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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) = (3γm – Eadh)(1 + Do/D)(2 Vm/D), where γm is the surface energy of the bulk metal, Eadh is the adhesion energy at the bulk metal/oxide interface, and Do is ∼1.5 nm, and Vm is the molar volume of the bulk metal. We further show that Eadh increases with (1) increasing heat of formation of the most stable oxide of the metal from metal gas atoms plus O2(gas) per mole of metal atoms, (2) decreasing enthalpy of reduction of the oxide to its next lower oxidation state plus O2(gas), per mole of oxygen atoms, and (3) increasing density of surface oxygen atoms on the oxide surface. The linear scaling of Eadh with these properties allows estimations of Eadh for a variety of metal/oxide combinations. Using this Eadh estimate in the above equation with known values for γm 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.
Campbell et al. (Tue,) studied this question.