Cluster growth kinetics

Regnlar arrays of platinnm were achieved by chemical reduction of a platinnm salt that had been deposited onto the S-layer of Sporosarcina ureae [132]. This S-layer exhibits sqnare lattice symmetry with a lattice constant of 13.2 nm. Transmission electron microscopy revealed the formation of well-separated metal clusters with an average diameter of 1.9 nm. Seven clnster sites per nnit cell were observed. UV-VIS spectrometry was nsed to study the growth kinetics of the clnsters. 

The nucleation stage is followed by two different kinetic regimes of cluster growth (i) a diffusional one (occurring at the earlier stage of growth) which is characterized by a time dependence of cluster radius scaling as where... 

Supported model catalysts are frequently prepared by thermally evaporating metal atoms onto a planar oxide surface in UHV. The morphology and growth of supported metal clusters depend on a number of factors such as substrate morphology, the deposition rate, and the surface temperature. For a controlled synthesis of supported model catalysts, it is necessary to monitor the growth kinetics of supported metal... 

Figure 4 Growth kinetics of silver clusters observed through their absorbance at 400 nm in the presence of (a) cyanide or (b) sulfate. (From Ref 54.)...

All seven steps require time, resulting in a rate of incorporating clusters into the growing crystal surface, which is called crystal growth kinetics. The following two sections consider translation of such a rate into a macroscopic equation for correlation and prediction. It is difficult to say which of the steps control the process, or even if the conceptual picture is valid. However, the first step—species transport to the solid surface—is well established and a brief description is given in Section 3.2.1.2. 

A similar method is to allow metal atoms to cluster in cold organic solvents. This method can be practiced on large scale with relatively low expense, and so has been widely practiced for almost 20 years, serving as a forerunner of all of those clustering methods. (25-30) Kinetic control of cluster growth may be realized, and unique structure/reactivity of such materials has been demonstrated many times.(4) Magnetic and electrical properties of such clusters are often unusual as well.(29,57)... 

Technically, this result follows only if kmn < A(m + n), where A is a positive constant. If this condition is not met, cluster growth to a unit comprising all the primary particles can occur after a finite time interval (cf. Eq. 6.20b), corresponding to gel formation and a nonconstant M,. For a discussion of this point, see F. Leyvraz, Critical exponents in the Smoluchowski equations of coagulation, pp. 201-204 in F. Family and D. P. Landau, op. cit.7 and F. Leyvraz and H. R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14 3389 (1981). 

Figure 5 Nucleation and growth kinetics of Pd clusters on MgO(l 00) from a TEAS study, (a) Series of nucleation kinetics curves for various substrate temperatures (atomic beam flux 1.1 x 1013 cm-2 s-2. (b) Arrhenius diagram of the saturation density, (c) Growth kinetics at various substrate temperatures. Atomic beam flux 1.1 x 1013 cm-2 s-2.

In the past TEM has been extensively used to study the nucleation and growth kinetics (see the review by Poppa [66]). These studies are in general made sequentially and ex situ because the sample has to be thinned to be transparent to the electron beam. For clusters larger than 1 nm and that are not reactive with air, TEM gives reliable results but these studies are very time consuming. Some studies of nucleation and growth have been made in situ in an UHV-TEM mainly by Poppa [66, 82]. 

While steady-state radiolysis of metal ions solutions is a powerful method to generate small and monodisperse metal clusters and to synthesize metal nano-objects with controlled size, shape and struc-ture, pulse radiolysis technique enables to follow, in particular by time-resolved spectroscopy, the nucleation steps and the growth kinetics of the nanoparticles. ... 

Self-generating step creation, such as that provided by the BCF model, involves inherently more rapid growth kinetics because of the more favorable energetics for addition of a molecule or cluster to the structure. 

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