Volcano-curves

Microkinetic Expressions Derivation of Volcano Curve 9 A closed expression for 9c can be deduced ... 

The controlling parameters that determine the volcano curve are the BEP constants kdiss and tH. It is exclusively determined by the value of p. It expresses the compromise of the opposing elementary rate events dissociation versus product... 

Figure 1.9 Volcano curve dependence of rate of methanation, R, on Eads (schematic).

The volcano curve is bounded by the rate of dissociative adsorption of CO and hydrogenation of adsorbed carbon. This is illustrated in Figure 1.9. 

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. 

As the adsorption of hydrogen is rather weak, the corresponding term in the denominator may be omitted. The rate expression shows that the reaction is suppressed by H2S. Hence, the most active catalysts (which appear at the top of the volcano curve of Fig. 9.7)... 

Bligaard T, Nprskov JK, Dahl S, Matthiesen J, Chistensen CH, Sehested J. 2004. The Br0nsted-Evans-Polanyi relation and the volcano curve in heterogeneous catalysis. J Catal 224 206-217. 

It has been predicted that a Pd skin on a PdsFe core would sit close to the top of the activity/O binding energy "volcano" curve and thus have significantly higher activity than Pt and Pt/Pd core-shell materials. If these materials could be shown to be stable to long-term PEM conditions, then these could represent viable replacements for Pt. As with other alternative non-Pt catalysts, very few stability studies have been reported. 

The outcome (Figure 7.5) is a so-called volcano curve, where poor catalysts are located on the extreme left-hand side, strong catalysts are located in the extreme right-hand side and moderate catalysts are placed around the apex of the curve. 

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. 

Volcano curves lay down the grounds for a predictive tool in electrocatalysis. 

One definite problem in establishing a volcano curve is the actual values of the quantity D(M-B), which is seldom known for conditions resembling those relevant to an electrode reaction. As illustrated later, this issue is approached case by case, depending on the nature of the electrode reaction. 

A complete theory of electrocatalysis leading to volcano curves has been developed only for the process of hydrogen evolution and can be found in a seminal paper by Parsons in 1958 [26]. The approach has shown that a volcano curve results irrespective of the nature of the rate-determining step, although the slope of the branches of the volcano may depend on the details of the reaction mechanism. 

Figure 7.5 Sketch of the dependence of the electrocatalytic activity on the intermediate adsorption bond strength (volcano curve).

Most transition metals (for Fe, Co and Ni see the following paragraphs) are located on the descending branch of the volcano curve. For these metals, the adsorption of H is strong and 5h close to saturation, making H2 desorption from the surface difficult. For these metals, the inhibiting effect of 5h prevails over the... 

Figure 7.6 Experimental volcano curve for H2 evolution on metals. M-H bond strength from overpotential data. Adapted from Ref [28].

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. 

The apparently contradictory behavior of Fe, Co and Ni is in fact explained by their ability to absorb atomic hydrogen, which reduces the strength of H adsorption. The shift of Fe, Co and Ni from the descending to the ascending branch of the volcano curve indicates that D(M-H) > V2l3(H-H) in the gas phase but < /2D(H-H) in solution under H2 evolution. These phenomena of H absorption are presumably responsible for the time-dependent properties of some electrodes during H2 discharge. 

If OHads is adsorbed strongly, its formation is fast and successive steps of OHads desorption become rate determining. Under similar conditions, the Tafel slope is lower and electrode materials are electrocatalytically more active. Along the same conceptual lines of volcano curves, if the adsorption of OHads is too strong, its removal becomes very difficult and the overpotential increases again. Thus, in principle, a volcano curve should be expected as in the case of H2 evolution. 

The name of the mechanism comes from the chemical formation of a surface oxide. Thus step (7.26) is a chemical step and the mechanism can be written as EEC if step (7.26) is rate determining, thus predicting a Tafel slope of 30 mV for low OHads coverage (i.e. on the ascending branch of the volcano curve). Should step (7.27) be rate determining, the mechanism would be EEEEC with a predicted Tafel slope of 15 mV. Unfortunately, an electrode exhibiting such a low Tafel slope has never been observed, so that so an active material still remains a dream. 

Trasatti, S. (2003) Adsorption - volcano curves, in Handbook of Fuel Cells -Fundamentals, Technology and Applications, Vol. 2, Part 2 (eds W. Vielstich, A. Lamm and H.A. Gasteiger), John Wiley Sons, Ltd, Chichester. 

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... 

To analytically determine such volcano curves for the simple model reaction, we need to make some further assumptions (the assumptions are realistic at least for the case of NH3 synthesis) ... 

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. 

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