Metal-Catalysed Reactions of Hydrocarbons / 05-Introduction to the Catalysis of Hydrocarbon Reactions

atoms to a reaction requiring them diminishes as a size is decreased. However the requirements for ensemble size and for atoms of low co-ordination number are in conflict, as they move in opposite directions as size increases. One cannot predict which will be the dominant factor, the various possibilities being shown in Figure 5.10: the existence of a minimum in the TOF vs. size plot is unlikely. Where TOF increases with dispersion, the terms ‘positive’ or ‘sympathetic’ sensitivity have been used (curve 3); for the converse (curve 2), the terms ‘negative’ or ‘antipathetic’ are applied.24 But whatever misgivings one may have concerning the quantitative interpretation of the results, their qualitative meaning is clear; and in reactions of hydrocarbons allowing multiple products, variation of product yields with surface composition reveals further aspects of ensemble-size sensitivity.

One last point: little consideration is given to the co-ordination number requirements of active ensembles in bimetallic catalysts. Statistical calculations have assumed an infinite flat surface, although the Monte Carlo treatment by King places active atoms preferentially in high co-ordination sites,83 because in those positions they minimise the surface energy. The non-equivalence of ensemble-size sensitivity and particle-size sensitivity must be kept clearly in mind.

5.6. THE PHENOMENON OF ‘COMPENSATION’27,84–89

It is said that ‘In argument there is much heat but little light’, and its truth is amply verified by the extensive literature on compensation phenomena: for on no other subject in the field of catalysis has so many words been expended to such little purpose. The experimental observation is in essence very simple: in a series of catalysts or reactions sharing a common feature there is often observed a linear correlation between activation energy and pre-exponential factor, of the form

and its occurrence is so frequent, and its precision sometime so great, that theoretical attention to it is inevitable. In most cases the values of E and ln A have been obtained by plotting the logarithm of the rate versus T −1 according to the Arrhenius equation in the form (Section 5.25)

ln Aa being the intercept when T −1 is zero (Figure 5.1). In such cases the compensation equation should be written

This relation was first observed by F.H. Constable in 1925, and was subsequently noted by G.-M. Schwab,90 who was the first to use the term ‘compensation’, and

who also devised the name ‘Theta Rule’, because of a supposed dependence of activation energy on reduction temperature. E. Cremer was also one of the earliest students of the phenomenon. The use of the term ‘compensation’ is apposite, since an increase in activation energy, which causes a decrease in rate, is compensated by an increase in the pre-exponential factor, and indeed exact obedience to equation (5.34) requires there to be a point at which the rates of all members of the set are identical.84 This is the isokinetic point, and at temperatures lower than the isokinetic temperature Ti the member having the lowest activation energy displays the fastest rate; the reverse is however true above Ti . By simple algebra, the reciprocal of the slope m equates to RTi . Thus depending on the location of Ti with respect to the experimental results, one may observe either compensation, negative compensation or no compensation (Figure 5.11). Negative compensation is rare

Figure 5.11. Various types of compensation produced by progressive increase of Ti : A, positive compensation; B and D, no compensation; C, negative compensation.

and of doubtful occurrence; cases of no compensation where rate is determined solely by ln A permit a quite straightforward explanation. Would that this could be said of ‘compensation’ itself.

It is also important to note that the most active catalyst of a group is only that with the lowest activation energy when measurements are made below Ti : above this temperature, the opposite is true, thus negating the commonly held (and taught) correlation of activity with a lowering of activation energy, which is (as the Arrhenius equation shows) not the sole determining factor.

The phenomenon of compensation is not unique to heterogeneous catalysis: it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson’s equation12). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation; it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation.88 This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now.

