Clusters growing

Figure 2 illustrates a proposed growth process[3] of a polyhedral nanoparticle, along with a nanotube. First, carbon neutrals (C and C2) and ions (C )[16] deposit, and then coagulate with each other to form small clusters on the surface of the cathode. Through an accretion of carbon atoms and coalescence between clusters, clusters grow up to particles with the size fi-... 

The mechanism for the formation of complex hydrocarbons through fullerenes is loosely taken from Helden et al.119 and Hunter et al.,120 and is depicted in Figure 2. As in the work of Thaddeus,117 linear carbon clusters grow via carbon insertion and radiative association reactions, although in this case a large number of additional reactions involving neutral atoms such as C, O, and H and neutral molecules such as H2 are also included. Reactions with H and H2 serve to produce... 

In a real system there will be several clusters growing simultaneously. At first the clusters are separated, but as they grow, they meet and begin to coalesce (see Fig. 10.5), which complicates the growth law. For the case of circular growth considered here, the Avrami theorem [4]... 

Both Eqs. (10.28) and (10.31) predict a current density which first rises as the perimeters of the clusters grow, and then decreases rapidly as the clusters begin to overlap. They can be cast into a convenient dimensionless form by introducing the maximum current density jmax and the time fmax at which it is attained. A straightforward calculation gives for instantaneous nucleation and progressive nucleation, respectivly,... 

During aging and startup/shutdown, the authors found that poisoning by carbonate-type species was not a major issue. Rather, by HR-TEM and CO chemisorption, the authors concluded that sintering of Pt occurred, with clusters growing from about 1.5 nm to 2.7 nm over the aging period. 

The degree of polymerization of hard clusters increases with evolution of the system as a whole. The hard clusters already exist in pregel molecules. Before the macroscopic gel point of the system is reached they remain usually small. Later on, the hard clusters grow faster and eventually a gel point (percolation threshold) of the hard structure is reached. Below this point, clusters are embedded in the soft matrix beyond the percolation threshold, the hard and soft structures interpenetrate (Figure 5.7). Below the percolation threshold, hard clusters are essentially dendritic when the percolation threshold is surpassed, circuits (cycles) develop within the hard structure. 

In a three-component polyurethane system with OH groups, wherein crosslinker is a triol, one finds them substantially more reactive than those of the macro-molecular diol. The hard clusters grow substantially larger, at relatively low conversions. Their size remains almost constant because all triol units have been used up in the reaction. In the opposite case, the lower reactivity of OH groups found in macromolecular diol compared with that of triol, the clusters remains small throughout the reaction and grows larger only at its end. 

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

The rate of formation of stable nuclei can now be obtained by considering the rate at which clusters grow by adding (and sometimes losing) atoms as they advance through cluster space. If IVjy is the number of clusters of size Af in the system, the flux of clusters which are growing from size Af to size Af + 1 may be written as... 

The growth of (Z2) (the particle accumulation) is accompanied by the growth of clusters of similar particles (cf. [91]). The characteristic spatial dimension of the cluster grows according to the same law as the mean square displacement of a single particle,... 

Clusters grow until a critical cluster size (nucleus) is reached that is energetically favorable to sustain growth... 

Labile cluster liquid water molecules are arranged around a dissolved solute molecule in a prehydrate structure, with essentially the correct coordination number. A conceptual hypothesis exists for clusters growing to larger structures at an interface. 

Figure 3. IMS findings (Ref. [8]) for Si cations examples of raw spectra (left) and summary plot exhibiting a transition to compact structures once clusters grow beyond n = 24 (right).

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