Turnover frequency definition

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]. 

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... 

Correlation between the two observed Mn species and catalytic activity properties was attempted. For this purpose, turnover frequencies (TOF) referred to the bulk content of the different Mn species were derived from the results of catalytic activity tests in CH4 combustion. TOF referred to Mn in Al(2) site was found to be almost constant on varying the overall Mn content. This suggested a possible correlation between catalyst activity and this Mn species. However, an alternative correlation was found by normalizing the catalytic activity to the surface area. Such normalized activity correlated well with the overall Mn content. No further evidence was found in favor of either these two alternatives, so that no definitive conclusion could be drawn. 

The turnover frequency allows performance comparison between different catalyst systems, biological and/or non-biological. Its threshold is at 1 event per second per active site. According to the definition, a turnover frequency can be determined only if the number of active sites is known (Chapter 9, Section 9.2.3). For an enzyme reaction obeying Michaelis-Menten kinetics, Eq. (2.15) holds. 

The catalyst turnover number (TON) and the turnover frequency (TOF) are two important quantities used for comparing catalyst efficiency. Their definitions, however, vary slightly among the three catalysis fields. In homogeneous catalysis, the TON is the number of cycles that a catalyst can run through before it deactivates, i.e., the number of A molecules that one molecule of catalyst can convert (or turn over ) into B molecules. The TOF is simply TON/time, i.e., the number of A molecules that one molecule of catalyst can convert into B molecules in one second, minute, or hour. In heterogeneous catalysis, TON and TOF are often defined per active site, or per gram catalyst. This is because one does not know exactly how many... 

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 ... 

In this respect it is recommended that a good definition is given of this activity, preferably in terms of (i) reaction rate per unit mass or volume of catalyst or per unit mass of active phase or (ii) a turnover frequency (reaction, events per site and per unit time). 

For heterogeneous reactions involving fluid and solid phases, the areal rate is a good choice. However, the catalysts (solid phase) can have the same surface area but different concentrations of active sites (atomic configuration on the catalyst capable of catalyzing the reaction). Thus, a definition of the rate based on the number of active sites appears to be the best choice. The turnover frequency or rate of turnover is the number of times the catalytic cycle is completed (or tumed-over) per catalytic site (active site) per time for a reaction at a given temperature, pressure, reactant ratio, and extent of reaction. Thus, the turnover frequency is ... 

We have taken pains to present these definitions because it seems that the organization and understanding of catalytic results is hampered by lack of agreement on these simple details. Rates may be expressed as turnover frequency, atomic rate, activity, or volumetric rate, provided the authors determine also H/M, C, and pB, and defend their choice of H/Ms. Of course, d should be measured independently if possible, as should the morphology of the metal particles. We emphasize the simplicity of Eqs. (1-5). It would seem desirable to express all kinetic results in terms of these rates. 

In Table 3.1 C is the initial acetylene alcohol concentration, Q is the catalyst concentration, S is the selectivity (%), A is the acetylene alcohol conversion (%), turnover frequency (TOP) is the mole of substrate converted over a mole (Pd) of the catalyst per second, Xt is the relative concentration Xi= Q /Q (where Q is the current concentration of the substrate at i= 1 and product at i=2). Strictly speaking TOP should be calculated per Pd atoms participating in the catalytic reaction (available surface atoms), but for the sake of comparison with hterature data, in this chapter we will use the TOP definition given above. To find the kinetic relationships, we have studied the reaction kinetics at different substrate-to-catalyst ratio SCR=Co /Q. Kinetic curves for DHL hydrogenation with Pd and bimetallic catalysts are presented in Pig. 3.4. 

The interpretation follows from the limiting case of Equation 4-8. Consider the limiting case of a high reactant concentration which is so high that the catalytic sites are saturated and [5 ] K - Then, the rate equation reduces to = cat[ ]tot and kcat is recognized as a first-order rate constant. If the rate were written per enzyme molecule rather than per unit volume, then the reaction would be of zero order, and kcat would be the rate at saturation (the maximum number of reactant molecules converted per catalytic site per unit time) this is the definition of the turnover frequency. 

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. 

Note that this is the reaction rate or activity. However, this definition takes into account the reaction medium, be it volume, surface, or interface, and not exactly the active sites. Not all mass or surface is active, but part of its outer surface has active sites, which are truly the sites where the chemical reaction occurs. Therefore, rj in fact represents the apparent rate. An important example of reaction that allows to differentiate the apparent from the true rate is the hydrogenation of carbon monoxide to form methane, which is conducted with different catalysts. With iron and cobalt catalysts, the rate per unit of mass of catalyst, used as reference, has shown controversial values. The activity of the catalysts in the Fischer-Tropsch synthesis to form hydrocarbons would decrease according to the order Fe > Co > Ni. However, when the rate per active site was defined, the order of activity was different, i.e., Co > Fe > Ni. This controversy was resolved by Boudart, who defined the intrinsic activity, i.e., the rate per active site. To make it more clear, the turnover frequency (TOF) was defined. Thus, the intrinsic activity is determined, knowing the active sites, i.e. ... 

Turnover Frequency. Two definitions for turnover frequency (TOF) appear in the literature. The first and most commonly used, is a rate of formation of D divided by the nominal moles of transition-metal used (precursor) IVtm- For convenience, this will be denoted as TOF. The second is the instantaneous rate of formation of D divided by the instantaneous moles of intermediates N. This will be denoted TOF. It is immediately apparent that TOF < TOF and that the two terms can vary greatly due to actual moles of intermediates present. The actual moles of intermediates present at a particular reaction time will depend, in large part, on the kinetics and selectivity of the precataljrtic transformations. Statistical and numerical aspects concerning the evaluation of TOF from in situ spectroscopic data are well vmderstood (15). The characteristic time scale for the catalysis will be denoted ttof, which has units of seconds, and it will be defined as Ttof = TOF-i. 

But this proposal is not so strict scientifically due to the lack of clear definition of activity. The catalytic activity of ammonia synthesis catalyst can be expressed by outlet ammonia concentration of converter, conversion ratio of ammonia, reaction rate and rate constant of kinetics and turnover frequency of ammonia (TOF). 

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