Langmuir mechanism

Langmuir referred to the possibility that the evaporation-condensation mechanism could also apply to second and higher molecular layers, but the equation he derived for the isotherm was complex and has been little used. By adopting the Langmuir mechanism but introducing a number of simplifying assumptions Brunauer, Emmett and Teller in 1938 were able to arrive at their well known equation for multilayer adsorption, which has enjoyed widespread use ever since. 

When extended to the second layer, the Langmuir mechanism requires that the rate of condensation of molecules from the gas phase on to molecules already adsorbed in the first layer, shall be equal to the rate of evaporation from the second layer, i.e. 

Because of non-adherence of the site sorption mode to a strict Langmuir mechanism, as noted previously, Eq. (18), as well as Eqs. (20) or (20 a), must, at the quantitative level, be validated experimentally. This can be done most conveniently by varying the partial pressure of one component at various constant partial pressures of the other. Sorption data of this type have recently been reported for PMMA-C02, C2H4 at 35 °C69 70). As shown in Fig. 7, the agreement between experiment and calculation from the pure component isotherms, though not perfect, is nevertheless quite impressive. 

The only heat of adsorption we have found in the literature is a figure of 17 kcal. per mole (27) for thiophene on a supported chromia catalyst. This figure was obtained by analysis of reactions carried out in a static system, assuming a Langmuir mechanism for thiophene and hydrogen adsorption and neglecting the effects of H2S and butene adsorption. 

By introducing a number of simplifying assumptions, Brunauer, Emmett and Teller (1938) were able to extend the Langmuir mechanism to multilayer adsorption and obtain an isotherm equation (the BET equation), which has Type II character. The original BET treatment involved an extension of the Langmuir kinetic theory of monomolecular adsorption to the formation of an infinite number of adsorbed layers. 

It is now generally accepted that there is no sound reason why isotherms on micro-porous solids should conform any more closely to the classical Langmuir mechanism than isotherms on non-porous or mesoporous adsorbents. Indeed, a considerable amount of the evidence now available gives strong support to the view that the limiting uptake is controlled rather by the accessible micropore volume than by the internal surface area (Gregg and Sing, 1982). 

The parameter B in the model reflects the relative values of the adsorption constants of the reactant and products. On both catalysts its value indicates that there is strong corrpetition for adsorption sites by the product species. The value of this parameter is found to be larger for Cattl than Cat 2/ suggesting that product species are less strongly adsorbed on Cat l Thus one would expect the monomolecular Langmuir mechanism to be more favoured on Catll due to a relatively lower surface coverage by products. This agrees with the analysis of the A1 and A2 parameters discussed above. 

The simplest case results when a non-localised adsorption is assumed (Baret 1968a, b), so that jjd C(, and r. As the result we obtain Eq. (4.31), where are k j and kj are the rate constants of adsorption and desorption, and c is the bulk concentration of the adsorbing species. On the basis of a localised adsorption the Langmuir mechanism Eq. (4.32) results. Further transfer mechanisms used to describe the kinetics of adsorption are given in Section 4.4, Eqs (4.31) - (4.34). To use these so-called transfer mechanisms for model of dynamic adsorption layers they have to be coupled with the transport process in the bulk. Baret (1969) suggested replacing c by the so-called subsurface or sublayer concentration. This is per definition the bulk concentration adjacent to the adsorption layer c(0,t) localised at x = 0. The following two flux balance equations for the molecular transfer results. 

Further models of adsorption kinetics were discussed in the literature by many authors. These models consider a specific mechanism of molecule transfer from the subsurface to the interface, and in the case of desorption in the opposite direction ((Doss 1939, Ross 1945, Blair 1948, Hansen Wallace 1959, Baret 1968a, b, 1969, Miller Kretzschmar 1980, Adamczyk 1987, Ravera et al. 1994). If only the transfer mechanism is assumed to be the rate limiting process these models are called kinetic-controlled. More advanced models consider the transport by diffusion in the bulk and the transfer of molecules from the solute to the adsorbed state and vice versa. Such mixed adsorption models are ceilled diffusion-kinetic-controlled The mostly advanced transfer models, combined with a diffusional transport in the bulk, were derived by Baret (1969). These dififiision-kinetic controlled adsorption models combine Eq. (4.1) with a transfer mechanism of any kind. Probably the most frequently used transfer mechanism is the rate equation of the Langmuir mechanism, which reads in its general form (cf. Section 2.5.),... 

Here, jgj and are the adsorption and desorption fluxes, respectively. Considering a Langmuir mechanism, Eq. (4.52) takes the final form ... 

Following Baret [9] the coupling of transfer mechanisms with the diffusion equation (4.12) can be arranged by replacing the bulk concentration c by the subsurface concentration c(0, t) which for the Langmuir mechanism (4.13) leads to... 

The difference between the Volmer equation and the Langmuir equation is that while the affinity constant remains constant in the case of Langmuir mechanism, the apparent affinity constant in the case of Volmer mechanism decreases with loading. This means that the rate of increase in loading with pressure is much lower in the case of Volmer compared to that in the case of Langmuir. 

Here the rate of desorption of a species is unaffected by the presence of all other species. In general, one would expect that the rate constant for desorption k j is a function of fractional loadings of all other species. However, it is treated as a constant in this analysis because of the one molecule per site and the no lateral interaction assumptions in the Langmuir mechanism. 

By adopting the Langmuir mechanism and introducing a number of simplifying assumptions, Brunauer et al. (11) were able to derive an equation to describe multilayer adsorption (Type II isotherm) which forms the basis for surface area measurement. The equation, commonly referred to as the BET equation, can be expressed in the form... 

It is at once evident that there is a remarkable degree of similarity between the shapes of L-type solute isotherms and Type I physisorption isotherms. However, this similarity is misleading since the adsorption mechanisms involved are likely to be quite different. We have seen already that Type I physisorption isotherms for gas-solid systems are normally associated with micropore filling. In contrast, the plateau of an L-type solute isotherm usually corresponds to monolayer completion. In this respect, solute adsorption appears to correspond more closely to the classical Langmuir mechanism. If this is indeed the case it would seem to be possible to calculate the surface area from nj by the application of a simple equation of the same form as Eq. (2). 

Adsorption and desorption processes are the reverse of each other and are always considered as occurring, whatever the nature of the solid and gas. During chemical transformations there is chemisorption. When this double process occurs as steps of a reaction mechanism, the Langmuir mechanism is satisfied. 

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