Langmuir-Hinshelwood formulation

Langmuir s research on how oxygen gas deteriorated the tungsten filaments of light bulbs led to a theory of adsorption that relates the surface concentration of a gas to its pressure above the surface (1915). This, together with Taylor s concept of active sites on the surface of a catalyst, enabled Hinshelwood in around 1927 to formulate the Langmuir-Hinshelwood kinetics that we still use today to describe catalytic reactions. Indeed, research in catalysis was synonymous with kinetic analysis... 

Kinetic redox models, as formulated by Mars and van Krevelen [204], have not been considered in any recent work. Although the combined dependence on both propene and oxygen pressures does arise in certain investigations, the authors seem to ignore redox mechanisms completely and correlate their data with Langmuir—Hinshelwood type models. 

Herzfeld and Langmuir-Hinshelwood-Hougen-Watson cycles, could be formulated and solved in terms of analytical rate expressions (19,53). These rate expressions, which were derived from mechanistic cycles, are phrased, however, in terms of the formation and destruction of molecular species without the need for computing the composition of reactive intermediates. Thus, these expressions are the relevant kinetics required for molecular models and are rooted to the mechanistic cycles only implicitly by the mechanistic rate constants. The molecular model, in turn, transforms a vector of reactant molecules into a vector of product molecules, either of which is susceptible to thermodynamic analysis. This thermodynamic analysis helps to organize these components into relevant boiling point or solubility product classes. Thus the sequence of mechanistic to molecular to global models is intact. 

The same approach as for irreversible Langmuir-Hinshelwood-type models can be extended to reversible reactions. Kao and Satterfield [61] developed a graphical method for monomolecular reversible reactions of the type Ai Aj, which is presented here as our last example. The method is based upon the following formulation of the net reaction rate ... 

Two reaction mechanisms were proposed [602] a) the catalyst acts as a simple adsorbent on which the reactants react on the surface (Langmuir-Hinshelwood type) b) the active catalyst sites are successively oxidized and reduced by the adsorbed reactants (Rideal-Eley type). Evaluation of the vast amount of experimental material leads to the conclusion that the HT shift (and also the LT shift) proceeds via mechanism (b), which schematically may be formulated as shown in Figure 62. 

Selective oxidation of CO in hydrogen over different catalysts has been extensively examined. Most research to date has occurred with formulations that include a precious metal component supported on an alumina carrier. The catalyst-mediated oxidation of CO is a multistage process, commonly obeying Langmuir-Hinshelwood kinetics for a single-site competitive mechanism between CO and 02. Initially, CO is chemisorbed on a PGM surface site, while an 02 molecule undergoes dissociative chemisorption either on an adjacent site or on the support in order for surface reaction between chemisorbed CO and O atoms to produce C02. 

The first step consists of the molecular adsorption of CO. The second step is the dissociation of O2 to yield two adsorbed oxygen atoms. The third step is the reaction of an adsorbed CO molecule with an adsorbed oxygen atom to form a CO2 molecule that, at room temperature and higher, desorbs upon formation. To simplify matters, this desorption step is not included. This sequence of steps depicts a Langmuir-Hinshelwood mechanism, whereby reaction occurs between two adsorbed species (as opposed to an Eley-Rideal mechanism, whereby reaction occurs between one adsorbed species and one gas phase species). The role of surface science studies in formulating the CO oxidation mechanism was prominent. 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

The Langmuir Hinshelwood kinetic model based on this reaction scheme is formulated assuming that all reactions are in equilibrium except for reaction steps (2), (4), (7) and (11). Reaction steps (2), (4) and (7) are all steps which may be slow during the shift reaction [5,6], whereas reaction step (11) represents the slow step for methanol synthesis [8], The kinetic and thermodynamic parameters are taken from available Cu single crystal experiments. We call this type of model a static microkinetic model since the number of active sites are assumed constant (i.e., independent of reaction conditions) [21]. 

