Sabatier volcano-curve

The occurrence of a compensation effect can be readily deduced from Eqs. (1.6) and (1.7). The physical basis of the compensation effect is similar to that of the Sabatier volcano curve. When reaction conditions or catalytic reactivity of a surface changes, the surface coverage of the catalyst is modified. This change in surface coverage changes the rate through change in the reaction order of a reaction. 

Figure 4.38. Sabatier volcano-curve The limiting case of the exact numerical solution of the microkinetic Model 1.

For the general case, the limiting Sabatier Volcano-Curve can be defined as ... 

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. 

We now investigate the dependence of the methanation rate rcn defined in Equation (1), on AEg. In Figure 2, the dependence of rcn on X is illusfrafed schematically. A volcano-t)q)e dependence on X is found. The maximum of the Sabatier volcano curve is located at... 

A schematic Sabatier-volcano curve for the ORR is shown in Figure 3.20. It illustrates the negative net activation potential of the ORR, as a function of... 

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. 

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... 

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). 

FIGURE 2 Schematic representation of normalized methanation rate rcH, as a function of X. The Sabatier maximum in the volcano curve results from the competition between the increase in rate of Cf hydrogenation and the decrease of 6 when X increases. Adapted from Ref (53). 

This apparent optimum situation for oxidoreductases or transport (corroborated by model complex studies each) markedly differs from that for hydro-lase/phosphatase activity (organophosphate cleavage Wagner-Jauregg et al. 1955) or for autocatalytic peptide formation associated with Cu(II) (Le Son et al. 1998), the first akin to Sabatier- or volcano-curve... 

In recent years, the Sabatier-volcano principle and the theoretical methodology based thereon have been developed into a practical approach of catalyst screening. Adsorption energies of reaction intermediates can be readily calculated with DFT methods. These calculations allow predictions on the reactivity to be made, which can be compared with experimental activity studies. Several studies have demonstrated an agreement between predicted volcano curves and measured surface reactivities (Greeley et al., 2009 Nprskov et al., 2004). 

The catalytic reactivity of a material can be described by Sabatier s principle [41, 87], It states, that catalytic reactions proceed best if the interaction between reactant/adsorbate and surface is neither too strong, nor too weak ° thus the optimum reactivity is related to the heat of adsorption. Sabatier s principle is reflected in volcano curves [88], where the reactivity of different elements towards a particular reaction is plotted as a function of its position in the periodic table, and thus its elec-tron(ic) configuration [87]. As a result of experimental and theoretical observations plotted as volcano curves, often Pt turns out to be the optimum catalyst material [89]. This is the reason for the choice of Pt in this thesis with respect to CO oxidation [1, 20] and for the hydrogenation of ethene [21, 35], where Pt is known to be ideal. The optimum reactivity of Pt (compared to other al-metals) is further well described using the popular d -band model [18-21]. The model describes trends in the interaction between an adsorbate and a fil-metal surface to be governed by the coupling to the metal rf-bands [90]. 

Comparison of the volcano curves obtained from a Sabatier analysis and full microkinetic models at different approaches to equilibrium y. Reprinted from T. Bligaard, et al., J. Catal., 2004, 224, 206-217 with permission from Elsevier. ... 

We have already performed a preliminary Sabatier analysis of the CO oxidation reaction in Section 1.5.2, and derived an analytic solution under the assumption that the adsorption of CO and O2 are quasi-equilibrated in Section 1.6. Now we will formulate a numerical solution to the complete microkinetic model as a function of the descriptors AEco and AEq- We will analyze the reaction mechanism in terms of rate and catalyst control, and at the end of this section, the effect of high surface coverages on the volcano curve will also be briefly addressed. 

Figure 9.7. The hydrodesulfurization activity oftransition metal sulfides obeys Sabatier s principle (Section 6.5.3.5) the curve is a so-called volcano plot. [Adapted from T.A. Pecoraro and R.R. Chianelli.J, Catal. 67 (1981) 430 P.Raybaud,). Hafner, G. Kresse,...

Sabatier and Balandin had predicted a relationship between catal)dic activity and heat of adsorption. If a solid adsorbs the reactants only weakly, it will be a poor catalyst, but if it holds reactants, intermediates or products too strongly, it wiU again perform poorly. The ideal catalyst for a given reaction was predicted to be a compromise between too weak and too strong chemisorption. Balandin transformed this concept to a semiquantitative theory by predicting that a plot of the reaction rate of a catal)Tic reaction as a function of the heat of adsorption of the reactant should have a sharp maximum. He called these plots volcano-shaped curvesl This prediction was confirmed by Fahrenfort et al." An example of their volcano-shaped curve is reproduced in Fig. 9.1. They chose the catalytic decomposition of formic acid... 

The magnitude of adsorption heat corresponds to the strength of adsorption bond, and so there should also be some relationship between adsorption and catalytic activity. The catal3dic activity is reversely proportional to adsorption strength when the surface coverage of reaction molecule reaches certain level, as indicated by Sabatier s theory of intermediate complex and experience. On the other hand, if adsorption is too weak, it is difficult to activate adsorbed molecules. The best activity can be obtained only in the case with suitable adsorption strength. This relationship is usually called as a volcano type curve, as shown in Fig. 2.4. 

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