Model dual site

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

At low 7t, the denominator simplifies to unity in each case and both models are linear in n. For sufficiently high n, the parenthesis in the denominator approaches Ketv, the initial rate for the dual-site model then approaches zero, and that of the single-site model approaches a constant value. Thus the plot of the experimental data will indicate that the dual-site model is preferable if a maximum exists in the data, or that the single-site model is preferable if a horizontal high-pressure asymptote exists. Hence, for the data of Franckaerts and Froment (FI) shown in Fig. 2, the dual-site model is preferred over the single-site model. 

The data should lie along a straight line when plotted as (7i/r0)1/2 vs n, if the dual-site model is adequate. If, in addition, the dual-site model is to be preferred over the single-site model, the plot of njr0 vs n should be curved... 

An analysis of variance can also be used to test the adequacy of more theoretical models. For example, two models considered in Section III for pentane isomerization are the single-site and dual-site models of Eqs. (30) and (31). These were linearized to provide Eqs. (32) and (33). The overall fit of these equations to the data may now be judged by an analysis of variance, reported in Tables V and VI (K3). It is seen that Eq. (33) fits the data quite... 

By using only simple hand calculations, the single-site model has been rejected and the dual-site model has been shown to represent adequately both the initial-rate and the high-conversion data. No replicate runs were available to allow a lack-of-fit test. In fact this entire analysis has been conducted using only 18 conversion-space-time points. Additional discussion of the method and parameter estimates for the proposed dual-site model are presented elsewhere (K5). Note that we have obtained the same result as available through the use of nonintrinsic parameters. 

The C2 plots of Fig. 26, however, indicate that a linear C2 dependence upon pressure will not be adequate. The use of the dual-site model will require three additional parameters for C2, in order that the model approximately describe the data. The single-site model, however, can be used if we take... 

In many reactions it has been demonstrated that more than one site is involved in the catalytic process. This is particularly often the case for dissociation reactions. The same procedure as depicted above for a single site model can be used for the derivation of the rate expression for a dual site model, but the result is somewhat different. This is exemplified for the following dissociation reaction A 2B, which is thought to proceed according to the three step sequence ... 

In the case of the dual site model the initial rate even passes through a maximum if the surface reaction step is rate determining (cf. Eqn. (3.24)). 

In an analogous way limiting cases can be distinguished for the dual site model, where even the order in A can become negative (cf. Eqn. (24)). 

Related to these matters has been the question whether two-component electrode metals (dual-site model) could lead to an electrocatalyst surface that exhibited catalytic properties better than either of its components. Qualitative ideas about electron spillover between one component and another at microcrystal grain boundaries, or transfer of the chemisorbed intermediate from one site to another, could suggest the possibility of such an effect. However, a quantitative theoretical analysis of this question by Parsons (149), based on his treatment of chemisorption effects at single metals (23) having various AG ,, h values, showed that, for practical applications, almost no... 

Hydrogenations of MAA were carried out both in gas-phase and liquid phase with flowing hydrogen. Optical 5delds were 8-15% in the former and 30-32% in the latter cases, and no significant structure sensivities were observed. In the range of 4-10 mn no influence of particle size was seen in the ee s of the methyl 3-hydroxybutyrate product The results were considered confirmation of the dual site model" (Sachtler which states that one sort... 

A dual-site model for the storage and the release of NH3 over a Fe-zeolite catalyst has been proposed by Colombo et al. [23]. The acid sites where ammonia is either weakly adsorbed or physisorbed are denoted as Site-1 while the strong adsorption sites are denoted as Site-2. The following rate expressions describe the rates of ammonia adsorption/desorption for each site ... 

Figure 6. Calculated vs. observed rate—dual site model...

Several models have been proposed to account for the non-random distribution of oligosaccharides formed when polysaccharides are hydrolysed by a-amylase. The preferred-attack model assumes that the probability of bond-cleavage depends on the position of the bond in the chain the repetitive (or multiple-attack) model assumes that a-amylase can form a cage-like complex with the substrate and attack it several times during a single encounter the multiple-enzyme (or dual-site) model assumes that the substrate is hydrolysed by the combined actions of exo- and en /o-enzymes. The effects of pH, inhibitors, and the chain length of the substrates have been studied in an attempt to decide which of the three models best fits the action of a-amylase. The effects of these variables on either the distribution of products or the action pattern of the enzyme were incorporated into the models, which were then used to interpret experimental data obtained with porcine pancreatic a-amylase. 

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