Time dependence of activity

The constants of the various time dependencies of activity are found by methods like those for finding constants of any rate equation, given suitable a,t) data. 

One example of a direct determination of the time dependence of active centres is the already cited work of Saegusa and Matsumoto [90] (see Fig. 11). 

They considered deactivation to occur by either pore-mouth (shell-progressive) or uniform (homogeneous) poisoning and examined the effect these types of deactivation had on overall activity and production rates for a single catalyst pellet. Analytical solutions were obtained for the production per pore by considering the time dependence of activity. Their results will be used here as the basis for the development of models for deactivation in fixed bed reactors. 

However, if the time dependence of activation of nuclei is required, other methods must be used. The data on time distribution of primary nucleation are usually obtained by direct microscopic observation of a crystallizing sample [27, 28], The time lag between the nucleation of two neighboring spherulites can be found from the curvature of their common boundary. 

The earliest effort to correlate the time dependence of activity was that of Voorhies (1945). He found ... 

Dependence of activity CL may be simply on time onstream. One index is the ratio of the rate at time t to the rate with fresh catalyst,... 

The time-dependence of enantioselectivity in the reaction thiophenol with 3-cro-tonoyl-2-oxazolidinone catalyzed by l ,J -DBFOX/Ph-Ni(C104)2-3H2O at room temperature in THF is shown in Scheme 7.44. After 3 h, the yield of the thiol adduct is 70% with the enantioselectivity of 91% ee, but the enantioselectivity was 80% ee at the completion of reaction after 24 h (yield 100%). Although the catalyst maintains a high catalytic activity, and hence a satisfactory enantioselectivity, at the early stage of reaction, the deterioration of catalyst cannot be neglected thereafter even under neutral conditions. 

In actual experiments we do not usually observe directly the desorbed amount, but rather the derived read-out quantities, as is the time dependence of the pressure in most cases. In a closed system, this pressure is obviously a monotonously increasing function of time. In a flow or pumped system, the pressure-time dependence can exert a maximum, which is a function of the maximum desorption rate, but need not necessarily occur at the same time due to the effect of the pumping speed S. If there are particles on the surface which require different activation energies Ed for their desorption, several maxima (peaks) appear on the time curve of the recorded quantity reflecting the desorption process (total or partial pressure, weight loss). Thereby, the so-called desorption spectrum arises. It is naturally advantageous to evaluate the required kinetic parameters of the desorption processes from the primarily registered read-out curves, particularly from their maxima which are the best defined points. 

We have already used the interactions of methotrexate with dihydrofolate reductase (DHFR) several times within this text to illustrate some key aspects of enzyme inhibition. The reader will recall that methotrexate binds to both the free enzyme and the enzyme-NADPH binary complex but displays much greater affinity for the latter species. The time dependence of methotrexate binding to bacterial DHFR was studied by Williams et al. (1979) under conditions of saturating [NADPH], In the presence of varying concentrations of methotrexate, the progress curves for DHFR activity became progressively more nonlinear (Figure 6.14). The value of kobs from... 

Adsorption versus Polymerization. It is instructive to examine further the time dependence of the corrosion inhibition. In acid corrosion inhibition tests, steady state is customarily assumed to be reached within 10 to 20 min after initial exposure of the metal specimen. Since the inhibitors function by reducing the available active surface area, we expect an increase in and a corresponding decrease in P. The degree of corrosion protection the inhibitor provides is given by... 

Recent studies of the processes of activation and deactivation111 have shown, as seen in Fig. 20, that the time dependences of the potential, upon the application of current steps, resemble those characteristic of porous film formation and that the differences are of a quantitative nature. The initial part, representing a typical galvanostatic charging curve (with the initial jump due to the... 

An example of activity developing with a Co catalyst is shown in Figure 9.9 (right). CO-conversion (respectively the yield of products) increases with time by a factor of about 10, from ca. 4% to ca. 55%.7,17 Figure 9.9 (left) shows the time dependence of FT with an iron catalyst. There are a strong initial carbon deposition (referring to iron carbide formation) and fast water gas shift reaction, and FT... 

The rate of hydrolysis depends strongly on the nature of all three building blocks, i.e. the leaving group, the coordinated arene, and the chelate, and can be varied over several orders of magnitude, opening a time-window of activation. A detailed study of the aquation and the reverse, anation reactions of three [Ru(rj6-arene)Cl(en)](PF6) complexes (arene — bip (10), dha (11), and tha (12)) showed that the rates of aquation... 

Now the voltage provides information on the activity according to Nernst s law whereas Eqs (8.53) and (8.54) indicate the time dependence of the concentration. This may be overcome by expanding Eqn (8.54) by d and by introducing the relation between changes in the concentration and the stoichiometry, dCj = (NJVff) d, where A/ is Avogadro s number... 

More recently, Landis et al. studied the polymerisation kinetics of 1-hexene with (EBI)ZrMe( t-Me)B(C5F5)3 64 as catalyst in toluene [EBI = rac-C2H4(Ind)2]. Catalyst initiation was defined as the first insertion of monomer into the Zr-Me bond, 65 (Scheme 8.30). Deuterium quenching with MeOD was used to determine the number of catalytically active sites by NMR. The time dependence of the deuterium label in the polymer was taken as a measure of the rate of catalyst initiation. This method also provides information of the type of bonding of the growing polymer chain to zirconium, as n-or sec-alkyl, allyl etc. Hexene polymerisation is comparatively slow, with high regio- and stereoselectivity there was no accumulation of secondary zirconium alkyls as dormant states [96]. 

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