Clusters particle shape effects

This structure sensitivity of the respective population between the various states of adsorbed oxygen could explain why it has long been found that ethylene oxidation is structure-sensitive, with higher selectivity, up to 60-70%, for nonpromoted catalysts with sizes of about 40-50 nm [68,69]. A similar result has been recently reported for model Ag/a-A Os catalysts of very narrow size distribution (Table 1) [70]. The particle-size sensitivity has been attributed to a change of the equilibrium Ag crystal shape with cluster size (geometric effect) [71]. This leads to a change in the relative concentration of facets and edges at the metal... 

The effects on the particle shape of particle formation from partially hydrolyzed monomers were also investigated. By choosing certain mixtures of monomers, Schaefer and Keefer generated all kinds of particle morphologies, from porous clusters to surface and mass fractals. 

Multiple studies of the viscosity of fiber suspensions have reported the significance of fiber properties. Guo et al. (2005) showed that the rheological properties of fiber suspensions increased with increasing fiber volume fraction and fiber aspect ratio. These effects also increased with decreasing shear rate. Numerical simulations by Switzer Klingenberg (2003) reported the strong influence that particle shape and inter-fiber friction have on the viscosity of fiber suspensions. The clustering of these suspensions also has a marked impact... 

Many equations have been proposed for the transport properties of two-phase systems and in-depth details of the existing models are discussed elsewhere [4]. Noticing that virtually all the early theories neglected the effects of the particle shape, their packing density, and the possible formation of anisotropic clusters, Lewis and Nielsen modified the Halpin-Tsai equation for the elastic modulus of composite materials by incorporating the maximum volume fraction of filler cpm while still maintaining a continuous matrix phase [33,34]. Transposed to thermal conductivity Lewis and Nielsen s equation becomes... 

When we consider many particles settling, the density of the fluid phase effectively becomes the bulk density of the slurry, i.e., the ratio of the total mass of fluid plus solids divided by the total volume. The viscosity of the slurry is considerably higher than that of the fluid alone because of the interference of boundary layers around interacting solid particles and the increase of form drag caused by particles. The viscosity of a slurry is often a function of the rate of shear of its previous history as it affects clustering of particles, and of the shape and roughness of the particles. Each of these factors contributes to a thicker boundary layer. 

Since carbon black and amorphous silica tend to form clusters of spheres (grasping effect), an additional modification of the Einstein equation was made to account for the nonspherical shape or aspect ratio (L/D). This factor (/) is equal to the ratio of length (L) to diameter (D) of the nonspherical particles (/= L/D). 

A further result of this analysis, as shown in Fig. 4, is that while the relative spectral intensities are determined by the individual site f-factors, the temperature dependence of all the sub-spectra together in the temperature range studied is determined by the motion of the center of mass of the whole Auj, cluster. This can be seen by the uniform decrease of the total intensity with increasing temperature, without any visible change in the general shape of the spectrum. In effect, this means that the f-factors for the individual sites must be multiplied by an f-factor due to the motion of the whole particle [24]. See also Refs. [95,96,97], where this concept was originally developed. The use of such an inter-cluster f-factor, in addition to the usual intra-cluster f-factor, also resolved the problem of the apparent deficiency in the total f-factor at 1.25 K when compared to bulk gold. 

Once that the enhancement of the anisotropy due to the nanometric dimensions of the particle has been proven in our samples beyond doubt, the pertinent question is whether we can find the physical origin of this enhancement. A number of possible mechanisms can give rise to this strong variation in anisotropy size effects due to the increasing ratio of surface to bulk atoms, electronic confinement within the cluster leading to 3d band narrowing, surface oxidation, stress induced anisotropy, or even shape anisotropy due to a departure of sphericity. The two latter ones can be readily disregarded. The interatomic Co distance is estimated from the analysis of EXAFS spectra of these clusters. They are shorter than the bulk fee Co and comparable to that found for free Co clusters [11,12], Therefore... 

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