Volcano plots

FIGURE 6.8 Volcano plot for the hydrogen evolution electrochemical reaction showing the exchange current density vs. M-H bond energy. (Adapted from Trasatti, S., J. Electroanal. 

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Figure 6.3. Examples for the four types of global electrochemical promotion behaviour (a) electrophobic, (b) electrophilic, (c) volcano-type, (d) inverted volcano-type, (a) Effect of catalyst potential and work function change (vs I = 0) for high (20 1) and (40 1) CH4 to 02 feed ratios, Pt/YSZH (b) Effect of catalyst potential on the rate enhancement ratio for the rate of NO reduction by C2H4 consumption on Pt/YSZ15 (c) NEMCA generated volcano plots during CO oxidation on Pt/YSZ16 (d) Effect of dimensionless catalyst potential on the rate constant of H2CO formation, Pt/YSZ.17 n=FUWR/RT (=A(D/kbT).

Figure 8.29. NEMCA-generated volcano plots obtained by increasing the catalyst work function above its open-circuit value during CO oxidation on Pt pCo=0.2 kPa, Po2=t 1 kPa, , T=560°C, r0= 1.5x1 O 9 mol O/s O, T=538°C ro=0.9xl0 9 mol O/s.36 Reprinted by permission of Platinum Metals Review.

Lambert and coworkers,7 18 25 who were first to study this interesting system, have shown that the nature of the anion (nitrate or carbonate) formed on the catalyst surface in presence ofNa+ plays an important role in the sharpness of the volcano plot obtained upon varying Uwr.-... 

A very useful analysis of catalytic reactions is provided for by the construction of so-caUed volcano plots (Figure 1.2). In a volcano plot, the catalytic rate of a reaction normahzed per unit reactive surface area is plotted as a function of the adsorption energy of the reactant, product molecule, or reaction intermediates. 

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 8.25. Predicted volcano plots for ammonia synthesis, showing the turnover frequency versus the relative bonding strength of N atoms to the surface for ammonia concentrations of 5%, 20%, and 90%. The left-hand panel corresponds to conditions of...

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 critical role of the M/M—OH redox system in determining the population of the surface active metal sites is, with high probability, the actual reason for the strong predictive power of the M—Ox bond strength with regard to the relative rates of ORR at different metal surfaces. In fact, a better presentation of the volcano plot would be obtained by using, for the ordinate of the plot the value (1 /Z + 1) exp(— /RT),... 

For the ascending branch of the volcano plot, the term (1/Z + 1) could serve by itself as an effective ORR activity predictor, whereas, for the descending branch, (1/Z + 1) becomes close to unity at 0.85 V, and the exponential factor exp(—A//, /R70, then determines the ORR rate based on the residual interaction of dioxygen with the (excessively) noble metal catalyst surface. 

The expression (1/Z+ 1)] exp[— AHl /RT] at 0.85 V, better reflects the reality of a partially oxidized Pt surface and the critical effect of active site availability on the rate of the ORR. Effects of site availability were not considered in the calculations in Nprskov et al. [2004] of ORR activity for various metals. The expression used to calculate activity defined the ordinate parameter in the ORR volcano plots presented. This parameter was defined in Nprskov et al. [2004] as kT min,- log(k,/ko). 

Figure 3.16 Volcano plot for the hydrogen evolution reaction (HER) for various pure metals and metal overlayers. Values are calculated at 1 barof H2 (298K) and at a surface hydrogen coverage of either 0.25 or 0.33 ML. The two curved lines correspond to the model (3.24), (3.25) transfer coefficients (not included in the indicated equations) of 0.5 and 1.0, respectively, have also been added to the model predictions in the figure. The current values for specific metals are taken from experimental data on polycrystalline pure metals, single-crystal pure metals, and single-crystal Pd overlayers on various substrates. Adapted from [Greeley et al., 2006a] see this reference for more details.

DFT-calculated a familiar volcano plot emerges (Fig. 9.14). Like the Pt3Co alloy... 

Logadottir A, Rod TH, N0rskov JK, Hammer B, Dahl S, Jacobsen CJH. 2001. The Br0nsted-Evans-Polanyi relation and the volcano plot for ammonia synthesis over transition metal catalysts. J Catal 197 229. 

Figure 20.7 Volcano plot showing fold change versus f-test p value of eight runs of yeast cell lysates, four runs of aerobically grown yeast and four runs of anaerobically grown yeast. Reproduced with permission from Reference 16.

No catalyst has an infinite lifetime. The accepted view of a catalytic cycle is that it proceeds via a series of reactive species, be they transient transition state type structures or relatively more stable intermediates. Reaction of such intermediates with either excess ligand or substrate can give rise to very stable complexes that are kinetically incompetent of sustaining catalysis. The textbook example of this is triphenylphosphine modified rhodium hydroformylation, where a plot of activity versus ligand metal ratio shows the classical volcano plot whereby activity reaches a peak at a certain ratio but then falls off rapidly in the presence of excess phosphine, see Figure... 

Of course, changing the electrode material entails more than just changing the adsorption energy, so we cannot expect more than a rough correlation. Nevertheless, volcano plots are observed for several reactions involving adsorbed intermediates. 

FIGURE9.t. Volcano Plot of formic acid decomposition. Abscissa Calculated A HadsofHCOOH Ordinate Temperature at which rate of HCOOH decomposition reaches the same value for all metals. 

For the metals on the left leg of the volcano plot, an increase of the heat of adsorption will ensue enhanced catalytic activity. This consequence applies most obviously to gold which in its standard state is a poor catalyst because heats of adsorption of most molecules are very low on gold. Indeed, Hamta and other authors confirmed that gold becomes very active when present as nanoparticles. 

Fig. 20. The volcano plot for HCOOH decomposition on high surface area catalysts ( ) and single crystals ( ) (102a). Reprinted with permission of North-Holland Publishing Company, Amsterdam, 1979.

From the comparison of calculated oxygen and OH adsorption energies to M(lll) versus activity of the metals toward O2 reduction, a peak shaped curve is obtained, Pt being situated almost on top of the volcano plot [63] palladium and platinum activities should be quite close. The relation between the amount of adsorbed oxygen and the number of unpaired d electrons of the metal had been mentioned earlier [48]. 

Figure 4.37. Variation of volcano plots with the molecular precursor adsorption energy.

Several important conclusions can be drawn from Figure 4.38. It appears that in general a simple catalytic reaction, which includes the dissociation of a diatomic molecule, will have this dissociation as the rate-determining step, when the reaction takes place under conditions close to equilibrium. This agrees well with the ammonia synthesis being dissociation rate-determined, as this process is the prototype of an equilibrium-limited reaction [128]. When the reaction is taking place far from equilibrium, the actual approach to equilibrium becomes unimportant, and the volcano plot very closely follows the volcano defined by the minimum value among the maximal possible rates for all reaction steps. 

For the hydrogen electrode reaction (HER) on different metals, it is predicted that the curve log ja vs. AG ds has a maximum with log j0 decreasing both at positive and negative values of AGads. This is due to the opposite effects of the free energy of adsorption on the geometric and exponential factors in the electrokinetic equation (volcano plots). 

Figure 2.15 Examples of volcano plots, describing the reaction rate as a function ofthe heat of adsorption (left), and the activity of the second-row and third-row transition metal sulfides in the hydrodesulfurization of dibenzothiophene (right).

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