The recipient of the ACS Award in Petroleum Chemistry points out that “measured kinetics is not what it seems” so long as we do
JAMES WE1
DISGUISED KINETICS hen I first arrived at Mobil with a fresh Ph.D.,
W I, like most of the people in my class, believed-
with or without justification-that I knew a lot about the world. I n fact, we all knew exactly how lucky industry was to get someone like us. \Yell, a lot of surprises were in store for me, and it did not take long to find out what an extraordinary group of scientists were gathered there, people who knew a lot more than I. By talking to them, listening to their advice, and reading the books they suggested, one could learn a lot about catalysis, as well as physics, chemistry, and mathematics. M y education was just beginning, and I went about it with great enthusiasm. I learned so much, that at last I deserved a Ph.D. I t is important to note, however, that the most valuable things the)- shared with me were not the technical subjects a t all, but their spirit of inquiry, standards of excellence, and scientific discipline. Many of my colleagues have made enormous contributions to my education; the one who did the most is C. D. Prater. One of
1Vei is Senior Research Associate in M o b i l Oil’s Central Research Laboratory, Princeton, N . J . H i s research into com$lex reaction systems has led to signzjicant contributions to chemical kinetics, dzffusion, irreversible thermodynamics, and stability i n distributed parameter systems and i s the basis f o r his being named as 1966 winner o j the A C S A w a r d in Petroleum Chemistry sponsored by Precision Scient& Co. AUTHOR J a m e s
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the principles I learned from him is the “Principle of Optimum Sloppiness”-a simple but profound truth, like the Golden Rule. Briefly, one should use all the precision in the world where it is needed, but be sloppy where great effort is not required and would be better spent elsewhere. This principle is good for any endeavor, not just in science. However, it is easier to state than to apply in real life, where rather fine lines have to be drawn to locate the optimum. Another thing he taught is that “theoretical research is significant only as it explains, correlates, and describes the world in which we live.” Once, I conceived the idea of dealing with kinetic data by using density matrices-a device popular with quantum physicists. Another time, I cast kinetic problems in terms of curvature tensors and geodesics-techniques popular with people in general relativity. Both times, I worked out treatments that looked very elegant and learned, even admirable. But there was a big flaw-these formulations are useless. I had reduced kinetic problems to problems in geodesic and density matrices; but these problems are harder, not easier, than kinetic problems. T;l’e sympathize with the young lady in the cartoon at the right. According to the rules of the game we play, these formulations are not contributions and were not published. I started work at hlobil under the direction of P. B. Weisz and C. D. Prater. They, physicists by training, feel right at home with the more glamorous approaches
to catalysis, such as solid state physics, infrared absorption, and electron paramagnetic resonance. However, they did not believe that catalysis can be explained by these theories and techniques alone, because an explanation requires making at least a correlation between physical parameters (such as the Fermi level and the relaxation times) and kinetic parameters (such as the reaction order and activation energy). Nearly all interesting kinetic systems are complex, and quantitative knowledge of complex kinetic systems is hard to come by in the literature. We look for theoretical treatments that assist in the EQL'IVALENT 5ET5.':, , NON-EQUI VALENT SETS ,':, 'gET5 OF ONE'%ET5 OF TWO:'. "
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planning and interpretation of experiments and that provide more understanding and insight into the structure of kinetic problems. However, we do not want to stop at the stage of "rhetorical algebra." For example, the statement: " A reacts to form B, and then to C. But aging causes the poisoning of the B to C reaction, and the concentration of B piles up, and has to be diverted into D,"is what we call a theory worked out in rhetorical algebra. What we try to do is to quantify these arguments with mathematics and compare the results with known experiments. Better still, we should predict further results that are either supported or refuted by future experiments. Unless we do all these, we cannot say that everything is fully explained. Therefore, the planning and execution of experiments to obtain precise kinetic information are an important part of the program. I n 1958, R . L. Smith of our group was studying the dehydrogenation of cyclohexane to form cyclohexene and benzene. We were planning to get good data on conversion us. contact time in a differential reactor with conversion less than 1%. Two things intervened. Figure 1 shows that from a feed of pure cyclohexane, the concentration of cyclohexene rises quickly to o.09y0 and then remains stationary. The reactor is simply not differential at less than 0.1% conversion! The next problem was that the data of conversion us. contact time were not very reproducible because of various uncertainties such as differences in treatment, moisture