Langmuir adsorption mechanism

The UPD of Zn on Pt(lll) electrode in phosphate solutions (pH 4.6 or 3.0) was studied by Aramata and coworkers [194] in the presence of adsorbed anions. In phosphate solutions, the Zn UPD obeyed the Langmuir adsorption mechanism. On the addition of 10 M Br ions, the Zn + ion UPD potential shifts 120 mV to more negative values. The desorption of specifically adsorbed anions is suggested to trigger the UPD of Zn. 

The linearized Eq. 30 is used to verify the Langmuir adsorption mechanism. The constant /3 can be estimated from the slope of regression lines. For a two-point adsorption, when a molecule adsorbs after a former dissociation at the interface, Eq. 30 gets the form... 

Figure 2.2-1 Schematic diagram of Langmuir adsorption mechanism on a flat surface...

Substitution of the local isotherm equation (3.2-2) and the energy distribution (eq. 3.2-3) into eq. (3.2-4a), and after some approximations, Zeldowitsch derived the Freundlich isotherm. Thus, the Freundlich equation has some theoretical basis at least for heterogeneous solids having an exponential decay energy distribution and Langmuir adsorption mechanism is operative on all patches. 

The local isotherm was assumed to follow the Langmuir equation, and by assuming a patchwise topography the overall isotherm can be readily obtained by averaging the local isotherm over the distribution of the Henry constant. One should note here that since there is no interaction between the adsorbed molecules (assumption of the Langmuir adsorption mechanism), the surface topography is irrelevant. This approach of Sircar yields an isotherm which has a finite slope at... 

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 ... 

In a typical Langmuir adsorption mechanism, the elementary reaction between two adsorbed speeies is very fast. In this ease, sueh a fast reaetion oeeurs between adsorbed oxygen and adsorbed earbon monoxide, that is, k Pco k - Consequently, we can... 

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. 

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. 

Combined with their kinetic measurements, the authors proposed CO from the gas phase could directly react with oxygen atoms in the surface oxides, accounting for relatively high reactivity of this phase for CO oxidation. This mechanism, termed as Mars-Van Krevelen mechanism, challenges the general concept that CO oxidation on Pt group metals is dominated by the Langmuir-Hinshelwood mechanism, which proceeds via (1) the adsorption of CO and the dissociative adsorption of 02 and (2) surface diffusion of COa(j and Oa(j atoms to ultimately form C02. 

The provenance of expressions like that in Equation 3 has never been shown to be uniquely an adsorption mechanism. On the contrary, it is possible to derive special cases of Equation 3, such as the classical Langmuir equation... 

Rate equations for simple reversible reactions are often developed from mechanistic models on the assumption that the kinetics of elementary steps can be described in terms of rate constants and surface concentrations of intermediates. An application of the Langmuir adsorption theory for such development was described in the classic text by Hougen and Watson (/ ), and was used for constructing rate equations for a number of heterogeneous catalytic reactions. In their treatment it was assumed that one step would be rate-controlling for a unique mechanism with the other steps at equilibrium. 

However, there is no reason to use more complicated isotherm models if two-parameter models, such as Langmuir and Freundlich, can fit the data well. It should be clarified that these models are only mathematical functions and that they hardly represent the adsorption mechanisms. 

Most solid sorbents rely on vapors being sorbed by a physical adsorption mechanism the substance enters the internal pores of the sorbent and is held there by attractive forces considerably weaker and less specific than those of chemical bonds. These weakly attractive forces facilitate desorption for subsequent analysis. The mechanisms for physical adsorption have been studied extensively and are described mathematically by equations such as the Langmuir isotherm. 

Deviations from this simple expression have been attributed to mechanistic complexity For example, detailed kinetic studies have evaluated the relative importance of the Langmuir-Hinshelwood mechanism in which the reaction is proposed to occur entirely on the surface with adsorbed species and the Eley-Rideal route in which the reaction proceeds via collision of a dissolved reactant with surface-bound intermediates 5 . Such kinetic descriptions allow for the delineation of the nature of the adsorption sites. For example, trichloroethylene is thought to adsorb at Ti sites by a pi interaction, whereas dichloroacetaldehyde, an intermediate proposed in the photo-catalyzed decomposition of trichloroethylene, has been suggested to be dissociatively chemisorbed by attachment of the alpha-hydrogen to a surface site... 

