Isothermic processes Langmuir-Hinshelwood isotherms

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 model that will be used for forced oscillation studies is one which was first proposed by Takoudis et al. (1981) as a simple example of an isothermal surface reaction without coverage dependent parameters in which limit cycles can occur. The bimolecular reaction between species A and B is presumed to occur as a Langmuir-Hinshelwood bimolecular process except that two adjacent vacant sites on the surface are required for the reaction to take place. 

Kinetic models referred to as adsorption models have been proposed, especially for olefin polymerisation with highly active supported Ziegler-Natta catalysts, e.g. MgCl2/ethyl benzoate/TiCU AIR3. These models include reversible processes of adsorption of the monomer (olefin coordination at the transition metal) and adsorption of the activator (complexation via briding bonds formation). There are a variety of kinetic models of this type, most of them considering the actual monomer and activator concentrations at the catalyst surface, m and a respectively, described by Langmuir-Hinshelwood isotherms. It is to be emphasised that M and a must not be the same as the respective bulk concentrations [M] and [A] in solution. Therefore, fractions of surface centres complexed by the monomer and the activator, but not bulk concentrations in solution, are assumed to represent the actual monomer and activator concentrations respectively. This means that the polymerisation rate equation based on the simple polymerisation model should take into account the... 

For SiC deposition from CH3SiCl3, the adsorption processes are competitive adsorption of H and SiCl3 on the C site, as well as Cl and CH3 on the Si site of the SiC crystal structure. This leads to the general equation of the Langmuir-Hinshelwood isotherm adsorption equation [3] ... 

In surface chemistry, adsorption isotherms describe the equiUhrium situation. However, just as in the consideration of the gas-phase chemistry in the interstellar medium, it is the kinetics of surface processes which are more relevant. Two mechanisms for surface-catalysed reactions can be distinguished and are illustrated by the cartoons in Fig. 1.6. In the Eley-Rideal mechanism, it is assumed that reaction occurs when a species (say, A) from the gas-phase impacts on a species (say, B) that is adsorbed on the surface. At significant surface coverage, the rate of reaction will be proportional to the product of the fraction of the surface covered in B (6b) and the pressure (p ) of the species A, which will be proportional to the rate of collisions of A with unit area of the solid surface. An alternative picture is encapsulated in the Langmuir-Hinshelwood mechanism. Here it is assumed that reaction occurs in encounters between species both of which are adsorbed on the surface. Then the rate of reaction will be proportional to the product of the fractions of the surface covered by A and by B that is proportional to 0a b-... 

The similarities of eqs.12-14 to a Langmuir adsorption isotherm have led to inference that the mineralization process takes place on the photocatalyst s surface. Turchi and Ollis [39] have shown that regardless of whether both, one only, or neither of oxidant ( OH) and reductant (pollutant) are adsorbed on the catalyst at the moment of radical attack, the overall rate equation will still follow an apparent Langmuir-Hinshelwood form if there is only one dominant reaction mechanism. 

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