Much trouble has been taken to find statistical criteria that will establish the validity of an isokinetic relationship (IKR)84,91,92. The compensation equation (5.35) is not statistically sound, because both slope and intercept are derived from the same results and are therefore not independent: error in one determines the error in the other. The existence of an isokinetic point can only be established by showing that the individual Arrhenius plots have a common solution. This entails the somewhat fruitless discussion of how accurate is ‘accurate’, and also involves careful assessment of experimental errors.92,93 This is however a minefield into which we need not enter: it is sufficient to know there are very many cases where activation energy varies over a wide range, much greater than can be excused by experimental error, and even though the points do not lie exactly on a compensation plot (sometimes called a Constable plot89) we know that there is a correlation between the two kinetic parameters that requires our attention (see Figure 5.12 for an example). It has been suggested that the term ‘compensation’ be used in such cases, the name IKR being retained for those in which a proper statistical analysis confirms the existence of an isokinetic point.

It would be tedious and of no great value to review the many and varied attempted explanations of the phenomenon of compensation (see Further Reading), because as we shall see shortly, they may be wide of the mark at least as far as reactions of hydrocarbons go. There are however a number of review articles that may be consulted if desired.86–89,94 On reflection however it seems more fruitful to focus attention on the reason for the variation in the activation energy, and perhaps

Figure 5.12. Compensation (Constable) plot for the hydrogenolysis of alkanes on EUROPT-1 (6.3% Pt/SiO2 ).

O Total rates of reaction for linear C3 C6 alkanes and neopentane; hydrogenolysis rates only; isomerisation rates only; broken line, results for ethane.

to try to connect this with some attribute of the catalyst or reaction, the variation of which is causing it. It is necessary to remind ourselves that the Arrhenius equation properly applies to the rate constant (equation (5.1)), and that when rate is used in an Arrhenius plot, the activation energy must be regarded as apparent, i.e. the true value moderated by the appropriate heats of adsorption, unless and until it can be shown that the surface concentrations do not change significantly over the range of measurement, when orders of reaction will be zero (Section 5.2.5). This simple truth is unfortunately overlooked by many of those seeking an explanation of compensation. There is a very strong possibility that, at least within the area of our interest, compensation is simply an inevitable consequence of the use of apparent kinetic parameters, and that a major cause of the variation of Ea lies in the varying contributions made by the heats of adsorption terms (Section 5.2.5).

In the case of the hydrogenation of alkenes (Chapter 7), surface coverage by reacting species is high and not very temperature-dependent: activation energies are often in the region of 40 kJ mol−1 and compensation is rarely seen. The same applies to the hydrogenation of alkynes (Chapter 9), where activation energies are often about 60 kJ mol−1. It therefore seems likely that, following the Temkin equation (5.30), these are the true activation energies for those processes, and

that as expected they do not respond much to changes in catalyst structure or composition. They are therefore widely regarded as being structure-insensitive reactions. Some refinement of these statements may be proved necessary in due course, because although orders in the hydrocarbon are often close to zero, those in hydrogen are usually about first. This matter will be taken up again in Chapters 7 to 9. The hydrogenation of benzene and other aromatics is also a special case to be considered in Chapter 10.

Entirely different behaviour is found with the hydrogenolysis of alkanes (Chapters 13 and 14). Here activation energies are high, typically 100–250 kJ mol−1, but sometimes reaching the astronomic value of 400 kJ mol−1. Orders in alkane are about unity, but the rate as a function of hydrogen pressure passes through a maximum, the position and sharpness of which depend upon the alkane and upon temperature.89 Most significantly, apparent activation energy increases with hydrogen pressure95 (Figure 5.13), as model calculations confirm33 (Section 5.2.4), and the pre-exponential factor varies sympathetically,95 as is also the case with the model calculations.33 Thus compensation is observed within a single

Figure 5.13. Dependence of Eapp on hydrogen pressure for hydrogenolysis of propane and of n-butane on EUROPT-3 (0.3 % Pt/Al2 O3 , curves are calculated by eqn. ES5B (see Chapter 13) using constants of best-fit.

