Ripening-resistance of Pd on TiO₂(110) from first-principles kinetics

Suppressing sintering of supported particles is of importance for the study and application of metal-TiO₂ system. Theoretical study of Ostwald ripening of TiO₂(110)-supported Pd particles would be helpful to extend the understanding of the sintering. In this paper, based on density functional theory (DFT), the surface energy of Pd and the total activation energy (the sum of formation energy and diffusion barrier) of TiO₂-supported Pd were calculated. Since the total activation energy is mainly contributed from the formation energy, it is indicated that the ripening of Pd particles would be in the interface control limit. Subsequently, the calculated surface energy and total activation energy were used to simulate Ostwald ripening of TiO₂(110)-supported Pd particles. As a result, in comparison with larger particles, smaller particles would worsen the performance of ripening-resistance according to its lower onset temperature and shorter half-life time. The differences on ripening-resistance among different size particles could be mitigated along with the increase of temperature. Moreover, it is verified that the monodispersity can improve ripening resistance especially for the smaller particles. However, the different performances of the ripening originating from difference of the relative standard deviation are more obvious at higher temperature than lower temperature. This temperature effect for the relative standard deviation is the inverse of that for the initial main particle size. It is indicated that the influence of dispersity of TiO₂(110)-supported Pd particles on ripening may be more sensitive at higher temperature. In this contribution, we extend the first principle kinetics to elaborate the ripening of Pd on TiO₂(110). It is expected that the information from first principle kinetics would be helpful to the study in experiments.