Biographical nonuniformity

Two different assumptions are generally used for the description of the physical chemistry of the real adsorbed layers either surface sites are different or there is a mutual influence of the adsorbed species. The first case is defined as biographical nonuniformity and the second one - induced nonuniformity. On biographical nonuniform surfaces a certain distribution of properties is considered. Such nonuniformity can be either chaotic, when adsorption energy on a given site is independent on the neighbor site or discrete. Flowever, if... 

In the framework of the Temkin theory of biographically nonuniform surfaces discussed in detail in Chapter 3, we introduce X= q-qo widi its highest value =l= i- o. The value of , (equal to the AG°/RT) depends on the surface site. If the Polanyi transfer coefficient a is equal for both steps from the general expressions of the rate constants of adsorption and... 

In the instance of apriori (biographical) nonuniform surface it holds that... 

The derivation above considered a two-step sequence on biographically nonuniform surfaces and followed the treatment first developed by Temkin. For induced nonuniform surfaces the reaction rates of elementary reactions are described by eq. 3.103-3.105. These general equations which take into account all the possible lateral interactions between all the surface adsorbed species on the surface can be applied to treat the same two-step sequence. 

Similarly to the concept of the biographical nonuniform surfaces mechanism (7.97) can be used to derive a rate expression in supposition of lateral interactions. Assuming that surface species other than chemisorbed nitrogen are present on the surface in inferior quantities, which is backed by experimental evidences showing that nitrogen adsorption on iron catalysts proceeds at a rate approximately equal to that of ammonia synthesis, the equilibrium constant of step 2 in eq. (7.97) can be expressed, following the general treatment, as... 

In certain conditions the rate of the ammonia synthesis reaction in the reverse direction is very small and the overall reaction rate is determined by the ammonia synthesis rate in the forward direction. According to the conventional derivation based on the model of biographically nonuniform surfaces this rate in the forward direction is given by... 

Two different assumptions are generally used for the description of the physical chemistry of the real adsorbed layers either surface sites are different or there is a mutual influence of the adsorbed species. The first case is defined as biographical nonuniformity... 

The treatment based on the two-step sequence for nonideal surfaces originates from the complexity of deriving the expHcit form of rate equations for other reaction mechanisms on biographical nonuniform surfaces. At the same time, models based on lateral interactions have no restrictions from this point of view, as the impHcit form can be and is used for the data fitting. At the same time, it should be noted that there are certain numerical challenges related to kinetic modehng on induced nonuniform surfaces with lateral interactions. 

Thus for a case of nonuniform surfaces (eg, lateral interactions in the adsorbed layer), the equilibrium constant for the reaction route is expressed with a classical equation for the equilibrium constant, which is determined as the ratio of constants of the forward and reverse reactions. These constants do not include the lateral interactions in the adsorbed layer, hence analysis of the kinetic parameters in terms of their thermodynamic consistency can be also performed for reaction mechanisms with empty routes independent of the presence of lateral interactions. The same conclusion is vaHd for intrinsically inhomogeneous surfaces (so-called biographical nonuniformity), where the rate is obtained by summation of rates on active catalytic centers with different affinity to reactants and products. At the same time, the equihbrium constant is equal to unity in case of empty routes for each and every site. 

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