Site competition models

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

Some deactivation processes are reversible. Deactivation by physical adsorption occurs whenever there is a gas-phase impurity that is below its critical point. It can be reversed by eliminating the impurity from the feed stream. This form of deactivation is better modeled using a site-competition model that includes the impurities—e.g., any of Equations (10.18)-(10.21)— rather than using the effectiveness factor. Water may be included in the reaction mixture so that the water-gas shift reaction will minimize the formation of coke. Off-line decoking can be... 

A strict kinetic limitation based on the gas-phase reactant can be modeled using a variable value for h although experience shows that a first order rate expressions with n=l often provides an excellent fit to experimental data regardless of the underlying reaction mechanism. A site-competition model such as Equation (10.12) can also be used. 

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

For the development of a selectivity model it is helpful to have a picture of the surface of the catalyst to ht the explanation of how the product spectrum is formed. The fundamental question regarding the nature of the active phase for the FT and water-gas shift (WGS) reactions is still a controversial and complex topic that has not been resolved.8 Two very popular models to describe the correlations between carbide phase and activity are the carbide9 and competition models.10 There are also proposals that magnetite and metallic iron are both active for the FT reaction and carbides are not active11. These proposals will not be discussed in detail and are only mentioned to highlight the uncertainty that is still present on the exact phase or active site responsible for the FT and WGS reactions. 

The solute competes with eluent molecules for the ac ve adsorption sites on the surface of the stationary phase. Interactions tetween solute and solvent molecules in the liquid phase are cancelled by milar interactions in the adsorbed phase. This model has been introdu d by Snyder (2) and by Soczewinski (77, 78) and is called the competition model."... 

Results from sensory evaluation of mixed solution are seen in Table IV. The data list the theoretical response for both the independent and competitive receptor hypothesis as well as the actual sensory score. The actual sensory scores were found to agree fairly well with the competitive model. The minor dissimilarity between the actual and theoretical is due to the inability of individual to taste bitterness in solutions that are extremely sweet, i.e., there is some masking of overall sensory perception which is concentration dependent. The data, therefore, clearly indicate that sweetness and bitterness act in a competitive manner and should be considered to compete for the binding sites at the same receptor. 

BFD from Pseudomonas putida has been characterized in detail with respect to its biochemical properties [4, 5] and 3D structure [6, 7]. Like other enzymes of this class, BFD is a homotetramer with a subunit size of about 56 kDa. The four active sites are formed at the interfaces of two subunits. The structure was published in 2003 [7] and contains the competitive inhibitor (R)-mandelate bound to the active sites, allowing model-based predictions about the interactions between active site residues and the substrate. 

In this chapter, recent results are discussed In which the adsorption of nitric oxide and its Interaction with co-adsorbed carbon monoxide, hydrogen, and Its own dissociation products on the hexagonally close-packed (001) surface of Ru have been characterized using EELS (13,14, 15). The data are interpreted In terms of a site-dependent model for adsorption of molecular NO at 150 K. Competition between co-adsorbed species can be observed directly, and this supports and clarifies the models of adsorption site geometries proposed for the individual adsorbates. Dissociation of one of the molecular states of NO occurs preferentially at temperatures above 150 K, with a coverage-dependent activation barrier. The data are discussed in terms of their relevance to heterogeneous catalytic reduction of NO, and in terms of their relationship to the metal-nitrosyl chemistry of metallic complexes. 

Two models have been developed to describe the adsorption process. The first model, known as the competition model, assumes that the entire surface of the stationary phase is covered by mobile phase molecules and that adsorption occurs as a result of competition for the adsorption sites between the solute molecule and the mobile-phase molecules.1 The solvent interaction model, on the other hand, suggests that a bilayer of solvent molecules is formed around the stationary phase particles, which depends on the concentration of polar solvent in the mobile phase. In the latter model, retention results from interaction of the solute molecule with the secondary layer of adsorbed mobile phase molecules.2 Mechanisms of solute retention are illustrated in Figure 2.1.3... 

