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An improved, exact analysis of surface Ostwald ripening of a collection of nanoparticles is presented in an effort to redefine the critical radius involved in the kinetic models of ripening. In a collection of supported particles of different sizes, the critical radius is the size of the particle that is in equilibrium with the surrounding adatom concentration. Such a particle neither grows nor shrinks due to Ostwald ripening, whereas larger particles grow and smaller particles shrink. We show that previous definitions of critical radius are applicable only for limiting regimes where the Kelvin equation has been linearized. We propose a more universally applicable definition of critical radius that satisfies the constraints of mass balance.

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Sintering plays a major role in the deactivation of heterogeneous catalysts. However, there is limited understanding of the underlying mechanisms. The two leading mechanisms for sintering are coalescence, the movement of smaller particles migrating along the support and joining other small particles to form larger particles, and Oswald ripening, the movement of adatoms emitted from one particle and by either surface or atmospheric diffusion to join other particles to form larger particles. The rate determining step for Ostwald ripening may be the emission of adatoms, or their diffusion over the support (Fig. 2 a). These steps are difficult to unravel on the tortuous, porous catalyst supports, which make direct observation of the metal catalyst difficult. With flat, single crystal model supports, all of the metal can be readily observed. In this work, we report observation of these model catalyst samples under vacuum, to study adatom emission rates (Fig. 2b). Our hypothesis is that the rates of metal evaporation may play an important role in determining rates of metal particle ripening. We postulate that the support may play a role in this process as shown in the schematic diagram in figure 2b by enhancing the rates of metal evaporation.Three different model supports were chosen for this study, quartz, sapphire, and yttria stabilized zirconia (YSZ). Supports had 1.5 nm (nominal thickness) of Pd deposited by evaporation; the samples were then oxidized in air at 700°C to form a palladium oxide layer. The palladium oxide layer was then heated in vacuum to 900°C to desorb the oxygen and to cause de-wetting of the Pd to form spherical particles on the support. After this step, the samples were first imaged using a High Resolution Scanning Electron Microscope (HR-SEM) to determine the initial particle size distribution. Samples were then aged under a vacuum environment. The evaporation experiments were run at 3x10 -5 Torr and 900 °C. Samples were aged for 30-minute intervals then imaged via HR-SEM.The particle size distributions in the samples aged in vacuum allow us to determine the rate of metal evaporation, which can then be compared with the Langmuir model for direct evaporation [1]. The observed rate loss was calculated directly from SEM images by assuming the Pd particles were spheres and taking into account the Gibbs-Thompson effect. The rates of metal evaporation were then compared with those predicted from a direct evaporation route. Our results show that while the rate of loss from Pd/YSZ is indicative of direct evaporation, the Pd loss from quartz is much faster, indicating a significant role of the support (Table 1).The enhanced rate of metal emission from quartz substrates suggest that some of the adatoms are diffusing on the surface and then evaporating. This is possible because the metal atoms at the metal-support interface are usually found to have a lower binding energy compared with atoms on the metal particle, leading to enhanced emission rates. The higher rates of Pd evaporation could lead to greate...