content, and impurities. But the data of product distribution us. conversion (or, we may say, selectivity) turned out to be very reproducible. That is how we got to doing "phase plane" analysis for integral reactors-that is to say, analysis based on reaction paths on plots of concentration us. concentration. The first batch of data contained quite a surprise. We computed the position of the equilibrium point from Rossini data on free energies. I t was quite a bit higher than the straight-line direction of the reaction path. There was no doubt the reaction path would have to reach the equilibrium point eventually by way of an S-shaped curve. This implied a point of inflection, a most peculiar phenomenon. Now the reaction was probably first-order, or at least pseudo first-order (meaning first-order divided by a Langmuir isotherm). Our phase plane analysis did not distinguish between the two. We assumed a number of reaction rate constants and computed the corresponding reaction paths. None of them had this peculiar Scurve. Then we sat down to prove a theorem: that it is impossible to have a point of inflection in a first-order reaction system. This took many months and much mathematics, but we were eventually successful. So, either the reaction system was not first-order, or the equilibrium point was not there-one or the other. The question was resolved by a set of experiments: The equilibrium point is really down the straight line. The Rossini free energy data just are not accurate to enough places to distinguish between the two. After all that theoretical work, we were then able to VOL. 5 8
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.5 .4 Y
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1
2
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MOLE % BENZENE
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27 2a 29 30
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% BENZENE
Fzguie 7. Cjclohexane dehjidrogenation and the equilibrium point from Rossini data
6
%
4 2 CYCLOHEXANE
Figure 2. Cyclohexane dehydrogenation and benzene hydrogenation
I-BUTENE
1
CYCLOHEXENE
cis-2-BUTENE CYCLOHEXANE Figure 3.
/
BENZENE
Triangular plot of cyclohexane delydrogenation
make many predictions concerning reaction paths. R. L. Smith provided us with many of them. Figure 2 shows the first batch of data, as well as the results of a mixed feed of cyclohexane and cyclohexene. We also have runs from a feed of pure benzene and from mixed benzene and cyclohexene. They all converge quickly to a straight-line reaction path. All these reaction paths were exactly predicted by the theory, and everything looked wonderful. But it really was not good enough yet. Figure 3 shows that we had experimental confirmation of the theory only in the two lower corners. In this figure the vertical distance of the straight-line reaction path is exaggerated to make it visible. W e needed experimental confirmation over a vast expanse of space, especially for a reaction path from a feed of pure cyclohexene, which I calculated to be another straight-line reaction path. Well, Smith threw up his hands at these requests. These experiments are not feasible-the reaction rates would be too fast and the heat effect would be terrific. By then, we had obtained a lot of theoretical by40
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trans-5-BUTENE
Fzgure 4. Comparzson of calculated reaction paths with experimentailj observed compositions for butene isomerization. The poznts are observed composition, and the solid lines are calculated reaction paths
products : the existence of the straight-line reaction paths; the slow reaction path with condensing properties; the minimax property; and many others. They really called for experimental confirmation, and the system of cyclohexane dehydrogenation did not seem suitable. W. 0. Haag suggested that we begin to study the isomerization of the butenes, three in number. We were very fortunate to have R.h l . Lago who performed this exceedingly elegant and satisfying set of experiments. That was a period of almost continuous flow of ideas between the theoretical and experimental sides. M'e learned and developed many things that are not available to mere theorists. M'e will show you only one figure from the beautiful results of Lago, surely already classic in kinetics literature. Figure 4 shows a triangular composition diagram and the results of l l sets of experiments, from 11 different initial compositions. The lines are all theoretica1 calculations. Notice the tight cluster of points and small deviation from theory. The calculations involve only two adjustable parameters for all 11 curves. Wc: have the distinct feature of two
ORTHOXYLENE
Figure 5. Experimental points and calculated reaction paths for xylene isomerization
GAS PHASE
DIFFUSION CONVECTION
@
0
VICINITY OF SURFACE
