Coordination number particle-size dependence

The hydrogenation of butadiene is structure-sensitive on Pd and Rh but lacks particle-size dependence in the case of platinum. The strong complexation of the diene to atoms of low coordination number is a possible explanation for this phenomenon where it occurs37,38. 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

The overall pore volume of the bed of packed spheres is mainly determined by the. size of the inner cavities, which is in turn dependent on the particle radius, R, and the coordination number, N. The effective Kelvin radius corresponding to this major stage of capillary condensation is approximately given by the radius, r, of the inscribed sphere within the cavity (Karnaukhov 1971). 

Figure 28. Top EXAFS analysis strategy used by Frenkel (1999) to determine nanocrystal size in meM particles. The number of observed neighbors is dependent on the crystallite size. The more distant neighbors provide the most sensitive measure of coordination number and thus ciystalhte size. Bottom plot is the analogous function for semiconductor tetrahedrally coordinated stmctures. After Frenkel (1999).

Normally, the particles within a system have different sizes. Therefore, a mean or average particle size characterizes the system only insufficiently. It is necessary to know the entire particle size distribution, particularly because the arrangement of particles in the system and, thus, the coordination number, which is very important for agglomeration, depend on the particle size distribution. 

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