Dispersed crystallite model

Recently, ultrathin evaporated films have been used as models for dispersed supported metal catalysts, the main object being the preparation of a catalyst where surface cleanliness and crystallite size and structure could be better controlled than in conventional supported catalysts. In ultrathin films of this type, an average metal density on the substrate equivalent to >0.02 monolayers has been used. The apparatus for this technique is shown schematically in Fig. 8 (27). It was designed to permit use under UHV conditions, and to avoid depositing the working film on top of an outgassing film. ... 

One can go a step further and use the /P//s ratio for a quantitative estimate of the dispersion. Through the years, several methods have been proposed to predict XPS intensity ratios for supported catalysts. Angevine et al. [29] modeled their catalyst with crystallites on top of a semi-infinite support, as sketched in Fig. 3.9a. However, as the inelastic mean free path of, for example, Si02 is 3.7 nm, photoelectrons coming from particles inside pores as deep as 10 nm below the surface still contribute to the XPS signal and the assumption of a semi-infinite support is probably too simple. Indeed, the model predicts /P//s ratios that may be a factor of 3 too high [30],... 

The easiest model to treat theoretically is the sphere, and many colloidal systems do, in fact, contain spherical or nearly spherical particles. Emulsions, latexes, liquid aerosols, etc., contain spherical particles. Certain protein molecules are approximately spherical. The crystallite particles in dispersions such as gold and silver iodide sols are sufficiently symmetrical to behave like spheres. 

We have seen in Chapter 4 that microhardness is primarily determined by the crystalline phase, which in the case of polymers is always dispersed in an amorphous matrix. In the present case the PBT crystallites are embedded in a two-phase amorphous matrix, the amorphous PBT segments and the soft PEO segments as depicted on the model in Fig. 6.7 in which the four possible phases are shown. The PEO is distinguished by very low viscosity at room temperature - PEO of molecular weight of 1000 melts around 30 °C and being incorporated in a polymer chain its Tm is even lower - around 0 °C (Fakirov Apostolov, 1990). 

As in the case of commercially-relevant supported metals, sintering kinetics of model supported catalysts are generally correlated well by a GPLE of order 2. This result has important mechanistic implications since a number of fundamental processes such as emission of atoms from crystallites, diffusion of adatoms on a support, collision of crystallites, or recombination of metal atoms may involve second order processes. Based on quantitative GPLE treatments of sintering kinetics it is possible to define effects of metal, metal dispersion, metal concentration, and support thermal stability which are very similar to those observed (and discussed above) for commercially-relevant supported metal cal ysts. 

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