Other chemisorption models

The dependence of the surface coverage with the heat of adsorption was accounted on two other models. The Freundlich model presents the coverage surface as  

The heat of adsorption decreases logarithmically with the surface coverage, 

Noteworthy is that despite of all limitations, the Langmuir model is used in majority for kinetic models. 

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The similarity of the results obtained for finite elusters and the infinite slab allows to eonclude in favour of the validity of the eluster model of adequate size (6 or 8 molybdenum atoms). In addition to the chemisorption of organic molecules on solid surfaces which is generally considered as a localized phenomenon, the interaction between molybdenum oxide and an adsorbate can also be represented by a loeal eomplex formed by a finite eluster and the adsorbed molecule. Indeed, the study of the evolution of the electronic properties as a funetion of the cluster size shows that, for a eluster eontaining 6 or 8 molybdenum atoms, most of the electronic properties converge towards limit values. This eonvergence is sensitive to the direction of the cluster growth. On the other hand, the electronic properties of the (001), (010) and (100) faces are not identieal, the type of surface atoms being different these results allow to predict that the characteristics of the chemisorption step will depend on the particular face on which it takes place. 

Fig. 3.3 gives a model for the adsorption states. In physical adsorption the molecule is adsorbed as such (without dissociation) the forces are of the van der Waals type. In chemisorption chemical bonds have been formed for H2 this is only possible at the cost of dissociation. In the transition state the H-atoms are bonded both to each other and to Ni-atoms in the surface of the metal crystal. 

The articles by J. R. Anderson, J. H. Sinfelt, and R. B. Moyes and P. B. Wells, on the other hand, deal with a classical field, namely hydrocarbons on metals. The pattern of modem wTork here still very much reflects the important role in the academic studies of deuterium exchange reactions and the mechanisms advanced by pioneers like Horiuti and Polanyi, the Farkas brothers, Rideal, Tw igg, H. S. Taylor, and Turkevich. Using this method, Anderson takes ultrathin metal films with their separated crystallites as idealized models for supported metal catalysts. Sinfelt is concerned with hydrogcnolysis on supported metals and relates the activity to the percentage d character of the metallic bond. Moyes and Wells deal with the modes of chemisorption of benzene, drawing on the results of physical techniques and the ideas of the organometallic chemists in their discussions. 

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

The only other effect of chemisorption included in the model is the modification of the surface CP from as to ac (while 07 is assumed to be unchanged). One possible effect not included is that of chemisorption-induced changes in the concentrations cs and q, (see, e.g., Modrak 1997) - although potentially important, for simplicity, we ignore this phenomenon. 

By considering the extreme case of a crystal completely covered by a layer of foreign atoms, we have already seen in Sec. III,B that, if chemisorption involves the formation of localized electron pair bonds, some interesting interaction effects are to be expected. In this section, we approach the problem from the other extreme by considering just two atoms chemisorbed on a crystal surface. If the localized level formed by the interaction does not lie too far below the normal crystal band (or any surface band), the wave function for the localized level is damped only slowly in the crystal. Therefore, two chemisorbed atoms will be in interaction at distances when the interaction between the isolated atoms would be entirely negligible. To investigate this effect, we take the simplest model which may be expected to yield useful results 11). The crystal is represented by a straight... 

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. 

The frozen in photoconductivity, as was concluded by Melnick, will arise from effects of the surface barrier layer or, of course, would arise similarly from any other rate-limiting process in the adsorption of oxygen. For our model in this discussion we shall use electron transfer over the surface barrier as the rate-limiting reaction. In this case, the rate at which adsorption occurs is proportional to exp ( —Ei/kT), where E2 is the barrier height. Thus if we measure the decay in photoconductivity (the chemisorption of oxygen) at room temperature, and then suddenly quench the sample to 130°K, it is obvious that the rate of decay in photoconductivity will decrease considerably. The change in the rate will be dependent on Ei and the temperature to which the sample is quenched. 

As has been discussed above, knowledge of the dispersion of the catalyst is extremely difficult to obtain, especially in the promoted systems. This is the main obstacle to clear differentiation between the promoter models proposed and remains so today. Chemisorption techniques to count the active sites present on the sulfided surfaces have had limited success. 02 chemisorption has been associated with edge vacancies (active sites) on pure M0S2 (100). However, the same authors showed that it was impossible to correlate activity and amount of 02 chemisorbed on Co- or Ni-promoted molybdenum sulfide (101). The use of other test molecules was disputable, particularly NO, which can strongly modify the structure of the surface during the measurement (102). 

The flat model requires the introduction of an energy either of physical adsorption or of chemisorption by the formation of a a bond. The other models require the introduction of the resonance of the 77 electrons. Thus we obtain a conjugated model if the metal atoms are in the plane of the ethylene molecule. We obtain... 

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