Langmuir-type adsorption model

Co-adsorption and mutual interactions between the reactants on the surface form the basis for understanding the microscopic steps of the reaction. Since product formation takes place rather rapidly above room temperature, this information mainly became available from low-temperature studies. As a result, these processes are much more complicated than can be described by a Langmuir-type adsorption model (i.e., simple competition for free adsorption sites) and, moreover, an asymmetric behavior is found which means that pre-adsorbed CO inhibits the adsorption of oxygen, whereas the reverse is not the case. At very low surface concentrations of CO and Oad these will be randomly distributed over the surface as illustrated schematically by Fig. 32a (88). 

According to the Langmuir-type adsorption model, a differential equation for time dependence of the amount of FeCp-X adsorbed on the droplet (m) is given as... 

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

An assumed instantaneous distribution between the adsorbed and free solute is modelled by a Langmuir-type adsorption isotherm, where... 

One drawback of Langmuir-type adsorption isotherms is the conjunction between the initial slope of the isotherm and its curvature. This can be overcome by the Toth isotherm model (Toth, 1971) (Eq. 2.42) ... 

The fact that experimental adsorption data fit the Langmuir equation does not mean that the assumptions on which the Langmuir model is based are fulfilled. In the case of surfactants, these assumptions, particularly the absence of lateral interactions, are almost never valid. In spite of this, many surfactants show Langmuir-type adsorption from solution because of the mutual compensation of several factors that affect the shape of the Langmuir isotherm. Some of these factors and the manner in which they modify the shape of the isotherm are as follows (Kitchener, 1965) ... 

The kinetics of each process are determined by the slower processes (3a) and (3b). These lead to an olefin-type surface intermediate (or its precursor) via a dehydration step requiring two sites for its completion, one to accommodate the olefin-related species and one a water molecule. The requirement for a second, vacant site is characteristic of the model, leading in the case of increasing alcohol pressure to autoinhibition due to decreasing availability of vacant sites. With additional assumptions of (i) Langmuir-type adsorption isotherms for both alcohol and oxygen adsorption, and (ii) the absence of inhibition by product, rate expression (42a) was deduced for acetone formation from alcohol. 

A variant of the common Langmuir type models is obtained if it is assumed that both alkene molecules are chemisorbed (Langmuir adsorption) on the same active center. If it is further assumed that there are two different adsorption steps, the following set of reaction equations for the initial stages of the metathesis of propene is obtained ... 

Non-compliance with the simple Langmuir adsorption model is indicative of violation under experimental conditions of certain assumptions used to derive the model. Therefore, while developing the theoretical models adequately describing experimental data one usually resorts to one of two approaches either introduces the notion of a inhomogeneous surface [36, 37] or accounts for various types of interaction developing between the particles absorbed [4, 38]. 

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

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