system of catalyst and reactants, and its origin is thereby proved to lie in variations of surface coverage caused by differences in heats of adsorption. The high activation energies are attributed to the existence of an endothermic pre-equilibrium in which the alkane first loses several hydrogen atoms; the concentration of this critical dehydrogenated intermediate therefore increases with temperature, and Et is therefore less than Ea , unlike the classic situation where coverage by the adsorbed intermediate falls because it is exothermically adsorbed. The often-noted decrease of Ea with the alkane’s chain length also receives a ready explanation, as coverage by hydrogen atoms decreases simultaneously. Comparison of alkane reactivities therefore needs to be made at equivalent surface concentrations. Adsorbed hydrocarbon species are present in comparatively small amounts, requiring somewhat specific sites: hydrogenolysis of the C––C bond is therefore regarded as being structure-sensitive, and we have therefore succeeded in connecting sensitivity, reaction kinetics, activation energy and compensation in one reasonably satisfying picture (Figure 5.14). In a bimolecular process, it is the adsorption requirement of the more weakly adsorbed reactant that determines the degree of structure sensitivity. Additional flesh will be added to this skeleton in later chapters.

Figure 5.14. Schematic dependence of rate (full line) and of Eapp (broken line) on θH , showing the locations of three different values of K H .

5.7. THE TEMKIN EQUATION: ASSUMPTIONS AND IMPLICATIONS

We have seen in the last Section how distinguishing between true and apparent activation energies may resolve the long-standing debate over the significance of compensation phenomena, and in Section 5.2.5 how these distinct quantities are linked through the heats of adsorption of the reactants by the Temkin equation (5.31). It is now necessary to explore the assumptions underlying this equation, and to pursue certain implications that arise from it.

The terms that moderate the heats of adsorption in this equation are the orders of reaction x and y, so clearly the Power Rate Law formalism is being employed. While this is adequate to describe limited cases where x or y is unity or zero, a single exponent of the pressure cannot account for the variation of rate with pressure over a wide range, and the use of the Langmuir-Hinshelwood formalism then becomes obligatory (Section 5.2.4). Because in general surface coverages by the reactants will decrease with rising temperature, values of x and y in fixed ranges of pressure will tend to increase, and where tis occurs the measured activation energy should decrease as temperature is increased, because according to the Temkin equation the terms containing the heats of adsorption become more significant (the heats of adsorption are of course negative). There are few cases where the operation of the Temkin equation has been observed for certain, part of the difficulty being that a change in activation energy can have other causes, such as the onset of mass-transport limitation or decreasing rate due to deactivation. One possible example is the hydrogenation of aromatic compounds, where above a certain critical temperature the rates start to decrease, and negative activation energies result: the exact interpretation of this effect however remains uncertain (Section 10.2.4).

The fact that Arrhenius plots for hydrocarbon transformations are so often quite linear over the whole of the measured range raises a doubt that the Temkin equation can or should be applied to them, even although the orders of reaction would seem to demand it. The problem may be illustrated as follows. It has been suggested in the previous section that the somewhat low activation energies habitually found with the hydrogenation of alkenes, alkadienes and alkynes are true values, because it appears from the limited evidence on the temperaturedependence of the orders of reaction that surface concentrations are not changing much over the temperature range used (see Chapter 7, 8 and 9). Unthinking application of the Temkin equation would require the unknown heat of adsorption of hydrogen to be added to the apparent activation energy, since orders in hydrogen are often first (or greater). If, however, as seems possible, the slow step in these cases involves the collision of an undissociated hydrogen molecule with some chemisorbed hydrocarbon species, it would clearly be wrong to do this.

A related problem arises with the hydrogenation of aromatic molecules, where it is well documented that orders with respect to both reactants increase with

temperature, but the observed activation energy remains unchanged (Section 10.2.2); so according to the Temkin equation this would imply a variable true activation energy (Et ), which seems unlikely: and application of this equation, using heats of adsorption derived by kinetic analysis, led to astronomic values for Et , which if not impossible are at least improbable. We must therefore conclude that the Temkin equation (or a modification of it containing adsorption coefficients rather than reaction orders) should only be used where the mechanism is established, where reversible adsorption of both reactants is known to occur, and where surface concentration change significantly over the temperature range employed. An attempt to apply the equation to alkane hydrogenolysis, where pressure-dependence of activation energy is well established, will be discussed in Chapter 13 (see also Section 5.6).