The kinetics of the ammoxidation of xylenes over a vanadium catalyst and mixed vanadium catalysts were studied. The reaction rate data obtained were correlated with the parallel consecutive reaction scheme by the rate equations based upon the Langmuir-Hinshelwood mechanism where the adsorption of xylenes was strong. The reaction rates of each path are remarkably affected by the kind of xylene and catalyst. The results of the physical measurement of catalysts indicated that the activity and the selectivity of reaction were affected by the nature and the distribution of metal ions and oxygen ion on catalyst surface. 

The data on the rate of reaction of o-, m-, and p-xylene over vanadium oxide catalyst and of m-xylene over mixed vanadium oxide catalysts (chromium-vanadium and antimony-vanadium) were correlated with the reaction scheme below by the following rate expressions, which are based on the Langmuir-Hinshelwood mechanisms where the adsorption of m-xylene is strong. 

Interactions 2 and 4 represent a Rideal mechanism and Interactions 2a and 4a a Langmuir-Hinshelwood mechanism. However, to form C03"(adS), by Interaction 1 in Mechanism I, CO must first be adsorbed since Interaction 1 is a fast process, the adsorption of CO would be the slow step of Mechanism I, and the kinetics of the reaction would depend on pco- However, it has been shown (8, 28) that the reaction is zero order with respect to CO, and therefore the adsorption of CO and its conversion to COa udsi are faster processes than Interaction 2 which is the rate-limiting step and hence may be written in the form of 2a (Langmuir-Hinshelwood mechanism). 

For example, the Langmuir adsorption isotherm specifically describes adsorption of a single gas-phase component on an otherwise bare surface. When more than one species is present or when chemical reactions occur, the functional form of the Langmuir adsorption isotherm is no longer applicable. Thus, although such simple functional expressions are very useful, they are not generally extensible to describe arbitrarily complex surface reaction mechanisms. 

It is important to recognize that Kp is unitless, and is related to thermodynamic quantities by Eq. 9.93, for example. However, Eq. 11.17 has exactly the same form as the classic Langmuir adsorption isotherem, Eq. 11.11, if we take K = Kp/p°. Thus the two approaches are entirely equivalent. In addition the discussion above shows how the more restrictive form that is usually written for the Langmuir adsorption isotherm can be converted to the extensible mass-action kinetics form to be used, for example, within a more extensive surface reaction mechanism. 

If particles enter the surface activated complexes directly from the volume, e.g., when the reaction occurs as a result of impact of molecules from the gas phase upon the adsorbed molecules, the expression for the reaction rate will contain, together with surface concentrations, the values of volume concentrations. These impact mechanisms were long ago proposed by Langmuir (22) for the reactions of CO and H2 with 02 on the surface of platinum the reaction occurs at the impact of a CO or H2 molecule against an adsorbed O atom. Such reactions seem to be numerous (23). Along with this, the above-mentioned adsorption mechanisms that involve the reaction between two adsorbed particles are possible. Elementary acts of surface reactions in which more than two particles participate are hardly probable. 

If, on the other hand, surface reaction determined the overall chemical rate, equation 3.68 (or 3.69 if an Eley-Rideal mechanism operates) would represent the rate. If it is assumed that a pseudo-equilibrium state is reached for each of the adsorption-desorption processes then, by a similar method to that already discussed for reactions where adsorption is rate determining, it can be shown that the rate of chemical reaction is (for a Langmuir-Hinshelwood mechanism) ... 

In principle it is possible to write down the rate equation for any rate determining chemical step assuming any particular mechanism. To take a specific example, the overall rate may be controlled by the adsorption of A and the reaction may involve the dissociative adsorption of A, only half of which then reacts with adsorbed B by a Langmuir-Hinshelwood mechanism. The basic rate equation which represents such a process can be transposed into an equivalent expression in terms of partial... 

Numerous attempts have been made at developing mathematical expressions from postulated adsorption mechanisms to fit the various experimental isotherm curves. The three isotherm equations which are most frequently used are those due to Langmuir, to Freundlich, and to Brunauer, Emmett and Teller (BET). 

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