The thermodynamic transition-state theory (TTST) is utilized for the elementary steps within the Langmuir-Hinshelwood-Hougen-Watson (LHHW) framework to develop rate expressions for liquid-phase catalytic reactions in terms of activities for the family of tertiary alkyl ethyl ethers. The TTST formulation also provides a rationale for the extrathermodynamic correlations (ETC) observed. 

Unfortunately, a vast portion of the WO works reported in the literature deals with the non-catalyzed oxidation kinetics for single compounds. In a review by Matatov-Meytal and Sheintuch , it was found that pure compounds such as phenol, benzene, dichlorobenzene, and acetic acid obey a first-order rate law with respect to the substrates and mainly half order with respect to the oxygen concentration. A thorough kinetic investigation in an isothermal, differentially operated fixed bed reactor with the oxygen pre-saturated aqueous solutions has revealed that the catalytic oxidation of acetic acid, phenol, chloro-phenol, and nitro-phenol can be well expressed by means of the Langmuir-Hinshelwood kinetic formulation ° , namely... 

In kinetic studies of the hydrogenation of aromatic hydrocarbons, the dependence of rate upon reactant pressures has usually been expressed in Power Rate Law formulations, that is, by orders of reaction that are simple exponents of the pressures. These as we have seen (Section 5.2) are at best approximations to more fundamental expressions based on concentrations of adsorbed species," " although they may well represent results over the limited range in which measurements were made. The Langmuir-Hinshelwood formalism has however sometimes been used, and heats of adsorption of the reactants in their reactive states derived from the temperature-dependence of their adsorption coefflcients. ... 

For reactions that are catalyzed by solid porous catalyst particles, the sequence of elementary steps may include adsorption on the catalyst surface of one or more reactants and/or desorption of one or more products. In that case, a Langmuir-Hinshelwood (LH) kinetic equation is often found to fit the experimental kinetic data more accurately than the power-law expression of Eq. (6.19). The LH formulation is characterized by a denominator term that includes concentrations of certain reactants and/or products that are strongly adsorbed on the catalyst. The LH equation may also include a prefix, ti, called an overall effectiveness factor that accounts for mass and heat transfer resistances, both external and internal, to die catalyst particles. As an example, laboratory kinetic data for the air-oxidation of SO2 to SO are fitted well by the following LH equation ... 

Mechanistic formulations in this area usually begin from one of two simplified mechanisms, both of which assume the conditions of the Langmuir isotherm. The Langmuir-Hinshelwood mechanism assumes that the rate controlling step is between the two adsorbed species D S and E S, so that the overall mechanism includes steps (ii), (iii) and (vi) in Scheme 9.1. The Eley-Rideal or Rideal mechanism " assumes that the rate controlling step is between a species in solution and an adsorbed species. Thus, if D is the adsorbed species, the mechanism would include steps (ii) and (v) in Scheme 9.1. 

The chemical reactions are commonly described by global reactions and rate formulations of the Langmuir-Hinshelwood type. Such a description requires less computational effort compared to detailed elementary step mechanisms. However, kinetic parameters must be fitted to measurement data in advance. More details on the model equations and the numerical solution of the resulhng system can be found elsewhere [15, 16, 20, 22-25]. 

In addition to Mo co-catalyst, PtSn formulations have received considerable attention. The co-catalytic activity of Sn for the enhancement of CO oxidation has been well documented and the optimum catalyst composition was found to be Pt Sn = 3 1 (atomic ratio) [76-78]. Ross and co-workers proposed the following mechanism for Sn promotion in the framework of Langmuir-Hinshelwood kinetics, also implicating surface S11O2 in H2O dissociation [76] ... 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

It is pertinent here to emphasize that the Langmuir formulation of surface kinetics was restricted to those surface reactions in which the velocity of interaction on the surface was the rate-determining process. This condition was indeed fulfilled in the classic researches of Langmuir and in further developments by Hinshelwood, Rideal, Schwab and others. A 9... 

Interestingly already in the 50-60s there was an understanding that the formulation of the rate expressions based on the original theory of Langmuir adopted by Hinshelwood and widely applied in this form for technical process development is a crude approximation. 

---