Chemical Potential of Metal Atoms in Supported Nanoparticles: Dependence upon Particle Size and Support

Abstract

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( D ) = [(3γ m – E adh )(1 + D o / D )](2 V m / D ), 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.