Langmuir-Hinshel wood

Jakdetchai and Nakajima/Wang and coworkers—theoretical models favor redox mechanism. Beginning in 2002, a number of theoretical models were published in Theochem studying the water-gas shift reaction over Cu(110), Cu(lll), and Cu(100) surfaces. Perhaps the first was by Jakdetchai and Nakajima,325 relying on the AMI method. The main goal of the study was (1) to determine whether or not theoretical calculations are consistent with a redox or associative (e.g., formate) mechanism and (2) whether the kinetics are described best by a Langmuir-Hinshel-wood expression or an Eley-Rideal expression. That is, in the case of a redox model, does the adsorbed O adatom react with adsorbed CO or directly with gas phase CO Their approximate A//a[Pg.205]

A variety of models have been derived to describe the kinetics of semiconductor photocatalysis, but the most commonly used model is the Langmuir-Hinshel-wood (LH) model [77-79]. The LH model relates the rate of surface-catalyzed reactions to the surface covered by the substrate. The simplest representation of the LH model [Eq. (7)] assumes no competition with reaction by-products and is normally applied to the initial stages of photocatalysis under air- or oxygen-saturated conditions. Assuming that the surface coverage is related to initial concentration of the substrate and to the adsorption equilibrium constant, K, tire initial... 

A kinetic study carried out with a well-stirred reactor was reported by Cartlidge et al. [78,79], Temperatures below 420°C were used to avoid acrylic acid formation. At atmospheric pressure, the oxygen and propene concentrations were varied between 1 and 10, and 5 and 15%, respectively. Selectivities of 60—90% and a maximum acrolein yield of 28% were reported at 400° C. The kinetic results were fitted to a Langmuir—Hinshel-wood type of rate equation... 

However, simple kinetic models, especially of the Langmuir—Hinshel-wood type, can serve with advantage for correlation of experimental data in spite of simplifying assumptions which are necessary for their derivation. Experience shows that heterogeneous acid—base catalysis is the very field where they fit best. Their most frequent general form... 

The corresponding graph is illustrated in Fig 3(a). The Langmuir-Hinshel-wood mechanism contains a step which is an interaction between intermediates (step 3)... 

In this chapter focus has been given to the derivation and application of the so-called Langmuir-Hinshel-wood-Hougen-Waston models to describe catalyzed reactions. In spite of objections that can be made against their underlying assumptions these expressions have been proved to be quite successful. An important reason is probably the fact that it contains intrinsically a capacity, a limited number of catalytically active centers where the reaction takes place and which are distributed among the different adsorbing components. 

I) Reaction occurs while both species are adsorbed (Langmuir-Hinshel-wood kinetics). 

In the substantial majority of cases the reaction takes place between the adsorbed molecule, or their fragments. This is known as the Langmuir-Hinshel-wood mechanism. For very few reactions a so-called Eley-Rideal mechanism has been postulated, in which an adsorbed molecule or its fragment reacts with a molecule impinging from the gas(liquid)phase. 

Als Kriterium kann man hier fiir d>L>0,5 angeben, daB die Langmuir-Hinshel-wood-Beziehung anstelle der Reaktionsgeschwindigkeitsgleichung 1. Ordnung erst zu berucksichtigen ist, wenn K pAs > 0,2 zutrifft. 

The form of the resulting expression differs from the gas-phase reaction rate expressions due to the presence of a denominator representing the reduction in rate due to adsorption phenomena. The individual terms of this denominator respresent the distribution of the active sites among the possible surface complexes and vacancies. Expressions of this type are termed the Langmuir-Hinshel-wood-Hougen-Watson (LHHW) rate expressions in heterogeneous catalysis and Michaelis-Menten expressions in biocatalysis. 

These species also promote the complete oxidation of the organic adsorbate by a recombination of these species (from reactions (IV-V) and reactions (VI-XVII)) through a Langmuir-Hinshel-wood mechanism [131]. For example,... 

Futhermore, it was found that the benzyl alcohol formed in the reaction has no influence on the reaction rate. From aU the experimental results, a Langmuir-Hinshel-wood model was deduced, with a rate-determining influence of the surface reaction according to Equation 13-20. 

If the PCs are assumed to react with the adsorbed monomer molecules, the Langmuir-Hinshel-wood rate equation [Eq. (P9.4.13)] is applicable and the rate expression in the stationary zone then becomes... 

So we also eliminate model (d). For heterogeneous reactions. Langmuir-Hinshel-wood rate laws are preferred over power law models. 

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