Sabatier Principle — Volcano Plot

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. 

For practical heterogeneous catalyst kinetics this principle has the following consequence. Usually, the assumption of a homogeneous surface is not valid. It would be more realistic to assume the existence of a certain distribution in the activity of the sites. From the above, certain sites will, however, contribute most to the reaction, since these sites activate the reactants most optimally. This might result in an apparently uniform reaction behaviour, and can explain why Langmuir adsorption often provides a good basis for the reaction rate description. This also implies that adsorption equilibrium constants determined from adsorption experiments can only be used in kinetic expressions when coverage dependence is explicitly included otherwise they have to be extracted from the rate data. 

In this respect it can be mentioned that several authors have derived rate expressions for non-uniform surfaces. In Ref. [4], Boudart and Djega-Mariadassou 

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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.

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,...

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]. 

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 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]. 

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