Aggregation of Clusters

Analytical approaches to obtain the agglomerate size distribution are possible for well-mixed systems and when the rate of aggregation of clusters is defined by simple functions. In general, irreversible aggregation in well-mixed systems is described by Smoluchowski s coagulation equation, which... 

In general, silver clusters in solution are prepared by reduction of silver ions. Proper scaffolds, e.g., DNA, proteins, dendrimers and polymers, are essential to prevent the aggregation of clusters to larger nanoparticles. Although it is clear that the emission originates from few-atom silver clusters, many aspects of this exciting class of nanoscopic metals are not yet fully understood. 

The nanocrystals of such type form in various liquid media, such as organic solution [77, 81] or the softened quasi-liquid glass [82, 83], where there are no steric hindrances for the growth of equilibrium crystals without surface defects. At the same time, barriers for aggregation of clusters or atoms to metal nanocrystals in solid system that arises during the cryochemical solid-state synthesis favor the formation of crystals with structural defects,... 

Most numerical techniques employed for aggregation simulation are based on the equilibrium growth assumption and on the Smoluchowski theory. As shown in Meakin (1988, 1998), analytical solutions for the Smoluchowski equation have been obtained for a variety of different reaction kernels these kernels represent the rate of aggregation of clusters of sizes x and y. In most cases, these reaction kernels are based on heuristics or semi-empirical rules. 

INORGANIC POLYMERS TO PREPARE MICROPOROUS MEMBRANES 7.4.1 Formation and Aggregation of Clusters... 

TEM images of Ir/TiOz prepared by DP at 3 and 5 pH are also shown in Fig.5 (c) and (d). In the case of these catalysts, aggregates of clusters and small clusters were respectively deposited as the major species on the TiOz surfaces. This result and that of ICP analysis produce good evidence that the amount of loading and the structure of the Ir can be controlled by changing the pH of the precursor solution while using the DP method. 

Vicsek, T. and Family, F., Dynamic scahng for aggregation of clusters, Phys. Rev. Lett., 52, 1669, 1984. 

Most gels, however, form structures between these two extremes. The hydrolysis and polycondensation of metal alkoxide precursors yield an initial formation of fractal clusters, which upon reaching a critical size begin to form a continuous network or skeleton via cluster-cluster aggregation. Both the initial cluster formation and the subsequent aggregation of clusters are fractal in nature. There is a very distinct difference between these two processes, however, as is more evident in Sec. X. 

In Example 5.9, aggregation of clusters was carried out by the weighted average linkage methods. In general, the distance to a new object or cluster k (labeled in the example by a star) is computed by forming the average between the individual distances of objects A and B to object i. 

Kolb, M. Herrmann, H. J. Hie sol-gel transition modeled by irreversible aggregation of clusters. J. Phys. A, 1985,18(8), L435-L441. 

Aggregates are further classified as surface fractals, volume fractals or non-lfactal objects. Kolb and Herrmann [37] have introduced a mechanism to model aggregation of clusters at high concentration and investigated it by Monte-Carlo simulations. Surfaces of most materials are fractal on a molecular scale to chemically reactive surfaces. Farin and Avnir define the reaction dimension as characteristic parameter of the reaction which is related to the reaction rate v and particle radius R as... 

Another study on the reduction of [Pt3(GO)6]/ ( = 3, 4, 5) by dihydrogen has shown the reaction rate to be independent of the dihydrogen pressure, but second order in complex concentration. The reaction rates were found to be solvent dependent, with reduction being fast in DMF, but slow in solvents such as acetone, THE, or dichloromethane. The reverse reaction (oxidation by acid) is shown to be dependent in a non-trivial fashion on the concentration of H, indicating several protonation equilibria aggregates of clusters are also implicated. Another study by some of the same authors deals with the situation where the counterion is itself redox active. Thus, complexes with methylene blue, safranine O, nicotinamide benzyl chloride, and methylviologen counterions have been studied with selective and total reduction of these ions being observed. 

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