Dissociation chemisorption energies

As a first example of the use of the d band model, consider the trends in dissociative chemisorption energies for atomic oxygen on a series of 4d transition metals (Figure 4.6). Both experiment and DFT calculations show that the bonding becomes... 

Dissociative chemisorption energies calculated by density functional theory for various molecules on a number of stepped transition metal surfaces. All values are given in eV per molecule. Positive and negative values signify endothermal and exothermal chemisorption reactions, respectively. 

The microkinetic models in this section are built upon BEP-relations of the type described above. It will be shown that an underlying BEP-relation in general leads to the existence of a volcano relation. We shall also use the microkinetic models in combination with the universal BEP-relation to explain why good catalysts for a long range of reactions lie in a surprisingly narrow interval of dissociative chemisorption energies. 

In the other cases discussed above, the optimal catalyst is relatively close to the narrow region of dissociative chemisorption energies from —2 to — leV. It does, however, appear that the models developed so far could also have a problem describing why some high temperature and very exothermic reactions (with corresponding small approaches to equilibrium) also lie within the narrow window of chemisorption energies. To remove these discrepancies we shall relax the assumption of one rate-determining step, but retain an analytic model, by use of a least upper bound approach. 

Figure 4.45. Pareto plot of interpolated catalysts predicted to be good compromises with respect to cost and activity for methanation. The positions of the interpolated catalysts are determined by the cost of their constituent elements vs. their distance from the optimal dissociative chemisorption energy for CO with respect to the experimentally observed optimum (see Figure 4.44 right-bottom). Adapted from Ref. [55].

The slopes of these relations depend on the reaction studied. For dissociative adsorption processes involving simple diatomic molecules, the slope of the transition state energy as function of the dissociative chemisorption energy is often close to 1. This implies that the electronic structure of the transition state is similar to that of the final state, and hence, it is indicative of a late tfansition state. This behavior can be observed directly in the transition state structures for NO dissociation, as is shown in Figure 6.8b. 

It turns out that if one compares dissociation of a number of similar molecules, their transition state energy scale with the dissociative chemisorption energy in much the same way (see Fig. 6.9). This is a remarkable result indicating that the nature of the relationship between the final state and the transition state for dissociation of these molecules is quite similar. In fact, for the large number of systems considered in Figure 6.9, essentially, all transition states look the same for a given surface structure. 

The slopes of the relations are very similar and close to one, showing that the transition states of the reactants considered indeed are very final state like. The intercepts are different, and this difference identifies the structure dependence of the relations showing that for a given value of the dissociative chemisorption energy, over a range of relevant energies, the stepped surfaces have barriers that are much less than on the close-packed surfaces. 

FIGURE 7.8 Turnover frequency (TOP) of ammonia synthesis as a function of the dissociative chemisorption energy of nitrogen. Top panel Experimental data from Aika et al. (1973). Middle panel Result of the microkinetic model for stepped metal surfaces (blue Une). Reaction conditions are 673 K, 100 bar, Hj N2 ratio of 3 1, and y = 0.1. The effect of potassium promotion has been included (red Une). Effects of promotion will be discussed in Chapter 12. Lower panel Microkinetic model using a two-site model for the adsorption of intermediates. Adapted from Vojvodic et al. (2014). 

By choosing these particular BEP relations to estimate the activation barriers for steps (1) and (2), we have implicitly determined the reactivity descriptor for this reaction. Both barriers depend only on A j, which is the dissociative chemisorption energy of nitrogen, A n-... 

Table 1.1 Excerpt of the periodic table with dissociative chemisorption energies of N2 (AIJn) given in eV. Reprinted from T. BUgaard, et ai, J. Catal, 2004,224,206-217 with permission from Elsevier. ...

---