Models Hinshelwood

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

A dimer-dimer (DD) surface reaction scheme of the type (1/2)A2 + B2 B2A has been proposed in order to mimic the catalytic oxidation of hydrogen A2 is O2, B2 is H2, AB is OH and B2A is H2O. The model reaction proceeds according to the Langmuir-Hinshelwood... 

The monomer-monomer (MM) model, for the reaction A -H B —> AB, assumes the following Langmuir-Hinshelwood reaction schema ... 

The reaction scheme of the ZGB-DD model is based upon the Langmuir-Hinshelwood mechanism. Thus, it is assumed that the reaction occurs according to the following steps ... 

M.T.M. Koper, A.P.J. Jansen, and J.J. Lukkien, Lattice-gas modeling of electrochemical Langmuir-Hinshelwood surface reactions, Electrochim. Acta 45, 645-651 (1999). 

Finally the success of the model can be judged from Figures 6.25a and b which show the experimental and model-predicted rate dependence on pCo and work function during CO oxidation on Pt/pM-Al203.71 Note the transition from a classical Langmuir-Hinshelwood to a positive order rate dependence on pco with decreasing work function. Also notice that on every point of the experimental or model predicted rate dependence, the basic promotional mle ... 

Examples of Hougen-Watson kinetic models, which are also called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt and Perry s Handbook (see Suggestions for Further reading in Chapter 5) for collections of the many possible models. The models usually have numerators that are the same as would be expected for a homogeneous reaction. The denominators reveal the heterogeneous nature of the reactions. They come in almost endless varieties, but all reflect competition for the catalytic sites by the adsorbable species. 

The model considers the noble-metal catalyzed oxidation reactions of CO, two hydrocarbons of differing reactivities and H2, and the reaction kinetics was described by the global rate expressions of the dual-site Langmuir-Hinshelwood type [2]. 

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 ... 

Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) kinetic models... 

Kinetic Parameters from Fitting Langmuir-Hinshelwood Models... 

Hinshelwood model, and the corresponding values of the equilibrium constants. [From A. Borgna and J.W. Niemantsverdriet, to be published (2003).]... 

The fits indicate that the Langmuir-Hinshelwood model describes the measurements very well. The equilibrium constants point to a relatively strong adsorption of thiophene and, in particular, H2S, while adsorption of hydrogen is weak. Hence the term K may safely be ignored in Eq. (32). The order in H2 is 0.93, i.e. close to one, which is another indication that hydrogen adsorbs only weakly. 

All of these rates are measured on surfaces shown to be clean by AES, and this Indicates that these processes occur on surfaces containing only submonolayer coverages of reactant species, exactly the situation required for the Langmuir-Hinshelwood model of surface reactions. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

AU experiments to be described below are interpreted on the basis of the Langmuir-Hinshelwood (LH) mechanism for CO electro-oxidation suggested by GUman more than 40 years ago [Gihnan, 1964]. According to GUman s model, water needs to be activated on a free site on the surface, leading to surface-bonded OH ... 

A Langmuir-Hinshelwood reaction rate model for the reaction between an adsorbed nitric oxide molecule and one adjacently adsorbed hydrogen molecule is described by ... 

Since both hydrogen in the solution and the product A are weakly adsorbed species, equilibrium constants ka and k, are very small, which leads to KACA 1 and kh CH 1. Thus, the rate expression for the debenzylation can be simplified as a conventional Langmuir-Hinshelwood model. 

The reaction mechanism of the SMR reaction strongly depends on the nature of the catalytically active metal and the support (the detailed discussion is provided in the review [14]). The kinetics and mechanism of the SMR reaction over Ni-based catalysts have been extensively studied by several research groups worldwide. For example, Xu and Froment [16] investigated the intrinsic kinetics of the reforming reaction over Ni/MgAl204 catalyst. They arrived at the reaction model based on the Langmuir-Hinshelwood reaction mechanism, which includes several reaction steps as follows ... 

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