Active site concentration

Evaluation of the various kinetic parameters requires a determination of the active-site concentration. [C ] is usually determined from experiments in which the active sites are... 

Literature values of the active-site concentrations range from tenths or hundredths of a percent to tens of percents of the transition metal concentration [Lieberman and Barbe, 1988 Tait and Watkins, 1989]. Much of this is indicative of the range of activity of different initiators, especially when comparing older initiators to the recent high-mileage initiators. However, some of the variation is due to the problems inherent in measurement of [C ]. Literature values of kp and other rate constants also show a considerable range. 

The number of active sites per unit mass of catalyst [nj f ) can be referred to as active sites concentration. ... 

In the case of a porous catalyst, where the internal area contributes the most to the total area, Ss can be considered to be independent from the catalyst shape and size. Furthermore, the number of catalytic active sites per unit area can be considered a fixed property for a given catalyst. Consequently, the active sites concentration can (n/Ms) be also be... 

The previously reported relationship (eq. (3.10)) manifests one more important characteristic of the catalyst level rate coefficients—for the same reaction, temperature, catalytic agent, and support but for different surface arrangement, i.e. active site concentration, these coefficients will be different and this is an advantage of the usage of kp and in general, of turnover frequency (active site level reaction description). 

The active site concentration on the organochromium catalysts may be higher than that of the oxide catalysts. The activity usually assumes a more linear increase with chromium loading than on the oxide catalysts, at least up to 2% Cr. Yermakov and Zakharov, studying allyl-Cr(III)/silica catalysts, stopped the polymerization with radioactive methanol, and found that the kill mechanism is different from that on the oxide catalysts (59). The proton of the methanol, and not the alkoxide, became attached to the polymer. This suggests a polarity opposite to that of the oxide catalysts, with the site being more positive than the chain. 

Over the past five years, we and our colleagues have undertaken an extensive study of the acid-catalyzed dehydration of the four isomeric butyl alcohols. In so doing, we compared the performance of crystalline, molecular-sieve acid catalysts (HZSM-5) in a range of crystal sizes (so as to vary diffusion path and active-site concentration) with that of amorphous aluminosilicate (AAS) gels in which the pore size is significantly larger. Our results, which permit the... 

Typical results, exemplified by the dehydration of n-butyl alcohol over HZSM-5 (8j), are shown in Fig. 3, a characteristic feature being the gradual (ca. 8 min at 399 K) saturation of the catalyst with the alcohol. At saturation there are 8 X 1020 mol of adsorbed butyl alcohol per gram, which is more than 3.5 times the concentration of active (Bransted acid) sites. Under the same conditions, our amorphous A AS sample adsorbs 3 X 1020 mol of n-butyl alcohol per gram, which exceeds the active site concentration by ca. 2.7 times. 

Before we can discuss the measurement of active-site concentration, we need to consider the kinetics of the substrate reaction. The majority of kinetic studies of enzymes are carried out on systems described by Scheme 11.16 where all terms have their usual meanings and where the intermediates have come to a steady-state concentration otherwise, studies of the kinetics of the pre-steady-state conditions usually require the use of specialist, fast reaction, equipment. The Michaelis-Menten equation, Equation 11.12, where all terms again have their usual meanings, can be derived from Scheme 11.16 when the system has reached a steady state at this point the values of [ES] and [P] are still very much less than that of [S] ... 

Measurements of Crystallite Disorder in Catalysts. - Many authors have speculated that the unusual activity of a particular catalyst preparation might be related to the presence of microstrain within individual catalyst particles. Experimental observations to support this speculation are few however, since in any highly dispersed material it is difficult to separate the effects of microstrain from other effects such as crystallite size and active site concentration. One careful study measured the microstrain in nickel and copper catalysts49 but failed to connect the results explicitly with activity data. 

A more complete and mechanistically explicit model has been described that allows for competitive adsorption to reactive and nonreactive sites on Fe°, as well as partitioning to the headspace in closed experimental systems and branching among parallel and sequential transformation pathways [174,175]. This model represents the distinction between reactive and nonreactive sites by a parameter called the fractional active site concentration. Simulations and sensitivity analysis performed with this model have been explored extensively, but application of the model to experimental data has been limited to date. 

