Rate Sabatier principle

A catalytic reaction is composed of several reaction steps. Molecules have to adsorb to the catalyst and become activated, and product molecules have to desorb. The catalytic reaction is a reaction cycle of elementary reaction steps. The catalytic center is regenerated after reaction. This is the basis of the key molecular principle of catalysis the Sabatier principle. According to this principle, the rate of a catalytic reaction has a maximum when the rate of activation and the rate of product desorption balance. 

A volcano plot correlates a kinetic parameter, such as the activation energy, with a thermodynamic parameter, such as the adsorption energy. The maximum in the volcano plot corresponds to the Sabatier principle maximum, where the rate of activation of reactant molecules and the desorption of product molecules balance. 

The Sabatier principle deals with the relation between catalytic reaction rate and adsorption energies of surface reaction intermediates. A very useful relation often... 

Figure 1.2 Volcano plot illustrating the Sabatier principle. Catalytic rate is maximum at optimum adsorption strength. On the left of the Sabatier maximum, rate has a positive order in reactant concentration, and on the right of Sabatier maximum the rate has a negative order.

Here max Rt is the maximal rate of reaction step i, which is calculated by assuming optimal coverages for that reaction step. This (usually multi-dimensional) volcano-curve we shall refer to as the Sabatier volcano-curve, as it is intimately linked to the original Sabatier principle [132,133]. This principle states that desorption from a reactive metal catalyst is slow and will increase on less reactive metals. On very noble metals the large energy barrier for dissociation will, however decrease the dissociation rate. The best catalyst must be a compromise between the two extremes. As has been shown above, this does not necessarily mean that the optimal compromise is obtained exactly where the maximal desorption and dissociation rates are competing. That is only the case far from equilibrium. Close to equilibrium the maximum will often be attained while dissociation is the rate-determining step, and the maximum of the volcano-curve will then be reached due to a lack of free sites to dissociate into. 

Clearly, an optimum for the interaction of the catalytically active surface and the adsorbates exists, resulting in a maximum for the reaction rate (the Sabatier principle). To the left of the maximum the reaction has a positive order in the reactants, whereas to the right the order has become negative. 

Figure 3.6 demonstrates on both the Pt-skin as well as Pt-skeleton surfaces the relationship between the specific activity and the d-band center position exhibits a volcano shape, with the maximum catalytic activity obtained for PtjCo. This behavior is apparently a consequence of the Sabatier principle discussed earlier, and published in many recent studies [77, 78]. For metal surfaces that bind oxygen too strongly, as in the case of Pt, the d-band center is too close to the Fermi level and the rate of the ORR is limited by the availability of spectator-free Pt sites. 

A proper kinetic description of a catalytic reaction must not only follow the formation and conversion of individual intermediates, but should also include the fimdamental steps that control the regeneration of the catalyst after each catalytic turnover. Both the catalyst sites and the surface intermediates are part of the catalytic cycle which must turn over in order for the reaction to remain catalytic. The competition between the kinetics for surface reaction and desorption steps leads to the Sabatier principle which indicates that the overall catalytic reaction rate is maximized for an optimal interaction between the substrate molecule and the catalyst surface. At an atomic level, this implies that bonds within the substrate molecule are broken whereas bonds between the substrate and the catalyst are made during the course of reaction. Similarly, as the bonds between the substrate and the surface are broken, bonds within the substrate are formed. The catalyst system regenerates itself through the desorption of products, and the self repair and reorganization of the active site and its environment after each catalytic cycle. 

Figure 2.2. Sabatier principle. Catalytic rate is a maximum at optimum adsorption strength.

In this chapter we introduced the basic physical chemistry that governs catalytic reactivity. The catalytic reaction is a cycle comprised of elementary steps including adsorption, surface reaction, desorption, and diffusion. For optimum catalytic performance, the activation of the reactant and the evolution of the product must be in direct balance. This is the heart of the Sabatier principle. Practical biological, as well as chemical, catalytic systems are often much more complex since one of the key intermediates can actually be a catalytic reagent which is generated within the reaction system. The overall catalytic system can then be thought of as nested catalytic reaction cycles. Bifunctional or multifunctional catalysts realize this by combining several catalytic reaction centers into one catalyst. Optimal catalytic performance then requires that the rates of reaction at different reaction centers be carefully tuned. 

The dependence of the overall rate of the catalytic reaction on adsorption is extremely important in analyzing the kinetics for the overall rate of a zeolite-catalyzed reaction. We have already met this subject in Chapter 2 when analyzing the basis of the Sabatier principle. A proper understanding of adsorption effects is essential for establishing a theory of zeolite catalysis that predicts the dependence of kinetics on zeolite-micropore shape and connectivity. 

Sabatier s Principle is illustrated in Fig. 6.40 where the ammonia rate is plotted for similar conditions versus the type of transition metals supported on graphite. The theory outlined so far readily explains the observed trends metals to the left of the periodic table are perfectly capable of dissociating N2 but the resulting N atoms will be bound very strongly and are therefore less reactive. The metals to the right are unable to dissociate the N2 molecule. This leads to an optimum for metals such as Fe, Ru, and Os. This type of plot is common in catalysis and is usually referred to as a volcano plot. 

This chapter proceeds with a general discussion of the overall catalytic cycle and Sabatier s principle in order to illustrate the comparison of relative kinetic and thermodynamic steps in the overall cycle. This is followed by a fundamental discussion of the intrinsic surface chemistry and the application of transition state theory to the description of the surface reactivity. We discuss the important problem of the pressure and material gap in relating intrinsic rates with overall catalytic behavior and then describe the influence of the tatic reaction environment including promoters, cluster size, support, defects, ensemble, coadsorption and stereochemistry. Lastly, we discuss the transient changes to the surface structure as well as intermediates and their influence on catalytic performance. 

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