Heterogeneously Langmuir-Hinshelwood mechanism

This Langmuir-Hinshelwood mechanism is the one most commonly encountered in the heterogeneous catalysis of gas reactions and the appropriate rate expressions for various special cases are well known [9, 31, 42], In general, we may write... 

Wicke et al. [3] were the first to apply a MC simulation to a catalytic reaction based on the Langmuir-Hinshelwood mechanism. They studied the importance of the formation of clusters of adsorbed molecules on a catalyst surface. Many microscopic mathematical models of heterogeneous catalytic systems have been developed since then. However, the time dependence of the reactions in real time could not be followed. Recently more refined MC methods have been developed, so that with these new dynamic Monte Carlo (DMC) methods, the behavior of catalytic systems in real time can be simulated. 

The Langmuir-Hinshelwood mechanism of heterogeneous catalytic processes (graph 6) ... 

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

The oxidation of carbon monoxide takes place in the car exhaust cleaning by means of catalysts based on the platinum metals and represents the simplest heterogeneously catalyzed reaction [54,55]. It involves chemisorption of CO and dissociative chemisorption of oxygen, and COad -f Oad react with each other to CO2 via the Langmuir-Hinshelwood mechanism. As an example. Fig. 6.15 shows the ordered structures formed by these adsorbates on a Rh(l 11) surface [56]. The CO molecules are in this case bonded to the surface "on top" and always exhibit the tendency to form densely packed adlayers if the coverage becomes high enough (Fig 6.15a). The O atoms, on the other hand, occupy... 

The simplest mechanism for interpreting critical phenomena in heterogeneous catalysis is the Langmuir adsorption mechanism, also referred to as the Langmuir-Hinshelwood mechanism. This mechanism includes three elementary steps (1) adsorption of one type of gas molecule on a catalyst active site (2) adsorption of a different type of gas molecule on another active site (3) reaction between these two adsorbed species. For the oxidation of carbon monoxide on platinum, this mechanism can be written as follows ... 

Figure4.11.5 (Pre)selection ofthe appropriate kinetic equation influence of total pressure and partial pressure of one reactant on initial rate of a heterogeneously catalyzed bimolecular gas reaction of A and B (a) Langmuir-Hinshelwood mechanism for variation of total pressure p (b) Eley-Rideal mechanism for variation ofp (c) Langmuir-Hinshelwood for variation of partial pressure of one ofthe adsorbed reactants (e.g., Pa) (d) Eley-Rideal mechanism for variation of partial pressure of adsorbed reactantA (p ) (e) Eley-Rideal mechanism for variation of partial pressure of reactant B (not adsorbed).

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. 

The catalytic oxidation of CO on a Pt snrface has been extensively studied in view of its relevance to automotive gas pollution. Moreover, its relative simplicity motivated its extensive use as a model systan for heterogeneous catalysis. Molecular beam studies of the catal3dic oxidation of CO on the plane (111) on platinum indicate that the reaction follows a Langmuir-Hinshelwood mechanism [2],... 

All heterogeneous catalysis relies on the existence of reactions between adsorbed molecules or atoms (the Langmuir-Hinshelwood mechanism) or between adsorbed molecules or atoms and free molecules (the Rideal mecharrism). 

Althou the rate of heterogeneous reactions is usually expressed according to the Langmuir-Hinshelwood mechanisms (Walker et al. (18)), a simpler power law expression is recommended for most of the char-gas reactions. This is to reduce the mathemati- cal complexity in reactor modelling and the number of parameters needed to be determined by experimentation. Accordingly, the rate e q>ression for a volumetric reaction can be described in the following forms ... 

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. 

A reason for using microkinetics in heterogeneous catalysis is to have comprehensive kinetics and a transparent reaction mechanism that wonld be useful for re or design or catalyst development. Furthermore, in the long run, the exparimental effort to develop a microkinetics scheme can be less than that for a Langmuir-Hinshelwood (LH) or powa--law scheme because of the more fundamental nature of the reaction kinetics parameters. 

Direct reaction between an adsorbed species A(s) and a gas-phase molecule B is sometimes proposed. This reaction pathway is called the Eley-Rideal mechanism. Although such a mechanism may seem as reasonable as the Langmuir-Hinshelwood model discussed above, very few heterogeneous reactions are still thought to occur by the Eley-Rideal mechanism. (An exception seems to be when species B is a very reactive radical species, e.g., a gas-phase H-atom reacting with an adsorbed species, as is discussed in Problem 11.10, in which an Eley-Rideal pathway initiates the growth process.)... 

The second model results from a bimolecular surface reaction, A + B — products, with competitive Langmuir-Hinshelwood kinetics, which occurs in a heterogeneous differential reactor with perfectly mixed gas phase. The reaction is first order in both adsorbed A and B, and two vacant sites are required in the reaction mechanism. If the reaction products desorb immediately, the... 

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