Dispersion of Supported Particles from XPS

Kerkhof and Moulijn [33] suggested that a supported catalyst may be modeled as a stack of sheets of support material, with cubic crystals representing the supported particles. They used this stratified layer model (as illustrated in Fig. 3.10b) to calculate the intensity ratio Ip /Is for electron trajectories perpendicular to the support sheets, assuming exponential attenuation of the electrons in the particles and the support. 

Kuipers and co-workers [34] developed this model further into the randomly oriented layer model. These authors argued that powdered catalysts contain a 

In this respect, Kuipers made an important point (as illustrated in Fig. 3.10c), namely that layers of thickness x which cover the support to a fraction 6, have the same dispersion as hemispheres of radius 2 x, or spheres with a diameter 3x. Even more interesting is the fact that these three particle shapes with the same surface-to-volume ratio give virtually the same fp/fs intensity ratio in XPS when they are randomly oriented in a supported catalyst The authors tentatively generalized the mathematically proven result to the following statement that we quote literally For truly random samples the XPS signal of a supported phase which is present as equally sized but arbitrarily shaped convex particles is determined by the surface/volume ratio. Thus, in Kuipers model the XPS intensity ratio fp/fs is a direct measure of the dispersion, independent of the particle shape. As the mathematics of the model is beyond the scope of this book, the interested reader 

In order to translate the XPS intensity ratios of Zr and Si into dispersions with Kuiper s model, the following input parameters are required  

The result of the calculations is that the calcined catalysts obtained from nitrate have dispersions of between 5 and 15% only, whereas the Zr02 catalyst prepared from ethoxide has a favorable dispersion of 75 + 15% after calcination at 700 °C. The equivalent layer thickness for this system is 0.42 nm, and the support coverage about 27%. These results are summarized in Table 3.3. 

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