Critical size, cluster coalescence

Determinatioii of Critical Size and fcf It has been shown (Ji) that the features of the kinetics of cluster coalescence in competition with a... 

The clusters transform into the crystal nuclei having ability for the growth under certain conditions. Only clusters with some critical size r = 2 Oct/Ap can become potential centers of crystallization (here Cl is the specific volume of an atom or molecule involved into the cluster, a is the specific surface energy of interphase boundary and Ap is the difference in chemical potentials for the phases) [10]. There are two main possible ways to transform the clusters into the critical crystal nuclei as a result of fluctuations [1] (1) attachment of individual atoms (molecules) to the cluster and (2) coalescence of clusters with each other. It should be noted that in principle the critical nuclei formation as a result of coalescence of individual atoms (molecules) with each other is possible too. In all these cases the clusters must grow to the size r > r, in order the start a crystal growth process. 

The reactivity of short-lived bimetallic clusters has also been studied by the kinetics method. Under conditions when a transient alloyed cluster of Ag-Au was formed,reactivity with the electron donor MV+ was probed and compared with that of monometallic Ag clusters previously observed. Just after the pulse a mixed solution of Ag and Au cyanides is partially reduced into atoms Ag and Au , while is partially reduced to the redox probe MV+. It is observed that in the first 20 ms the kinetics, at 400 nm, of cluster growth are the same as in the absence of the probe. Thus the coalescence of atoms to form an alloyed small cluster is, at first, not affected. The mechanism should be the same as in Eqs. (20)-(23). After this period, however, the decay of MV" at 700 nm starts in correlation with the increase of the cluster absorbance which results from electron transfer (Fig. 12). When the bimetallic cluster formed reaches the critical size where its potential becomes slightly higher than °(MV +/MV+ ), it acts as a nucleus that initiates a catalyzed growth fed alternately by electron transfer from the donor and the adsorption of excess Ag or Au ions. For i +J > ny. 

It will be remembered that the formation of a new phase by homogeneous nucleation involves first the formation of small clusters of molecules, which then may disperse or grow in size by accretion until some critical size is reached, at which point the cluster becomes recognizable as a liquid drop. The drop may then continue to grow by accretion or by coalescence with other drops to produce the final aerosol. Normally, extensive drop formation is not observed unless the vapor pressure of the incipient liquid is considerably higher than its saturation value that is, unless the vapor is supersaturated. 

An extreme case of the size development occurs, despite also the presence of the polymer, when the nucleation induced by radiolytic reduction is followed by a chemical reduction. Because the donor potential is more positive than that of the ion/atom couple, the donor D does not create new nv lei d the electron transfer towards adsorbed ions starts exclusively after ra iolytic reduction and coalescence have produced clusters of critical nuc eaiity. Then the final size depends on the ratio between the concentration... 

The reactor vessel is usually a stirred tank. The monomer phase is subjected either to turbulent pressure fluctuations or to viscous shear forces, which break it into small droplets that assume a spherical shape under the influence of interfacial tension. These droplets undergo constant collisions (collision rate >1 s ), with some of the collisions resulting in coalescence. Eventually, a dynamic equilibrium is established, leading to a stationary mean particle size. Individual drops do not retain their unique identity, but undergo continuous breakup and coalescence instead. In some cases, an appropriate dispersant can be used to induce the formation of a protective Aim on the droplet surface. As a result, pairs of clusters of drops that tend to coalesce are broken up by the action of the stirrer before the critical coalescence period elapses. A stable state is ultimately reached in which individual drops maintain their identities over prolonged periods of time [247]. 

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