We must conclude that the effect of increasing temperature is two-fold:

(i) through diminishing surface concentrations of reactants in line with their (coverage-dependent) heats of adsorption, and (ii) through the operation of Et on each reacting centre. Now the height of the potential barrier to be overcome is also likely to depend on the strengths of adsorption, so the heat terms govern both coverage and reactivity. This suggests that we might look for some correspondence between Et and adsorption heats, and that it might be possible for Et to vary even when surface coverage remains close to unity in a series of related catalysts, because while coverage cannot exceed unity the heat terms can be higher to variable extents than needed to secure complete coverage. It is worth noting that the effect of decreasing heats of adsorption with increasing surface coverage, whether due to induced heterogeneity or to the arrival of weaker chemisorbed states, works to reinforce the effects of changing temperature and pressure on rates. Thus if an increase in temperature leads to a lower rate than expected because coverage has decreased, the resulting increase in adsorption heat will increase Et and give an even slower rate. Similarly if an increase in pressure gives a faster rate because there are now more reacting species, this increase in coverage leads to a lower heat of adsorption, a smaller Et and an even faster rate.

5.8. TECHNIQUES

5.8.1. Reactors98

The main types of laboratory reactor were introduced in Section 5.2.3, and, since (as the reader is constantly reminded) this is not intended as a handbook of catalytic practice, all that is necessary now is to add a little further detail, and briefly allude to other types of reactor that may be encountered.

First of all, it is not proposed to deal at all with pilot plant or industrialscale reactors, as this is a very specialised area, adequately covered in existing

texts,14–16,99 nor is it necessary to deal with three-phase reactors, although some results obtained with their use will be shown; this is an area where great care has to be taken to avoid mass-transport limitation.8 Most of our concern will be with gasphase reactions, where continuous-flow microreactors using 0.1 to 1 g catalyst are in common use. There are obvious limits to the rates that can be obtained at fixed temperature by altering flow-rate: the upper limit is dictated by possible entrainment of catalyst in the gas, and the lower limit by the difficulty of measuring very slow flow-rates. Meaningful results can however be obtained at conversions as low as 0.1% in favourable cases. The great advantage of constant-volume reactors is that they can be operated for long periods for very slow rates of reaction.

In the pulse-flow mode,13 shots of a hydrocarbon are injected periodically into a flow of hydrogen, and the whole mix of products and unchanged reactants analysed. In the short residence time, formation of carbonaceous residue is minimised, and the surface is cleansed between shots, but the actual composition of the reacting mixture is unknown, and the method is unsuited for obtaining quantitative kinetics. It is better to inject a hydrocarbon and hydrogen mixture into a hydrogen stream, and with care accurate kinetics are got by using times as short as 1 min: cleansing occurs between reaction periods as before, but if deactivation is unavoidable the regular use of standard compositions still allows viable results to emerge.95 Problems arise however with microporous catalysts (e.g. zeolite supports) because hydrocarbons are strongly retained and are not quantitatively recoverable in the short term.100 Microprocessor-controlled reactors allow lengthy sequences of varied conditions to be pre-programmed, and with data processing of product analysis by computer all that remains to do is to write the paper.101

Very useful information is obtained by the method of transient kinetics.40,102–106 Here an abrupt change is made to the conditions in a flow-reactor, and the temporal consequences of that change analysed. Most simply the flow of one reactant is stopped, and the change in product yield with time followed: thus, for example, if in hydrocarbon-hydrogen reaction the hydrocarbon flow is stopped, the integrated amount of produce subsequently formed measures the amount of intermediate species on the surface (Figure 5.16). A step change made to the

Figure 5.16. Transient kinetics: A, flow of reactant stopped; B, flow of reactant altered; C, isotopic variant of reactant introduced.