Site Specific Turnover Frequencies

It was mentioned previously that the rate of a heterogeneously catalyzed reaction is expressed as a turnover frequency (TOF) which is the number of times an active site reacts per unit time. Since active site concentrations have not been available, in most cases the TOF is expressed as the number of molecules formed per unit time per surface atom or unit surface area. The ability to use the STO procedure to measure active site densities also provides a means of determining specific site TOFs. It is apparent that the total number of molecules formed in a catalytic reaction per unit time is the sum of the production from each active site. Thus, the reaction TOF can be expressed as the sum of the products of the specific site TOF and the specific site densities as shown in Eqn. 3.6.21 

In this equation the Rate is the molar TOF of the reaction, moles of product formed/mole of metal catalyst/unit time. The terms in [ ] are the STO measured site densities given in moles of site/mole of metal. The specific site TOFs, A, B and C, have units of moles of product/mole of site/unit time. Of these factors, the site densities are available from an STO characterization of the catalyst and the Rate is determined for the specific reaction nm over the STO characterized catalyst. When a series of at least three STO characterized catalysts is used for the same reaction, run under the same conditions, the specific site TOFs can be calculated from the simultaneous equations expressed as in Eqn. 3.6. When this approach was used in the hydrogenation of cyclohexene over a series of seven Pt/CPG catalysts specific site TOF values for the Mr and MH sites were found to be 2.1, 18.2 and 5.2 moles of product/mole of site/second, respectively.21 Not surprisingly, that site with the weakly held hydrogen was the most active and that on which the hydrogen was strongly held was the least active. 

While each of the different types of saturation sites has a different reactivity in hydrogenation reactions, in the oxidation of CO or iso-propanol20 each of these sites has essentially the same activity. 

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Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

The single crystal catalysts, -1 cm in diameter and 1 mm thick, are typically aligned within 0.5 of the desired orientation. Thermocouples are generally spot-welded to the edge of the crystal for temperature measurement. Details of sample mounting, cleaning procedures, reactant purification, and product detection techniques are given in the related references. The catalytic rate normalized to the number of exposed metal sites is the specific activity, which can be expressed as a turnover frequency (TOF), or number of molecules of product produced per metal atom site per second. 

Frequently, the number of active sites is expressed in mole units (the number of active sites divided by the Avogadro number) and thus, turnover frequency is found in s"1 units. For a specific reaction, the turnover frequency depends on the nature of the catalytic active site, the temperature, and the reactants concentration. The above-defined catalytic rate could be described as an active-site level rate. 

The value of the turnover frequency can be reproduced in different laboratories, if the method of measurement of the rate and the counting of sites are kept the same. Moreover, the use of turnover frequency allows the comparison between two catalysts that differ in metal or size for a specific reaction. The great advantage of such a comparison is that the activity of different catalysts is compared at active site level without the considerations of catalyst arrangement. To be more specific, using turnover frequency, we can compare the activity of the pure active site, ignoring the specific area of the catalyst. 

By definition, the turnover frequency is expressed per number of active sites. So, catalytic samples that differ only in the amount active sites must exhibit the same values of turnover frequency. If not, heat and mass transfer phenomena are present. Specifically, the correct measurement of intrinsic kinetic data in heterogeneous catalysis is difficult due to the effect of heat and mass transfer, especially inside the pores of high specific-area materials. The turnover frequency reveals these phenomena. In other words, in the case of supported... 

Table 10.2 presents the kinetic information for the main reactions, in which the frequency factors have been calculated from turnover-frequency (TOF) data [8, 9]. This term, borrowed from enzymatic catalysis, quantifies the specific activity of a catalytic center. By definition, TOF gives the number of molecular reactions or catalytic cycles occurring at a center per unit of time. For a heterogeneous catalyst the number of active centers can be found by means of sorption methods. Let us consider that the active sites are due to a metal atom. By definition [15] we have ... 

Rates of catalytic reactions are obtained by measurement of the conversion of a key component, often the rate limiting reactant, in laboratory reactors and relating this to the amount of catalyst used and the amount or flow rate of reactants used, to obtain an intrinsic quantity, mols-1 amount-1. For practical application the mass or volume of a catalyst is most relevant as the amount but, for comparitive studies the amount of active phase on a supported catalyst, its specific surface area or the number of active sites may be preferred. In the latter case this yields the turnover frequency (TOF) [3], which is quite relevant for fundamental studies. The number of active sites is, however, usually hard to determine and the mass of the catalyst W will be used, resulting in a rate dimensions of mol s 1 kg-1. Other quantities are easily derived from this. 

More complex model reactions (selective butadiene hydrogenation) Apart from being accessible to surface spectroscopy, model catalysts also have the advantage that the nanoparticle morphology and surface structure can be accurately measured. This advantage allows the determination of the relative abundance of specific surface sites and calculation of surface site statistics, as shown, for example, in Table II. Knowledge of the exact number and type of available surface sites then allows calculation of more accurate (and perhaps more meaningful) turnover frequencies of catalytic reactions. 

The best way to determine if the reaction rates are really different for these two catalysts is to compare their values of the turnover frequency. Assume that each surface Pd atom is an active site. Thus, to convert a specific rate to a turnover frequency ... 

