The turnover frequency

The turnover frequency (TOP) based on surface-exposed atoms significantly increases with a decrease in the diameter of the gold particle from 5 nm [66]. This feature is unique to gold, because other noble metals usually show TOFs that decrease or remain the same with a decrease in the diameter [7]. The decrease in particle size gives rise to an increase in corner or edge and perimeter of NPs and change in electronic structure however, the origin of size effects on catalytic activity for CO oxidation is not clear. 

The propane aromatization was conducted under the differential condition by using Ga203/Ga-MOR catalysts thus characterized. The contributions of L, HI, and H2 sites to the propane conversion and the aromatics formation were estimated by assuming that the observed reaction rates are the sum of the reaction rate on each site which is equal to the product of the turnover frequency (TFij) and the amount of active sites per weight of catalyst (Aj) ... 

Before deriving the rate equations, we first need to think about the dimensions of the rates. As heterogeneous catalysis involves reactants and products in the three-dimensional space of gases or liquids, but with intermediates on a two-dimensional surface we cannot simply use concentrations as in the case of uncatalyzed reactions. Our choice throughout this book will be to express the macroscopic rate of a catalytic reaction in moles per unit of time. In addition, we will use the microscopic concept of turnover frequency, defined as the number of molecules converted per active site and per unit of time. The macroscopic rate can be seen as a characteristic activity per weight or per volume unit of catalyst in all its complexity with regard to shape, composition, etc., whereas the turnover frequency is a measure of the intrinsic activity of a catalytic site. 

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

Obtain meaningful data on the catalyst Usually for kinetic purposes is it the turnover frequency per active site (TOP) that of interest. But other parameters such as selectivity and yield are also of great importance for judging the potential of the catalyst. Instead of expressing the activity as a turnover frequency, it can also be given in terms of ... 

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...

CO oxidation is often quoted as a structure-insensitive reaction, implying that the turnover frequency on a certain metal is the same for every type of site, or for every crystallographic surface plane. Figure 10.7 shows that the rates on Rh(lll) and Rh(llO) are indeed similar on the low-temperature side of the maximum, but that they differ at higher temperatures. This is because on the low-temperature side the surface is mainly covered by CO. Hence the rate at which the reaction produces CO2 becomes determined by the probability that CO desorbs to release sites for the oxygen. As the heats of adsorption of CO on the two surfaces are very similar, the resulting rates for CO oxidation are very similar for the two surfaces. However, at temperatures where the CO adsorption-desorption equilibrium lies more towards the gas phase, the surface reaction between O and CO determines the rate, and here the two rhodium surfaces show a difference (Fig. 10.7). The apparent structure insensitivity of the CO oxidation appears to be a coincidence that is not necessarily caused by equality of sites or ensembles thereof on the different surfaces. 

These three steps account for the -60 mV/pH dependence of the turnover frequency at the potential-dependent part of the catal lc curve... 

The low limit on the rate constant fehetero of 0-0 bond heterolysis in the putative ferric-hydroperoxo intermediate by analyzing the turnover frequency of H2O2 reduction at potentials 0.6-0.4 V (vs. NHE at pH 7). 

Only three steps of the proposed mechanism (Fig. 18.20) could not be carried out individually under stoichiometric conditions. At pH 7 and the potential-dependent part of the catalytic wave (>150 mV vs. NHE), the —30 mV/pH dependence of the turnover frequency was observed for both Ee/Cu and Cu-free (Fe-only) forms of catalysts 2, and therefore it requires two reversible electron transfer steps prior to the turnover-determining step (TDS) and one proton transfer step either prior to the TDS or as the TDS. Under these conditions, the resting state of the catalyst was determined to be ferric-aqua/Cu which was in a rapid equilibrium with the fully reduced ferrous-aqua/Cu form (the Fe - and potentials were measured to be within < 20 mV of each other, as they are in cytochrome c oxidase, resulting in a two-electron redox equilibrium). This first redox equilibrium is biased toward the catalytically inactive fully oxidized state at potentials >0.1 V, and therefore it controls the molar fraction of the catalytically active metalloporphyrin. The fully reduced ferrous-aqua/Cu form is also in a rapid equilibrium with the catalytically active 5-coordinate ferrous porphyrin. As a result of these two equilibria, at 150 mV (vs. NHE), only <0.1%... 

Figure 3.9. Transient C02 formation rates on Pd30 (a) and Pd8 (b) mass-selected clusters deposited on a MgO(lOO) film at different reaction temperatures [74]. In these experiments CO was dosed from the gas background while NO was dosed via a pulsed nozzle molecular beam source. The turnover frequencies (TOFs) calculated from the experiments displayed in (a) and (b) are displayed in the last panel (c). C02 formation starts at lower temperatures but reaches lower maximum rates on the larger cluster. (Figure provided by Professor Heiz and reproduced with permission from Elsevier, Copyright 2005).

The high sensitivity of the reaction to particle size of Rh is confirmed at 230°C, in a mixture of 0.5% NO+1% CO, the turnover frequency increases from 0.017 s-1 for a highly dispersed catalyst to 0.74 s 1 for a catalyst dispersed at 1.7%, the activity per metal site on unsupported Rh catalysts being still much higher. 

There is mounting evidence to suggest that water effects during FTS may also be linked to Co particle size, as determined by the support interaction [18,19], even though the turnover frequencies of CO over the surface Co metal atoms on... 

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