Number of active sites

The structure of the dormant sites might be an irregular coordination of the monomer (Rg. 4.10b) or a change of the direction of the monomer coordination (Rg. 4.10c). Tlie polymerization reaction may be stopped after an irregular coordination of styrene. This also supports the chain-end controlled mechanism of stereospecilicity. 

More detailed investigations have recently been performed (i.e. by P. Tait and N. Haward) using labelled CO or allene they clearly show that the productivity increase found in the new generation of catalysts was essentially due to an increase in the number of actual active sites and not of kp. It also seems that stereoselective centers definitely display a higher kp that nonselective ones (which may be due to more difficult (i.e. hindered) competition from the Al-derivative). 

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This argument is sound if we imagine Che number of active sites per unit surface area to remain constant as the pore size is changed. However, if the number of active sites per unit pellet volume remains constant, will be independent of d, and then 1/ d. Neither of these re-... 

Some deactivation processes lower the number of active sites So- Others add mass transfer resistances. In either case, they cause a reduction in the reaction rate that is reflected in a time-dependent effectiveness factor ... 

The number of active sites is a multiplicative factor in the rate of the main reaction. See for example Equations (10.11) and (10.16). Thus, the decline in reaction rate can be modeled using a time-dependent effectiveness. A reasonable functional form for the time-dependent effectiveness factor is... 

The present research showed a dependence of various ratios of rutile anatase in titania as a catalyst support for Co/Ti02 on characteristics, especially the reduction behaviors of this catalyst. The study revealed that the presence of 19% rutile phase in titania for CoATi02 (C0/RI9) exhibited the highest number of reduced Co metal surface atoms which is related the number of active sites present. It appeared that the increase in the number of active sites was due to two reasons i) the presence of ratile phase in titania can fadlitrate the reduction process of cobalt oxide species into reduced cobalt metal, and ii) the presence of rutile phase resulted in a larger number of reduced cobalt metal surface atoms. No phase transformation of the supports further occurred during calcination of catalyst samples. However, if the ratios of rutile anatase were over 19%, the number of active sites dramatically decreased. 

In a number of studies a correlation was seen between the amount of nonstoi-chiometric oxygen in the spinel and the spinel s activity. It appears that excess oxygen consolidates the spinel s defect structure with a large number of active sites. Strong anodic polarization leads to ordering of this structure and thus to a decrease in catalytic activity. 

Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

Note that under steady-state conditions the rate of each reaction step equals the overall net rate, 0, 9a, and 6b represent the fractions of the total number of sites that are vacant, or occupied by A and B, respectively. Afr represents the total concentration of active sites. Conservation of the total number of active sites leads to the site balance expression ... 

This phenomenon, however, is not difficult to understand in view of the mechanism of dissolution under such conditions. Since the number of active sites increases linearly with current density and these sites are characterized by a film structure (or thickness or both) different from that at the OCP, one could expect corresponding increases in the corrosion rate. However, as was mentioned earlier, the active surface area in the pits increases with time, and hence one should expect the corrosion rate to increase correspondingly. Therefore, since the effect is not time dependent, one... 

However, when the particle size is decreased, the surface area of the material is increased, as is the number of active sites where molecules can adsorb and react to form radicals. The surface properties of the semiconductors are important in... 

N0 = number of active sites per unit surface area... 

The living ALi chains polymerize a small amount of DVB leading to the formation of a star molecule bearing within its core (microgel nodule of DVB) a number of active sites, which is theoretically equal to the number of incorporated A arms. Subsequent addition of monomer B yields the /z-star copolymer. 

Further studies have shown that the degree of aggregation, and hence the number of active sites, is a function of the alkoxide substituent.813 For example, in (270) one of the i.vo-propoxide groups bridges two aluminum centers the other three are terminal ligands and all three initiate the ROP of CL. Less aggregated species such as (270) generally exhibit simple first order kinetics. 

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