the fault of the theorists. AS long as there are no precise theoretical predictions, there is no demand or incentive for such precise and painstaking experimental results. Would we be able to discover experimentally that there are always straight-line reaction paths? I have presented here the work of many people, for this award represents the results of a large group effort. I am like the visible part of an iceberg floating on the ocean. Without my many extraordinary colleagues and the buoyant forces they provide, I would certainly not be floating here now. We have obtained some very exact and quantitative information about kinetic systems. What do they tell us about the events on the surface of the catalysts where the real actions are? After all, we are still basing everything on observations and measurements in the gas phase. One day we may be able to study heterogeneous catalytic kinetics correctly by directly following the events on the catalyst surface. We will then be able to identify all the adsorbed chemical species on the surface: to find out all their properties, to measure their concentrations, to find out which of them are true intermediates, and to study the surface rates as functions of surface concentrations. We may have sharp enough tools one of these days since a start has already been made with probing devices such as infrared, ESR, conductivity, and magnetism measurements. I n the meantime, we depend heavily on measuring concentration changes in the gas phase and hope that the kinetics we construct is a faithful representation of events on the surface. Quite often, the kinetics we measure in the gas phase is disguised and is really not what it seems. Of course, one of the principal functions of science is to inform everyone that things are not what they seem. You probably remember being told that :
A whale is not a fish
A jellyfish is not a fish Figure 6. Gas phase measurements are injuenced by physical transport, as well as by chemical reactions of adsorbed species
That should teach us to beware of school teachers and of definitions! These were followed by the even more astonishing: A rabbit is not a rodent All such disguises are not limited to biology. college chemistry, we Iearned that
straight-line reaction paths-one fast and one slow, both two-sided affairs. We have all the reaction paths condensing and converging toward the slow straight-line reaction paths as they approach equilibrium. Many of our theoretical predictions are realized precisely here. A few years later, this beautiful diagram was equaled by the results of A. J. Silvestri on the isomerization of xylenes, summarized by Figure 5, which is also a triangular diagram with l l sets of experimental results. To be fair, I must point out that there is one point that is not on the theoretical line-this should put to rest your suspicion that we have fudged the data. Why are such precise and satisfying kinetic data just beginning to appear? I think this might have been
In
Heat is not the stuff that resides in a bucket of hot water And now, we are to consider another: “Measured kinetics is not what it seems” The physical disguises I speak of are not very mysterious at all; they are simple manifestations of a single principle with which we are well acquainted. Consider a heterogeneous reaction system where species A is transformed into species B, as shown in Figure 6. We do all our measurements in the gas phase, but the events we are interested in take place on the solid surface, where we have scanty information. The overall reaction that we notice is the disappearance of A with the appearVOL. 5 8
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ance of B in the gas phase. Does this rate accurately represent the surface reaction rate of A* to B*? If the surface reaction rate is the slowest step in the overall process, then the overall rate is governed by the surface rate, and there is no disguise. However, if any of the other steps are comparably slow, the overall reaction rate as measured in the gas phase does not accurately reflect surface rates. Then we speak of physical disguises. The effects of this kind of disguise are twofold: (1) the rates are affected (usually decreased) and ( 2 ) the product distribution (or selectivity) is affected. Personally, I think that the latter effect is the more important one, both in science and in technology. First of all, no flow or static reactor is designed and operated so perfectly that every molecule spends the same length of time near the catalyst surfaces. We speak then of a distribution of residence times. I n Figure 7 , we see a perfect reactor with a residence time of three minutes-every molecule spends exactly three minutes in this reactor. The activity of the catalyst is indicated by a curve that gives the amount of conversion for each residence time. Since everything came out after the same three minutes residence time, the amount of conversion is 69.8%. Next we have another reactor with the same average residence time of three minutes, but not so perfectly designed, so that some molecules get through in one minute, and some take as long as five minutes. The overall performance of this reaction is then 68.3%. Next we have an even more imperfectly operated reactor with a wider spread of residence times, the performance is now only 66.891,. These differences are certainly not insignificant, but contact time is the only thing inentioned in the literature. Second, before catalysis can take place, the molecules have to be adsorbed on the catalyst surface. This chemisorption step may be slow compared with the rate of reaction. Figure 8 depicts a consecutive reaction A B + C. After A is adsorbed to give A* and then converted to BY,there are two choices open: B" may desorb to become B in the gas phase and be measured, or may react further to C* and desorb as C. If desorption is
1 2 CONTACT TIME OVERALL CONVERSION
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.5
69.8%
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68.3% Fzgure 7.