Mg2+ influences calcite dissolution rates the same way, but not to the same extent as Ca2+. The inhibition effects of Mg2+ can be described in terms of a Langmuir adsorption isotherm. Sjoberg (1978) found he could model results for the combined influences of Ca2+ and Mg2+ in terms of site competition consistent with ion exchange equilibrium. The inhibition effects of Mg2+ in calcite powder runs increase with increasing Mg2+ concentration and as equilibrium is approached. 

Fig. 6 Competition between 3H-paclitaxel and 14C-docetaxel for binding to microtubules. 11.3 pM tubulin was assembled at 37°C in PEDTA, ImM GDP, ImM GTP, 8mM MgCl2, pH6.7 by the addition of paclitaxel and docetaxel at a total concentration of 20 pM, at different molar ratios of paclitaxel to docetaxel. The total concentration of microtubules was 11.0 0.10 pM the concentration of tubulin in supernatants (not polymerized tubulin) varied between ca. 0.4 (in paclitaxel excess) and 0.2 pM (in docetaxel excess). Open circles, 3H-paclitaxel bound per polymerized tubulin dimer solid circles, 14C-docetaxel bound squares, total ligand (paclitaxel plus docetaxel) bound per polymerized tubulin dimer. The solid lines are the best fit to the data, employing a simple competition model of the two ligands for the same site, taken from [35]...

Snyder [350] has given an early description and interpretation of the behaviour of LSC systems. He explained retention on the basis of the so-called competition model . In this model it is assumed that the solid surface is covered with mobile phase molecules and that solute molecules will have to compete with the molecules in this adsorbed layer to (temporarily) occupy an adsorption site. Solvents which show a strong adsorption to the surface are hard to displace and hence are strong solvents , which give rise to low retention times. On the other hand, solvents that show weak interactions with the stationary surface can easily be replaced and act as weak solvents . Clearly, it is the difference between the affinity of the mobile phase and that of the solute for the stationary phase that determines retention in LSC according to the competition model. 

Two models have been proposed to describe the process of retention in liquid chromatography (Figure 3.3), the solvent-interaction model (Scott and Kucera, 1979) and the solvent-competition model (Snyder, 1968 and 1983). Both these models assume the existence of a monolayer or multiple layers of strong mobile-phase molecules adsorbed onto the surface of the stationary phase. In the solvent-partition model the analyte is partitioned between the mobile phase and the layer of solvent adsorbed onto the stationary-phase surface. In the solvent-competition model, the analyte competes with the strong mobile-phase molecules for active sites on the stationary phase. The two models are essentially equivalent because both assume that interactions between the analyte and the stationary phase remain constant and that retention is determined by the composition of the mobile phase. Furthermore, elutropic series, which rank solvents and mobile-phase modifiers according to their affinities for stationary phases (e.g. Table 3.1), have been developed on the basis of experimental observations, which cannot distinguish the two models of retention. 

Solvent competition model for normal-phase liquid chromatography. Like the solvent-interaction model, the solvent-competition model assumes that the stationary phase is covered with a monolayer of molecules of the strongest component of the mobile phase. This model also assumes that the concentration of analyte in the stationary phase is small compared with the concentration of solvent molecules and that solute-solvent interactions in the mobile phase are cancelled by identical interactions in the stationary phase. The competition between the analyte molecules, x, and the mobile phase molecules. A, for the active site or sites on the stationary phase is given by... 

Models with more constants will give better fits, but this does not justify their use. Statistical tests can help avoid overfitting data, but there may be simpler physical tests Is there any reason to believe that site competition is important Is the reaction essentially irreversible It may be that n = - va provides a good fit to the data so that n ceases to be an adjustable constant. Most importantly, is the residual sum of squares, SS, low enough to represent experimental error ... 

Let us consider as an example a hydrogenolysis reaction utilizing the concept of multiple sites for adsorption and competition between hydrogen and an organic compound for surface sites. The model presented below considers an uniform surface and does not include all the features related to possible defects present at the surface of real catalysts. 

Obviously, the assumption of non-dissociative adsorption as well as that of the reaction being first order in both reactants are gross simplifications, since both methane and oxygen will dissociate prior to the reaction, and the further surface reaction mechanism will involve several consecutive and parallel reaction steps. Nevertheless, the model should allow for a qualitative test of the assumption that site competition between methane and oxygen account for the observed trend in ignition temperatures. 

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