Sabatier-Volcano Principle

Since the ORR is a surface reaction that involves adsorbed intermediates, it is subdued to the Sabatier-volcano principle of heterogeneous catalysis (Balandin, 1969 Sabatier, 1920). This principle states that in order for a catalyzed surface reaction to proceed, some bonding of adsorbed intermediate(s) is necessary, whereas a bonding that is too strong will block the surface and slow down the reaction. Several examples of reactions in heterogeneous catalysis and electrochemistry that obey these principles are discussed by Parsons (2011). 

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 interpretation of CV data is ambiguous. However, if complemented with data from surface microscopy, x-ray absorption. Auger or photoelectron spectroscopy, and mass-sensitive techniques using electrochemical quartz crystal nanobalance (EQCN), 

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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. 

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,...

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. 

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]. 

The Sabatier analysis can in principle be performed for any reaction. In case that there are more than two reaction steps, the Sabatier volcano could be constructed in analogy to Equation (7.16) by assuming that all intermediates that go in the forward direction have optimal coverages and by calculating the approach to equihbrium for each forward rate from the given approach to equilibrium for the overall reaction (as done in Eq. 7.8 for the reaction earher) under the assumption that all other partial reactions are in equihbrium. This wiU give a first approximation to each forward rate of the reaction. The Sabatier volcano provides an upper limit to the total rate by setting this rate equal to the minimum of all forward rates ... 

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. 

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.

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). 

We have summarized these developments in two recent papers the first addresses the topic of structure sensitivity in combination with BEP relationships (14) and the second addresses the Sabatier principle (27). Sabatier-type volcano relationships can be deduced for activity as a function of adsorption energy, and they can also be used to predict trends regarding deactivation of Fischer-Tropsch catalysts by C—C recombination reactions (28). We refer to these texts as background information to the material presented here. 

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. 

The Sabatier principle of catalysis also finds extensive application in the area of electrocatalysis reactants should be moderately adsorbed on the catalyst/electro-catalyst surface. Very weak or very strong adsorption leads to low electrocatalytic activity. This has been demonstrated repeatedly in the literature by the use of volcano plots (Figs 23-25). In these plots, the electrocatalytic activity is plotted as a function of the adsorption energy of the key reactant or some other parameter related to it in a linear or near-linear fashion, such as the work function of the metal [5], or the metal—H bond strength when discussing the H2 evolution reaction (Fig. 24) [54] or the enthalpy of the lower-to-higher oxide transition when examining the O2 evolution reaction (Fig. 25) [55]. 

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