Langmuir-Hinshelwood models

Langmuir-Hinshelwood model is widely used to define heterogeneous catalytic reactions. This model includes two important steps. The first one describes adsorption of BH on the surface of the catalyst [111]. 

In this step, the Langmuir isotherm has two important assumptions  

Consider a single vapor A at pressure that adsorbs on the surface without dissociation. The rate of the adsorption is proportional to the rate of the collisions with unoccupied sites  

Surface coverage is 0 that describes the fraction of the adsorption sites to which a molecule has become attached. A statement for the fraction of the surface with unattached sites is therefore 1 - 0.  

Also the rate of desorption is proportional to number of molecules adsorbed  

---

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. 

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 ... 

Kinetic Parameters from Fitting Langmuir-Hinshelwood Models... 

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. 

Figure 7.18. Dependence of the rate of thiophene hydrodesulfurization on the partial pressures of thiophene at different temperatures, along with fits according to the Langmuir-Hinshelwood model, Eq. (32). [Fron A. Borgna and J.W. Niemantsverdriet, to be published (2003).]...

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. 

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. 

Propose a rate law based on the Langmuir-Hinshelwood model for each of the following heterogeneously catalyzed reactions ... 

The Michaelis-Menten equatioa 10.2-9, is developed in Section 10.2.1 from the point of view of homogeneous catalysis and the formation of an intermediate complex. Use the Langmuir-Hinshelwood model of surface catalysis (Chapter 8), applied to the substrate in liquid solution and the enzyme as a colloidal particle with active sites, to obtain the same form of rate law. 

Mann, Thurgood, and coworkers—Langmuir-Hinshelwood kinetic model for methanol steam reforming and WGS over Cu/Zn. Mann et al.335 published a complex Langmuir-Hinshelwood model for CuO/ZnO catalysts based on what one would encounter for a methanol steam reformer (MSR) for fuel cell applications. The water-gas shift rate, containing all MSR terms, was determined to be ... 

Non-linearities arising from non-reactive interactions between adsorbed species will not be our main concern. In this section we return to variations of the Langmuir-Hinshelwood model, so the adsorption and desorption processes are not dependent on the surface coverage. We are now interested in establishing which properties of the chemical reaction step (12.2) may lead to multiplicity of stationary states. In particular we will investigate situations where the reaction step requires the involvement of additional vacant sites. Thus the reaction step can be represented in the general form... 

There are only a few recent publications. Anshits et al. [29,30] have carried out adsorption studies with various Cu—O phases and determined kinetics at low pressure in a static system. One of their conclusions is that the kinetics of partial and complete oxidation are very different. The mechanism of the latter is supposed to be of the associative type, contrary to the redox mechanism of the partial oxidation. A kinetic study with a continuously stirred vessel (375—400°C, 1 atm) was carried out by Laksh-manan and Rouleau [185]. In contrast to the redox mechanism, a singlesite Langmuir—Hinshelwood model is proposed, for which the k values and activation energies are determined. 

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... 

With respect to the kinetics of aromatic oxidations, (extended) redox models are suitable, and often provide an adequate fit of the data. Not all authors agree on this point, and Langmuir—Hinshelwood models are proposed as well, particularly to describe inhibition effects. It may be noted once more that extended redox models also account for certain inhibition effects, for mixtures of components that are oxidized with different velocities. The steady state degree of reduction (surface coverage with oxygen) is mainly determined by the component that reacts the fastest. This component therefore inhibits the reaction of a slower one, which, on its own, would be in contact with surface richer in oxygen (see also the introduction to Sect. 2). 

Also, Langmuir—Hinshelwood models have been proposed as well as models based on a redox mechanism. 

The next problem of the Langmuir-Hinshelwood kinetics, the validity of the rate-determining step approximation, has not been rigourously examined. However, as has been shown (e.g. refs. 57 and 63), the mathematical forms of the rate equations for the Langmuir-Hinshelwood model and for the steady-state models are very similar and sometimes indistinguishable. This makes the meaning of the constants in the denominators of the rate equations somewhat doubtful in the Langmuir—Hinshelwood model, they stand for adsorption equilibrium constants and in the steady-state models, for rate coefficients or products and quotients of several rate coefficients. 

The physical meaning of the Langmuir—Hinshelwood model was also examined by means of several transesterification reactions in the vapour phase at 120°C on a macroreticular ion exchanger [439,440,442]. The... 

By assumption of the Langmuir-Hinshelwood model, the adsorbed surface species concentrations are not affected by reaction 11.30, and so they are the same as in the case of the competitive adsorption, discussed earlier ... 

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.)... 

Beissinger s and Leonard s model (Fig. 13 d) accounts for desorption of both native and denatured adsorbed species (States 1 and 2, respectively). They used the classical Langmuir-Hinshelwood model for catalytic reactions (the surface is the catalyst for conformational change or denaturation of the adsorbed protein), which assumes equilibrium at a steady state between adsorbed and solution molecules. They show ... 

The Langmuir-Hinshelwood model describes the most common situation in heterogeneous catalysis [15,16]. It assumes that the reactant must be adsorbed on the catalyst surface before it can react. The reaction then takes place at the active site, and the product is then desorbed from the catalyst back to the gas phase (Figure 2.7). 

---