Kinetic model for sintering of supported metal particles with improved size-dependent energetics and applications to Au onTiO2(110)

Abstract

A kinetic model for the sintering of metal particles on oxide or other support surfaces is derived and applied to simulate experimental measurements of the sintering of a model gold catalyst: gold nanoparticles supported on ${\mathrm{TiO}}_2\left(110\right)$. It follows the pioneering work of Wynblatt and Gjostein (WG), Progress in Solid State Chemistry (1975, p. 21), but removes several important assumptions that create dramatic errors in sintering rates for particles smaller than $6\mathrm{nm}$ in diameter, including (1) use of the Gibbs-Thomson relation assuming that the surface free energy of metal particles is independent of size, and (2) neglect of all but the first-order terms in a Taylor series expansion. Recent microcalorimetry measurements have shown these assumptions to be untrue in that metal particles smaller than $6\mathrm{nm}$ have much higher surface free energies than large particles. A modified bond-additivity model more accurately estimates particle energy versus size. This estimate was incorporated into the kinetic model of WG and applied to simulate the sintering of Au particles on ${\mathrm{TiO}}_2\left(110\right)$ as measured by temperature-programmed low-energy ion scattering. Our model reproduces well the broad temperature range over which sintering typically occurs in such experiments. This is analogous to accurate modeling of long-term sintering kinetics of metal nanoparticles under the isothermal conditions of real catalysis. These results also highlight problems with classical methods for determining the sintering mechanism based solely upon the shape of the sintered particle-size distribution.