Paul Wynblatt

The dependence of ostwald ripening kinetics on particle volume fraction

Abstract A spatially homogeneous rate theory model is developed to describe the time rate of change of the radius of a spherical particle embedded in a configurationally random array of particles of like nature but differing sizes. The growth rate so derived is incorporated within the Lifshitz-Slyozov and Wagner hydrodynamic model of particle coarsening and the asymptotic size distribution determined as a function of the particle volume fraction, φ. In agreement with earlier workers, it is shown that for diffusion-controlled coarsening the basic kinetic form r 3 ~Kt relating the mean particle radius, r, to the time, t , is maintained, with the rate constant K a function of the volume fraction. Derived values of K are, however, much less sensitive to φ than suggested by prior treatments and are thus shown to be more generally compatible with experimental observation. A critical test of the theory must await the acquisition of more accurate data than has been obtained hitherto.

Particle growth in model supported metal catalysts—I. Theory

Abstract A theoretical study of capillarity driven growth has been performed for several regimes of importance to the ripening of noble metal particles supported on flat, partially wetted, metal oxide substrates. Three related models are presented, and in each case two modes of interparticle transport are considered, namely: vapor phase transport and substrate surface diffusion. The first model is analogous to classical Ostwald ripening. The second is a simple extension of the first but allows for interparticle transport via a volatile oxide species. The third model is applicable to the growth of faceted particles and incorporates the concepts of “pill box” nucleation as a growth inhibiting factor. The growth kinetics predicted by the third model are quite different from those predicted by classical ripening models. In particular, changes in the initial particle size distribution, which cause only short-lived transients in the case of classical ripening, are found to have a profound effect on the growth kinetics as well as other characteristics of nucleation inhibited growth.

Particle growth in model supported metal catalysts—II. Comparison of experiment with theory

Abstract The growth of platinum particles supported on flat alumina substrates has been measured in the temperature range 600–800°C, in two different oxidizing atmospheres having oxygen partial pressures of 2 and 20 kPa respectively. Comparison of the measured growth kinetics with predictions of classical ripening models does not yield satisfactory agreement. However, good agreement is obtained when the data are compared with predictions of a model of nucleation inhibited growth.

Diffusion mechanisms in ordered body-centered cubic alloys

Abstract Calculations of defect migration energies by three different mechanisms are presented. The mechanisms considered were: cyclic vacancy motion by a correlated set of six nearest-neighbor jumps, next-nearest-neighbor vacancy jumps and divacancy migration. A modified Morse potential energy function was used to describe atomic interactions and model calculations were performed for the case of /gbAgMg. The results of the calculations indicated that the energetically favorable mechanism of diffusion in these alloys is the six-jump vacancy cycle. Furthermore, the results were found to be consistent with previous theoretical treatments concerning defect concentrations in ordered alloys.

Particle splitting and redispersion phenomena in model alumina-supported platinum catalysts

Abstract Transmission electron microscopy (TEM) has been used in an attempt to study the redispersion behavior of small platinum particles supported on flat, dense γ-alumina substrates. The alumina substrates were prepared both by anodizing and by sputtering techniques. A thin (1 to 2 nm) film of platinum was deposited onto these alumina substrates by sputtering. This film was subsequently transformed into discrete platinum particles by an initial heat treatment at 600 °C for 18 hr in air, and then “redispersed” by heating at 500 °C for 18 hr, also in an air atmosphere. Particle size measurements on TEM photomicrographs revealed no significant decrease in platinum particle size as a result of the “redispersion” heat treatment. These results are in contradiction to previous observations of platinum particle splitting under those conditions. The findings are discussed in the light of different concepts which have been used to explain redispersion phenomena.

Coarsening kinetics of platinum particles on curved oxide substrates

Abstract The elevated-temperature growth of platinum particles supported on curved alumina substrates has been studied. A simple theory has been derived, and shows that when particle radii are close to the radius of curvature of this substrate, particles migrate to concave substrate sites. As a result of this migration and subsequent collisions and coalescence, initial particle growth rates may be enhanced. In addition, long-time particle coarsening by interparticle transport may be retarded, in comparison with rates of coarsening of particles on flat substrates. Experiments with platinum particles supported on alumina substrates with controlled surface curvature are described. The growth behavior of particles on these curved substrates is generally consistent with theoretical predictions.

Coarsening kinetics of platinum particles on oxide substrates

Abstract The growth of platinum particles supported on flat alumina substrates, at 900–1100°C. has been studied for particles ranging in size from 35–120 nm. While the observed kinetics of growth were found to be inconsistant with classical (LSW) coarsening models, a reasonable interpretation of the results was obtained from an analysis based on nucleation-inhibited coarsening models. Comparison of the present results with those of earlier studies on smaller particles at lower temperatures has pointed out certain discrepancies which suggest possible directions for improvement of the kinetic models.

Loss of palladium from model platinum-palladium supported catalysts during annealing

Abstract The phenomena taking place during the annealing of bimetallic-supported catalysts may differ in several respects from those involving monometallic-supported systems. One such phenomenon can be the preferential loss from the catalyst of one of its active components. Reported here are the results of experiments on the thermal stability of model, supported platinum-palladium catalysts in which preferential loss of palladium was indeed observed. These experiments sought to determine the factors responsible for the loss. The variables investigated included the atmosphere surrounding the catalyst, the substrate material, and the effects of time and temperature.

Coarsening kinetics of alloy platinum-palladium particles on oxide substrates

Abstract Coarsening of small (5 nm initial radius) platinum-50 at % palladium particles supported on flat alumina substrates has been studied at temperatures from 600 to 900°C under oxidizing conditions. The mode of coarsening appears to be nucleation inhibited. At 800 and 900°C interparticle transport of PtO2 is rate-controlling, whereas at 600 and 700°C transport of either platinum species or palladium species appears to result in the same coarsening rates. In samples heat treated at 600 and 700°C agglomerations of the solid oxide PdO are present on the substrate along with the alloy particles.