Growth sites

This important equation shows that the stationary-state free-radical concentration increases with and varies directly with and inversely with. The concentration of free radicals determines the rate at which polymer forms and the eventual molecular weight of the polymer, since each radical is a growth site. We shall examine these aspects of Eq. (6.23) in the next section. We conclude this section with a numerical example which concerns the stationary-state radical concentration for a typical system. 

The values of branching probability with cobalt are in general more than two times higher in the beginning of an experiment than at steady state. It is concluded that initially the spatial constraints on the growth sites are lower than at steady state. This also indicates a change in the nature of the growth sites. 

Branching reactions appear to be a unique indication of the existence of spatial constraints at growth sites. Analogies between homogeneous and heterogeneous catalysis are pertinent. 

By extending the FT model to the formation of two kinds of products—olefins and paraffins—and including secondary olefin reactions, the kinetic schemes shown in Figure 9.15 are obtained. In parallel primary reactions (from the growth sites), paraffins and alpha-olefins are desorbed—by irreversible associative desorption (the paraffins) and by dissociative desorption (the olefins) (upper scheme in Figure 9.15). 

Increased spatial constraint effects on growth sites are evident from Figure 9.20. This figure shows the contents of individual monomethyl-branched compounds in carbon number product fractions. Note that their values decline by a factor of 5 to... 

FIGURE 9.20 Methyl-branched isomers in carbon number fractions at 1.2 bar (left) and 9 bar (right) during FT synthesis on cobalt as indications for spatial constraints on the growth sites. Further legend as in Figure 9.18. 

The kinetic scheme in Figure 9.23 pictures the alternative reaction possibilities of the alkyl species (here the CH3 species) on a growth site to react either with CO for hydroformylation or with CH2 for FT synthesis. 

Another category of inhibition may be exerted by cations or anions that become adsorbed on active growth sites. Well-hydrated Mg2+ interferes with the formation of caicite, apatite, and many other minerals. 

The surface processes may comprise adsorption, surface migration (across terraces or along steps), dehydration of ions, and integration in the growth sites which are assumed to be kinks in surface steps. Any of these processes may be rate controlling, either alone or several together (10-11). 

The value of the on-rate constant for a particular growth site will depend on n, the number of growing points on both ends of a tubule. For example, if the tubule is treated as a three-start helix with each helix starting point serving as a distinct growth site, then n will be sbc, and the on-rate constant will be about 3 x 10 M sk. Such a value would be about a factor of 10 below the theoretical limit for diffusion-controlled processes involving macromolecules. 

Dislocations. Screw dislocations are the most important defects when crystal growth is considered, since they produce steps on the crystal surface. These steps are crystal growth sites. Another type of dislocation of interest for metal deposition is the edge dislocation. Screw and edge dislocations are shown in Figure 3.4. 

In the discussion of atomistic aspects of electrodepKJsition of metals in Section 6.8 it was shown that in electrodeposition the transfer of a metal ion M"+ from the solution into the ionic metal lattice in the electrodeposition process may proceed via one of two mechanisms (1) a direct mechanism in which ion transfer takes place on a kink site of a step edge or on any site on the step edge (any growth site) or (2) the terrace-site ion mechanism. In the terrace-site transfer mechanism a metal ion is transferred from the solution (OHP) to the flat face of the terrace region. At this position the metal ion is in an adion state and is weakly bound to the crystal lattice. From this position it diffuses onto the surface, seeking a position with lower potential energy. The final position is a kink site. 

Adsorbed additives affect both of these mechanisms by changing the concentration of growth sites Cg on the surface [n Jcm (where is the number of growth sites)],... 

On the left-hand side of Fig. 1 are the various mineralforming components in their complexed and uncom-plexed forms. They can directly bind to the crystal growth sites or they can combine to form the crystallization monomers (half-filled squares). These processes can be blocked competitively by the presence of other substances that form nonproductive complexes, thereby depleting the concentrations of precursors through mass action. The diagram also shows a second phase that helps to explain the nature of oriented diffusion and subsequent adsorption of the monomers. This so-called dou-... 

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