Kinetics determining site density

There have been attempts to count active centers ever since their existence was postulated in 1925. Normally site densities, where the site density is the number of active centers per unit rea< are thought to be near the maximum value, 10 cm , but in some cases values which are several orders of magnitude smaller have been suggested. A direct method of determining site density is one which depends on results of kinetic studies. Several direct methods, including one using transition state theory, are described results are presented. Many indirect methods, along with results, are also discussed. 

There are both direct and indirect ways of determining site density. All the direct ways are kinetic. Some of the kinetic methods use trasition state theory (TST) while others do not. We shall look first at the direct, non-TST methods. 

Some methods of determining site density depend upon kinetics results but are still non-TST. An analysis of Boudart s facile reaction concept, described in 1966, provides a means of determining site densities in many systems ( ). If a reaction is not demanding, that is, if its rate is proportional to the number of (for example) surface platinum atoms, then it is highly likely... 

A measurement system that is able to quantitatively determine the interactions of receptor and G protein has the potential for more detailed testing of ternary complex models. The soluble receptor systems, ([l AR and FPR) described in Section II, allow for the direct and quantitative evaluation of receptor and G protein interactions (Simons et al, 2003, 2004). Soluble receptors allow access to both the extracellular ligandbinding site and the intracellular G protein-binding site of the receptor. As the site densities on the particles are typically lower than those that support rebinding (Goldstein et al, 1989), simple three-dimensional concentrations are appropriate for the components. Thus, by applying molar units for all the reaction components in the definitions listed in Fig. 2A, the units for the equilibrium dissociation constants are molar, not moles per square meter as for membrane-bound receptor interactions. These assemblies are also suitable for kinetic analysis of ternary complex disassembly. 

Hydrocarbon distributions in the Fischer-Tropsch (FT) synthesis on Ru, Co, and Fe catalysts often do not obey simple Flory kinetics. Flory plots are curved and the chain growth parameter a increases with increasing carbon number until it reaches an asymptotic value. a-Olefin/n-paraffin ratios on all three types of catalysts decrease asymptotically to zero as carbon number increases. These data are consistent with diffusion-enhanced readsorption of a-olefins within catalyst particles. Diffusion limitations within liquid-filled catalyst particles slow down the removal of a-olefins. This increases the residence time and the fugacity of a-olefins within catalyst pores, enhances their probability of readsorption and chain initiation, and leads to the formation of heavier and more paraffinic products. Structural catalyst properties, such as pellet size, porosity, and site density, and the kinetics of readsorption, chain termination and growth, determine the extent of a-olefin readsorption within catalyst particles and control FT selectivity. 

Cs+ selectivity initially increases with increasing pellet diameter (Table V), a trend suggesting that pellet size, like site density, increases the probability of readsorption and chain initiation by a-olefins. Ultimately, larger pellets become depleted of reactants because of CO transport limitations, leading to a decrease in C5+ selectivity. The intermediate value of pellet size and of the parameter [Eq- (15) or (25)] where maximum C5+ selectiv-ities occur depends on the volumetric rate within catalyst pellets, because such properties determine the kinetic rate of CO consumption that we must... 

The use of model reactions as probes of acid-base characteristics has been adopted in a number of studies. This type of test is frequently applied in a qualitative manner. In principle, careful determination of kinetics may yield parameters that relate to site strength and site density. However, this approach is not without limitations, the most signiflcant of which is that the pathway must be unique to the process to which it is being applied. For this point, in the case of sulfated metal oxides, there has been discussion as to the pathways for low temperature isomerization of ra-butane, and a number of which are nonreliant upon the superacidity previously assumed have been identified. Nevertheless in appropriate circumstances, probe reactions can be of use and some examples are detailed in the following sentences. COS hydrolysis is sensitive to basicity and has been used to probe basic surfaces (293), but the most frequently used reaction is the... 

From the site density Sp and the kinetic current density Jr ( t 0.8 V), one can determine the turnover frequency TOF (0.8 V), which is given in Table 16.2 for both, RDE as well as fuel cell measurements (columns G and H). 

It is more useful in describing attractive and repulsive interactions and also in determining the electrophilic and nucleophilic sites in molecules. The other quantity of interest is the kinetic energy density at the... 

In order to understand the origin of the mixed corrosion potential, we must utilize mixed potential theory and the Cu/Cu system as an example. A Cu/Cu system is removed from the equilibrium given by Equation. (4.34) by the application of a driving force or an overpotential, t]. The application of an overpotential results in the system attempting to return to equilibrium by driving reaction (4.23) either in the reverse direction, for a positive overpotential, or in the forward direction, for a negative overpotential. Because electrochemical reactions involve the flow of electrons, the reaction rate may be considered as a reaction current or current density. The reaction current is the rate at which electrons flow from the site of the anodic reaction to the site of the cathodic reaction. The rate at which the reaction proceeds is determined by kinetics, and the magnitude of the overpotential which is related to the reaction current density by ... 

Cs+ selectivity can be controlled by varying the density of sites within catalyst pellets and the diameter of these pellets. The density of sites determines the reactant requirements and the pellet size controls the required path length of diffusing molecules. Such modifications affect the value of x, causing the performance of these catalysts to move along the curve in Fig. 20. The shape of the selectivity curve, however, depends only on the intrinsic readsorption rate constant (/Sr) and on the kinetic dependence of chain growth pathways on reactant pressure. 

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