Solvent effect on specific site turnover frequencies (TOP) for the hydrogenation of 4-methyl-1-cyclohexene run over Pt/Si02 catalysts. 

Since the overall turnover frequency (TOP) for a hydrogenation reaction is the sum of the TOFs for each type of saturation site as described in Eqn. 3.6, it should be possible to determine the extent of solvent interaction with different types of sites by calculating the specific site TOFs for the same reaction run in different solvents. These data are listed in Table 5.3 for the hydrogenation of 4-methyl-1-cyclohexene over a series of STO characterized Pt/Si02 catalysts. ... 

The value for V, ax 27" (mole site) , is the maximum rate for this reaction when it is run under saturation conditions for both substrates. In contrast to the single type of active site found in most enzymes, there are a number of different types of sites present on the surface of the platinum catalyst used for these oxidations. It was shown in a parallel study that 2-propanol oxidation takes place over the coordinately unsaturated corner atoms, that is, the single turnover (STO) characterized M, and MH sites (see Chapter 2). It was also shown that the specific site turnover frequencies (TOF) for these sites are 5.5,7.9 and 5.0 moles O2 uptake/mole site/minute respectively. 

The more complex selective 1,3-butadiene (BD) hydrogenation was also examined [56, 57]. Butadiene hydrogenation produces 1-butene, tranx-2-butene, cti-2-butene, and n-butane, with 1-butene as the desired product. Pd-Al Oj model catalysts with mean particle diameters of 2-8 nm were applied to examine size effects. The abihty to accurately determine the relative abundance of specific surface sites (such as terrace, edge, interface atoms, etc. cf. surface site statistics in Table 1, 2 of [51]) is a tremendous advantage of model catalysts. Knowledge of the exact number and type of available surface sites allows the calculation of more accurate turnover frequencies. 

The rate of reaction expressed as molecules reacted (or formed) per unit time per catalytic site (or per exposed atom of active metal for metal catalysts) is called the turnover frequency. For supported metal catalysts the calculation requires knowledge of the dispersion, i.e., the fraction of the active metal available for adsorption of reactants. Boudart coined the term demanding (structure-sensitive) for catalyzed reactions for which the turnover frequency varies with the dispersion. Related to this is the ensemble effect, where the active site requires a specific multiatom grouping.f ... 

In addition, the presence of sulphur during the ageing of autocatalysts is known to lead to a significant deterioration in performance under certain conditions. Specifically, the rich-side NOx performance of Pd-based catalysts is often significantly reduced by rich ageing treatments in the presence of sulphur. Such poisoning can occur in at least two ways. First of all, it is possible that the number of active sites is lowered by the retention of reduced sulphur species on the active Pd sites. Secondly, it is possible that the formation of reduced sulphide species within the bulk of the Pd leads to a decrease in the turnover frequency of the active sites. The formation of such species within the bulk of Pd particles has been recently demonstrated [9], and it is possible that the electronic modification of the Pd particles induced by these sulphide species could reduce the NO dissociation probability on the Pd sites and hence reduce the effectiveness of the catalyst within the NOx reduction reaction. 

The Isotope Transient Kinetics (ITK) technique has been used to examine these thermally-induced and sulphur-induced ageing effects in mote detail, and specifically to assess whether the deactivation induced under a defined set of conditions is brought about as a result of a decrease in the number of active sites, or whether it is brought about by a decrease in the turnover frequency of the active sites. The CO-NO reaction was selected to probe these effects, since this reaction is known to be particularly sensitive to sulphur poisoning. 

The turnover frequencies (TOP), defined as the number of methanol molecules converted to formaldehyde per surface vanadia site per second, are presented for the different supported vanadia catalysts, at monolayer coverages, in Table 2. There is a dramatic variation in the TOFs with the specific oxide support and the variation spans approximately three orders of magnitude at monolayer coverages (the same surface density of surface vanadia species). The TOFs were also relatively independent of surface vanadia coverage... 

Catalysis is a kinetic phenomenon we would like to carry out the same reaction with an optimum rate over and over again using the same catalyst surface. Therefore, in the sequence of elementary reactions leading to the formation of the product molecule, the rate of each step must be of steady state. Let us define the catalytic reaction turnover frequency, as the number of product molecules formed per second. Its inverse, 1 /, yields the turnover time, the time necessary to form a product molecule. By dividing the turnover frequency by the catalyst surface area, (i, we obtain the specific turnover rate, (R (molecules/cm /sec) = /Ct ((R often called the turnover frequency also, in the literature). This type of analysis assumes that every surface site is active. Although the number of catalytically active sites could be much smaller (usually uncertain) than the total number of available surface sites, the specific rate defined this way gives a conservative lower limit of the catalytic turnover rate. If we multiply (R by the total reaction time, bt, we obtain the turnover number, the number of product molecules formed per surface site. A turnover number of one corresponds to a stoichiometric reaction. Because of the experimental uncertainties, the turnover number must be on the order of 10 or larger for the reaction to qualify as catalytic. 

Sometimes it is given as reaction rate per unit weight or specific surface area of the catalyst, but more instructive is its definition in terms of the turnover frequency (TOP). This is defined as the number of reaction events per active site and unit time and relies on the possibility to evaluate the correct density of active sites. 

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