Langmuir-Hinshelwood adsorption

In classical kinetic theory the activity of a catalyst is explained by the reduction in the energy barrier of the intermediate, formed on the surface of the catalyst. The rate constant of the formation of that complex is written as k = k0 cxp(-AG/RT). Photocatalysts can also be used in order to selectively promote one of many possible parallel reactions. One example of photocatalysis is the photochemical synthesis in which a semiconductor surface mediates the photoinduced electron transfer. The surface of the semiconductor is restored to the initial state, provided it resists decomposition. Nanoparticles have been successfully used as photocatalysts, and the selectivity of these reactions can be further influenced by the applied electrical potential. Absorption chemistry and the current flow play an important role as well. The kinetics of photocatalysis are dominated by the Langmuir-Hinshelwood adsorption curve [4], where the surface coverage PHY = KC/( 1 + PC) (K is the adsorption coefficient and C the initial reactant concentration). Diffusion and mass transfer to and from the photocatalyst are important and are influenced by the substrate surface preparation. 

The model followed mass action kinetics with Langmuir-Hinshelwood adsorption. 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Fig. 12.1. The Langmuir-Hinshelwood adsorption isotherm, showing the fractional coverage of the catalyst surface as a function of the partial pressure of p in the gas phase.

These forms show that multiple stationary states will be possible, provided n is greater than unity. As n is the number of vacant sites being recruited into the reaction step, it probably ought to be an integer. Thus multiplicity with simple Langmuir-Hinshelwood adsorption requires at least two vacant sites to be involved in the reaction. 

It is surprising that complicated dynamic behaviour proved to be characteristic of the simplest and quite ordinary kinetic models of catalytic reactions, namely of the Langmuir Hinshelwood adsorption mechanism. We are possibly at the initial stage of interpreting the kinetics of complex reactions and the "Sturm und Drang period has not yet been completed. 

Fig. 3. Bipartite graphs for the mechanism of CO oxidation on Pt. (a) Eley-Rideal (impact) mechanism (b) Langmuir-Hinshelwood (adsorption) mechanism.

For the Langmuir-Hinshelwood (adsorption) mechanism we will have... 

Assuming that the reversible ion-exchange reaction step can be described by the Langmuir-Hinshelwood adsorption/dcsorption hypothesis and the formation of a transitional... 

The reversible ion-exchange reaction step may be compared to the Langmuir-Hinshelwood adsorption/desorption mechanism. Using the traditional notation of heterogeneous catalysis, we can express the reversible ion-exchange reaction E16.1.3 as... 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

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 fonn a CO2 molecule that, at room temperature and higher, desorbs upon fomiation. 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 fomuilating the CO oxidation mechanism was prominent. 

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. 

The problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

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... 

In comparison with the case of a gas phase molecule that reacts in a monomole-cular reaction on a solid catalyst, the reciprocal of the Michaelis constant takes the place of the equilibrium constant of adsorption in the Langmuir-Hinshelwood equations. 

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. 

Rate constant specific dark adsorption) trends (Langmuir-Hinshelwood)... 

In the absence of TCE and chlorine, the possible active species are holes (h+), anion vacancies, or anions (02 ), and hydroxyl radicals (OH ). At constant illumination and oxygen concentration, we may expect h+, and O2 concentrations to be approximately constant, and the dark adsorption to be a dominant variable. If kh+, or ko2- does not vary appreciably with the contaminant structure, the rate would depend clearly on the contaminant coverage as shown in Figme 2a, and the reaction would therefore occur via Langmuir-Hinshelwood mechanism. (Note only rates with conversions below 95% are correlated here (filled circles), as the 100% conversion data contains no kinetic information). This rate vs. d>r LH plot is smoother than those for koH or koH suggesting that non-OH species (holes, anion vacancies, or O2 ) are the active species reacting with an adsorbed contaminant. 

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. 

We can conclude now that one electron returns to the conductivity band during each act of formation of the vacant site to adsorb sensitizer. Because adsorption centers Zr(. ) are not accounted for by (2.81) the energetics of the process does not depend on the manner in which R is closing in A, i.e. on the fact which recombination mechanism (either Langmuire-Hinshelwood or Ili-Ridil) takes place. 

Kinetic orders in CO oxidation on M/A1203 can be explained by the classical Langmuir-Hinshelwood expression for the rate equation, as a function of the rate constant k, the adsorption constants K and the partial pressures P ... 

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