weighted by its generalized degree of rate control (DRC). Since the DRC is zero for most of these species, even in very complex mechanisms, the weighted average includes only a few terms. This simplicity provides deep insights into the connection between the reaction-energy diagram and the apparent activation energy. We prove both this and the quantitative validity of this equation by analysis of numerous reaction mechanisms. We also show the failures or weaknesses of previous equations for the apparent activation energy.

The morphology, interfacial bonding energetics and charge transfer of Ni clusters and nanoparticles on slightly-reduced CeO2-x(111) surfaces at 100 to 300 K have been studied using single crystal adsorption calorimetry (SCAC), low-energy ion scattering spectroscopy (LEIS), Xray photoelectron spectroscopy (XPS), low energy electron diffraction (LEED) and density functional theory (DFT). The initial heat of adsorption of Ni vapor decreased with the extent of pre-reduction (x) of the CeO2-x(111), showing that stoichiometric ceria adsorbs Ni more strongly than oxygen vacancies. On CeO1.95(111) at 300 K, the heat dropped quickly with coverage in the first 0.1 ML, attributed to nucleation of Ni clusters on stoichiometric steps, followed by the Ni particles spreading onto less favorable terrace sites. At 100 K, the clusters nucleate on terraces due to slower diffusion. Adsorbed Ni monomers are in the +2 oxidation state, and they bind by ~45 kJ/mol more strongly to step sites than terraces. The measured heat of adsorption versus average particle size on terraces is favorably compared to DFT calculations. The Ce 3d XPS lineshape showed an increase in Ce 3+ /Ce 4+ ratio with Ni coverage, providing the number of electrons donated to the ceria per Ni atom. The charge transferred per Ni is initially large but strongly decreases with increasing cluster size for both experiments and DFT, and shows large differences between clusters at steps versus terraces. This charge is localized on the interfacial Ni and Ce atoms in their atomic layers closest to the interface. This knowledge is crucial to understanding the nature of the active sites on the surface of Ni-CeO2 catalysts for which metal-oxide interactions play a very important role in the activation of O−H and C−H bonds. The changes in these interactions with Ni particle size (metal loading) and the extent of reduction of the ceria help to explain how previously reported catalytic activity and selectivity change with these same structural details.

The chemical potential of metal atoms in supported nanoparticles provides a convenient descriptor of their performance as heterogeneous catalysts that captures the effects of particle size, support, and alloying. Based on microcalorimetric measurements, the chemical potential is shown to be predictable as a function of monometallic particle diameter and the adhesion energy of the particle to the support, and for oxide supports, this adhesion energy correlates predictably with metal oxophilicity. These correlations provide predictions of metal chemical potential that can enable catalyst design. They also suggest an improvement in the Gibbs−Thomson relation for free-standing nanoparticles, whether metals or molecular solids.

The heat of adsorption and sticking probability of phenol were measured on Ni(111) at 150 K and Pt(111) at 90 K using single crystal adsorption calorimetry (SCAC). Phenol adsorbs molecularly on both Ni(111) and Pt(111), with an initial heat adsorption of 200. kJ/mol on Ni(111) and 220 kJ/mol on Pt(111). The integral heat of adsorption at 1/9 ML coverage (−176 kJ/mol for Ni(111) and −175 kJ/mol for Pt(111)) gives a standard enthalpy of formation (ΔH f 0) for C6H5OHad of −272 kJ/mol on Ni(111) and −271 kJ/mol on Pt(111). The measured bonding energies for phenol to Ni(111) and Pt(111) were compared to density functional theory (DFT) calculations from previous literature, showing that DFT functionals that include van der Waals corrections are more accurate, although some calculations on both surfaces, even those with vdW corrections, still grossly underestimated the adsorption energy.