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fast, we shall see in the gas phase a gradual disappearance of A with an appearance of B-the appearance of C comes much later when there is already a sizable buildup of B in the gas. But if desorption is slow compared to reaction, we tend to make C*, which will desorb as C. From a feed of pure A , we have the simultaneous appearance of B and C, and we are fooled into believing that this is a parallel reaction. There was a time when we thought this disguise peculiar to differential reactors at a particular feed composition. I t turned out that for an integral reactor with any feed, the system looks consistently as if it were a parallel reaction. The disguise is excellent. Perhaps the best known example of this kind of disguise is Kemball's work on deuterium-hydrocarbon exchange. Figure 9 shows the destrtuction of ethane. I t is reasonable to believe that the replacement of H by D on the catalyst surface takes place one at a time. Over an evaporated tungsten film, there is no surprise. The initial product, which is not clearly specified but presumably means the product at less than lOy0 conversion, is predominantly DI-the monodeuterated molecules. But over a film of cobalt, the most abundant initial product is CzDs, the completely deuterated substance. This is especially curious when you consider that when equilibrium is established, the distribution of isomers will have to be binomial, with very little C2De. This effect is easily explained if we postulate that the rate of chemical reaction is about twenty times faster than the rate of desorption. Then when a molecule of ethane got on the surface and got off, the initial product represented only a single adsorption-desorption event, but at the same time it represented 20 catalytic exchange events, That is tvhy ~ 7 ehave so much completely deuterated ethane. Third, the molecules have to be transported from the gaseous bulk, where measurements take place, to the vicinity of the catalytic surface. This takes place by convection and diffusion in the reaction vessel (something that can be speeded up by good stirring and mixing). Then, they have to travel by diffusion inside
The influence of a distribution of resitimx times on overall conversion
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2
3 66.8%
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5
the pores of a catalyst (something that is aided by having catalysts with bigger pores). There is quite a literature on these subjects, dating at least as far back as Noyes and Nernst, and later enriched by the works of people such as Thiele, Wheeler, Damkohler, Frank-Kamenetski, Weisz, and Prater, and many others. The effect of diffusion on product distribution is shown in Figure 10. We consider again the consecutive reaction system of A -+ B + C in a long narrow pore inside a catalyst. Molecule A wanders inside the pore, hits a catalytic site, gets adsorbed and is converted into B. Before molecule B can drift outside in the main gas stream and be measured, it may collide with the catalyst wall a few times, and be converted to C in the process. Thus by measuring only the gas concentration, we only see A disappearing and the simultaneous appearance of B as well as C. The kinetics is again disguised into a consecutive reaction. One can avoid, or at least minimize, this disguise by shortening the catalyst pores (which means a smaller catalyst particle), making the pores larger (which means larger diffusivity), or making the reaction rate lower. Then the product molecule B would have a better chance to escape into the gas stream without further conversion into C. By these devices, we can minimize the disguised kinetic rate A -t C. Diffusional effects on the distribution of products can be rather unexpected. Take the same deuteriumethane exchange system mentioned before. For a metal film without sorption disguise, and for very low contact time, the product distribution is the normal one depicted on Figure 12. If the system is completely diffusion limited, the product distribution would shift to this U-shaped distribution where the most abundant products are the mono- and the completely deuterated species. This kind of distribution has been reported in the literature, and has been attributed to a two-site mechanismsay the different crystallographic planes of the metal crystals. This analysis suggests that diffusion effects could also be an explanation. There is another point of approach to the physical disguises on product distribution. I t is relatively easy to work out the retardation of rates in a single simple reaction by these physical disguises. I t is represented in Figure 12, where the disguised rate constant is plotted us. the true rate constant. Notice that as a general rule, the disguised rate is smaller The higher the true rate, the greater the retardation. We may say that physical