Some remarks can also be made about the temperature dependency of the reaction rate, as expressed in an apparent activation energy, JPP. It is assumed that the rate constant has an Arrhenius-type dependency, and that the equilibrium constant follows Van t Hoff and the active site concentration is constant ... 

The kinetics of the reaction are dictated by the concentration of reactants at the active site. If there are mass transfer limitations in the system, reactant concentration at the active site concentration is not the same as the bulk concentration, and the rate will vary. Mass transfer limitations may exist in a given catalyst or may be produced during operation - for example, by the deposition of coke or the closure of pores. 

In the MMO OB3b system, the values could be used to predict the concentration dependence of the MMOB enhancement on the rate of the multiple turnover reaction. The fit to the experimental data predicts that the maximum rate is attained when a stoichiometric ternary complex (based on active site concentration) is established. Excess MMOB is inhibitory, apparently due to the formation of inactive MMOB-MMOR and MMOB-MMOB complexes, or perhaps binding of MMOB in the MMOR binding site. Cross-linking experiments were used to demonstrate the formation of each of these inhibitory complexes. Component complexes also play a significant role during the single turnover reaction as described below. 

In Eq. (70.1), the product of the bimolecular rate constant ( cat/ m) and the enzyme active site concentration ([E]) is the first order rate constant. The amount of enzyme to be injected for degradation of toxic molecules in a very short time depends on the enzyme efficiency, i.e. k JKm- The higher the efficiency, the lower the dose of enzyme to be administered. The enzyme concentration that reduces the OP concentration to a nontoxie concentration in time t is ... 

As shown in Table I, complete deactivation for these three catalysts occurs around 0.6 to 0.8 wt% sulfur, based on the active site content. These values are typical for complete deactivation in a commercial reactor. The metal surface area measured by hydrogen chemisorption is almost three times the active site concentration determined from the fit of the model to the accelerated aging data. Some of this difference may be due to a poor separation of the product kg C" into the individual constants. How-... 

Equations 9 and 10 show how the thiophene mole fraction in the gas and the concentration of unpoisoned sites varies with time (T) and position (m ) in the reactor and both of these equations can be graphed using the calculated values for the rate of thiophene poisoning and active site concentration as well as the experimental conditions. Figures 2 and 3 show the ratio of the instantaneous to initial thiophene mole fraction and active site balance, respectively, as a function of reduced length down the bed at several different reduced times for Catalyst A . Figures 4 and 5 show the same ratios for Catalyst C . 

The value of for Catalyst C indicates that thiophene conversion will be much less than for Catalyst A , and Figure 4 shows that the conversion of thiophene is only about 50% on the fresh catalyst. In fact, the disappearance of thiophene and the active site concentration as a function of axial bed position for Catalyst C is nearly linear. Indeed, Figure 5 suggests a fairly uniform profile for active sites as a function of axial position. 

The enzyme activity was measured by a continuous spectrophotometric assay (see Methods), active site concentration was determined by FAD absorption at 452 nm (8 = 12.83 mM-icm-i) as described by Frederick et al. (1990) and the protein concentration was measured by the Bradford assay (BioRad reagent) using bovine serum albumin as standard, or by its absorption at 280 nm using a published factor of 1.67 O.D. per mg (Swoboda Massey, 1965). The specific activity was 430 U/mg, and the overdl yield of enzyme, based on active sites measurement (452 nm absorption), was about 40%. 

In the polymerization of ethylene by (Tr-CjHsljTiClj/AlMejCl [111] and of butadiene by Co(acac)3/AlEt2Cl/H2 0 [87] there is evidence for bimolecular termination. The conclusions on ethylene polymerization have been questioned, however, and it has been proposed that intramolecular decomposition of the catalyst complex occurs via ionic intermediates [91], Smith and Zelmer [275] have examined several catalyst systems for ethylene polymerization and with the assumption that the rate at any time is proportional to the active site concentration ([C ]), second order catalyst decay was deduced, since 1 — [Cf] /[Cf] was linear with time. This evidence, of course, does not distinguish between chemical deactivation and physical occlusion of sites. In conjugated diene polymerization by Group VIII metal catalysts -the unsaturated polymer chain stabilizes the active centre and the copolymerization of a monoolefin which converts the growing chain from a tt to a a bonded structure is followed by a catalyst decomposition, with a reduction in rate and polymer molecular weight [88]. 

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