Sphere, metals distribution within

In this specific case, the colloid stabilizers are dendrimers, for instance, polyamidoamine (PAMAM), which are hyperbranched polymers that ramify from a single core and form a porous sphere [103, 104] (Scheme 17.1). Dendrimer-encapsulated nanoparticles (DENs) are synthesized by sequestering metal ions within appropriate dendrimers, and then by chemically reducing the resulting composite. They can be synthesized in various media, such as water or ethanol. The size of the nanoparticles is usually nearly monodisperse, and can be tuned by varying the metal-to-dendrimer ratio prior to reduction. Supported catalysts can then he prepared by immobilizing DENs onto a sohd support. As in the case of colloids, the last step, which consists in the removal of dendrimers hy thermal treatment, may lead to an increase in both the metal-particle size and particle-size distribution. 

The drying process can affect the catalyst distribution within the support. The crystallite size of a supported metal catalyst may also be altered if a considerable portion of the soluble metal is occluded rather than adsorbed. Initially, evaporation occurs at the outer surface, but the liquid evaporated from small pores is replaced by liquid drawn from large pores by capillarity, possibly causing a nonuniform distribution of catalyst. In the precipitation method, the dried catalyst particles are formed into granules, spheres, tablets, and extrudates. In either method, the dried material is calcined to activate the catalyst. 

The double-layer capacity depends strongly on the nature of the electrode material, even in cases where there is no specific adsorption of ions and solvent. It was therefore suggested, first by O.K. Rice, that the metal makes a direct contribution to the double-layer capacity. This idea was quantitatively pursued within the -> jel-lium model, in which the distribution of the electrons at the surface is affected by the double-layer field. In essence, the surface electrons form a highly polarizable medium, which enhances the capacity. In combination with the hard sphere electrolyte model, it gives the correct order of magnitude for the capacity at the -> point of zero charge also, it predicts correctly that the capacity of simple sp-metals should increase with the electronic density. An extension of the jellium-hard sphere elec-... 

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

---