GAS
disguises are democratic levelers, and might be compared with progressive taxation where the rich are taxed more than the poor. For disguises due to intraparticle diffusion and to a distribution of residence times, the disguised rate constant can attain very high values. But for adsorption-desorption and convection disguises,
Dl
Da
D,
04
DS
D6
Figure 9. Kenball’s data on ethane deuterium exchange-initial product distribution over tungsten and cobaltjlms
DISGUISED GAS KINETICS
Figure 70. Dayusion disguise of a consecutive reaction into a parallel reaction
JI i -I c*
Figure 8. Adsorption-desorption disguise of a consecutive reaction into a parallel reaction
Figure 7 7 . Calculated initial product distribution for the ethane deuterium exchange system over tungsten jlm-white bars are for dayusion limited systems VOL. 5 8
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/
META
0’ //
XYLENE
OBSERVED RATE CONSTANT
SURFACE RATE CONSTANT
ORTHO
PARA
A - 2 *-i----B-T-C
’ 1.9
x-0
Y-0
CYCLOHEXANE
BENZENE
Figure 72. All physical disguises result in a decrease of the obserued rate constant relative to the surface rate constant. A descr$tion of dayusion effects on reaction paths according to the theory of monomolecular reaction systems
Fagure 73. The rate constants of the xylene isomerization and c y l o hexane dehydrogenation systems
there is an upper limit to the value of the disguised rate constant. Our study on complex first order systems tells us that a reaction system A e B C can always be considered to be equivalent to a simple uncoupled system of X + 0 and Y + 0. X and Y are the two straight-line reaction paths, where the rate on Y is twice the rate on X . From the lower left corner on Figure 12, these two rates give a reaction path (shown by the dotted line) that is initially tangent to the AB line. This means, of course, that the initial product is all B and no C, consistent with the consecutive nature of this reaction. But any physical disguise will penalize the fast reaction more than the slow one, so that the two are now more nearly equal. I n the event of sorption or convection disguise, the two rate constants could become equalgiving rise to straight-line reaction paths everywhere. Generally, the disguised reaction path will lie betw-een the original true path shown by the dotted line and a straight line to the equilibrium point. I n Figure 12 it is shown by a solid line. This means that the initial product will contain some C, as well as B. Therefore, the initial slope of the reaction path that we measure is always less than or equal to the true slope, never more. Any physical disguise will make us believe that we have a parallel reaction scheme. What are we going to do about the disguised step A -+ C when we measure kinetics in the gas phase? For mechanistic re;isons, we may rule out such a step on
the catalyst surface. But if we consider kinetics in the gas phase, this step is real all right, and there is no point in crossing it out for mechanistic reasons. Just build a processing plan and predict yields; >-ouwill see that this step is real enough. For example, Figure 13 shows the xylene isomerization system, where one may argue that it is not likely that oxylene can transform into p-xylene in a single step on the surface. As it turned out, the gaseous kinetics indicates that the 0- and p-rate constant is some thirty times smaller than the rest. I t is quite possible that this step does not exist on the surface. We will not know until we have made experiments where there is no possibility of physical disguises. Another example is the cyclohexane dehydrogenation experiment. I t appears that the bulk of the traffic is from cyclohexane to cyclohexene, and then to benzene. Cyclohexene truly qualifies as an intermediate. But does it have an exclusive role3 Is there some direct traffic from cyclohexane to benzene on the surface3 I t has been proposed that the route is indeed exclusive through cyclohexene. But no one, neither we nor anyone else, has enough evidence to say that the direct route is merely physical disguise. I n conclusion, I want to tell you that we really had a ball studying catalysis in the past and present. If progress in research were measured only by enjoyment of the practitioners, then our project is a rousing success, and I hope it will continue.
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