The principle of Sabatier

This plot is, for obvious reasons, called a volcano curve and the principle that the points will fall on a smooth curve is called the principle of Sabatier... 

The above conclusion, based on a simplified model, must be considered in the light of the experimental results, according to the above conclusion that an iron catalyst for ammonia synthesis is about half-covered with nitrogen during the steady state reaction. Another way to look at these results is to consider them as expressions of the principle of Sabatier, who considered that the optimum catalyst was capable of adsorbing an intermediate compound sufficiently, but not to stably. 

The key step in the synthesis of NH3 form N2 + 3H2 is to dissociate the N-N triple bond in the N2 molecule. The direct gas phase reaction would involve extremely endothermic and exothermic reactions. The resulting activation energies would be prohibitively high according to the principle of Sabatier. 

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.

Thus, according to Sabatier the hydrogenations of olefins and ketones are the same type of reaction, while according to the multiplet classification these two reactions are of different types, and indeed, the two reaction types require two different catalysts. Naturally, in the application of a given classification the thermodynamic nature of the reactions should be taken into account as well as their structural aspects. This classification and thermodynamic requirements do not yet deal with the kinetics of processes. The latter is involved in the principles of structural and energetic correspondence of the multiplet theory. 

Irrespective of the microscopic mechanism, a four-electron process must involve the breaking of an 0-0 bond and the formation of O-H bonds [17]. Surfaces that strongly bind an adsorbate tend to enhance the kinetics of bond-breaking steps. On the other hand, surfaces that bind species weakly tend to facilitate the kinetics of bond-making steps. Hence, according to principle of Sabatier [18], the catalyst which strikes the best balance between O2 adsorption and ORR intermediates removal will be the most active for ORR. 

The palladium clusters and islands, which we examined in Section 1.5, show another important property of a good catalyst They have various adsorption sites for hydrogen with different adsorption energies, so that the reaction can pass through those sites whose energy is optimal in the sense of Sabatier s principle. They are therefore more active than a monolayer of Pd on Ah(lll), which offers only two sites, neither of which has the optimum energy. 

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. 

Hence, we intuitively feel that the successful combination of catalyst and reaction is that in which the interaction between catalyst and reacting species is not too weak, but also not too strong. This is a loosely formulated version of Sabatier s Principle, which we encounter in a more precise form in Chapter 2 and in detail in Section 6.5.3.5. 

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. 

Identification of such universal relations between activation energies and heats of adsorption for particular classes of reaction can be seen as a more precise and more quantitative formulation of Sabatier s Principle. It is promising tool in the search for new materials on the basis of optimized interaction strength between relevant intermediates and the surface. 

The curve is a graphical representation of the Sabatier principle according to which the best catalysts are those adsorbing relevant species neither too weakly nor too strongly. Volcano curves are known also for catalytic reactions (on the other hand the principles are precisely the same), the only difference being that they are called Balandin curves. 

It is intriguing that analysis of the volcano curve predicts that the apex of the curve occurs at AH(H2)ads = 0 (formally, AG = 0) [26]. This value corresponds to the condition D(M-H) = 1/2D(H-H), that is, forming an M-H bond has the same energetic probability as forming an H2 molecule. This condition is that expressed qualitatively by the Sabatier principle of catalysis and corresponds to the situation of maximum electrocatalytic activity. Interestingly, the experimental picture shows that the group of precious transition metals lies dose to the apex of the curve, with Pt in a dominant position. It is a fact that Pt is the best catalyst for electrochemical H2 evolution however, its use is made impractical by its cost. On the other hand, Pt is the best electrocatalyst on the basis of electronic factors only, other conditions being the same. 

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. 

Early in the last century, Paul Sabatier1 pointed out A most important property of an excellent catalyst is that it has an ability to bind many molecules but not too strongly . This Sabatier s principle is also the principle for how an excellent catalyst for electrochemical reactions works. In electrochemical terms, an active... 

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. 

Sabatier s principle of the optimum site activity. Only optimum sites contribute to the reaction, resulting in an apparently uniform behaviour... 

These relationships, when incorporated into microkinetics models of catalytic reaction cycles, enable remarkable new predictive insights into the control of heterogeneously catalyzed reactions. Predictive models of catalytic activity as a function of catalyst composition as well as reaction conditiorvs have been constructed (22-24). The resultant volcano curves can be considered to be an application of the Sabatier principle (25,26). 

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