The role of vibrational energy in surface isomerization of cyclopropane

Surface Science 83 (1979) 453-470 0 North-Holland Publishing Company

THE ROLE OF VIBRATIONAL OF CYCLOPROPANE G. PRADA-SILVA,

D. LOFFLER,

Department of Engineering 06520, USA

ENERGY IN SURFACE ISOMERIZATION

B.L. HALPERN, G.L. HALLER and J.B. FENN

and Applied Science,

Yale University, New Haven, Connecticut

Received 24 July 1978; manuscript received in final form 10 January 1979

We report an investigation of the heterogeneous isomerization of cyclopropane to propylene on mica surfaces under conditions which made possible the independent variation of surface temperature, as well as the velocity and vibrational temperature of the incident cyclopropane molecules. Measured reaction probabilities ranged from 3.4 X lo6 to 5.4 X lo4 as the vibrational temperature was increased from 700 to 820 K while the surface temperature was constant at 756 K. This dependence upon vibrational temperature corresponds to an activation energy of 56 kcal/mol. The apparent activation energy corresponding to a similar variation in surface temperature is 21 kcal/mol. Model calculations indicate that these results cannot readily be accounted for in terms of simple energy exchange between the surface and a reactant molecule. We conclude that the overall process must involve activated adsorption followed by surface reaction and desorption of product propylene.

1. Introduction

In recent years the molecular dynamics of many gas phase reactions have been investigated. These studies have led to the formulation of some generalizations about the relative importance of translational, vibrational, and rotational energy in surmounting a reaction barrier [ 11. For reactions in which the barrier is encountered early in the approach of reactant molecules, translational energy is more effective than vibrational energy in promoting reaction. For reactions with a potential energy surface such that the main barrier to reaction occurs late (after closest approach has been achieved), vibrational energy in the bond under attack is much more effective than translational energy for producing reaction. The applicability of these generalizations to reactions involving surfaces has not been established because very few gas surface systems have so far been studied under conditions which would permit distinguishing the roles of particular kinds of energy. Balooch et al. have studied the reaction of molecular hydrogen with adsorbed deuterium on three crystal faces of copper [2]. Its rate is controlled by the dissociative adsorption of molecular hydrogen, i.e., the activation barrier for that adsorption. The adsorption probability was found to be independent of the surface tem453

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perature but it did depend upon the translational energy of the incident hydrogen molecules. Moreover, it was demonstrated that only the normal component of the translational energy was important. A subsequent classical trajectory study confirms the effect of translational energy and suggests that vibrational excitation will also affect the adsorption probability [3], The adsorption of hydrogen on copper is in sharp contrast to the case of methane on rhodium where Steward and Ehrlich found the rate of adsorption independent of methane translational energy and surface temperature but their surface temperatures (145-245 K) were always much below the methane temperature (300-710 K) [4,5]. The vibrational energy of the incident methane molecule played the key role. Similarly, the reaction rate of nitrous oxide with a copper surface to form a gas phase nitrogen molecule and an adsorbed oxygen has been found by Bass and Fanchi to depend on vibrational energy in the nitrous oxide at the time of collision with the surface [6]. In these three studies three different techniques were used to control and vary independently the translational and internal energy of the reacting molecules. Balooch et al. used a nozzle beam source which resulted in a fairly narrow distribution of velocities in the incident Hz molecules. The rotational energy was equivalent to a temperature of about 83% of the nozzle temperature and the vibrational energy was essentially equal to that in the nozzle before expansion. Steward and Ehrlich also used a molecular beam but their effusion source resulted in Boltzmann distributions of both translational and internal energies corresponding to the source temperature [S]. They varied the vibrational energy (at constant translational energy) by replacing CH4, with CHaD? or CD4 as the source gas at a given source temperature. Bass and Fanchi varied the vibrational energy of their reacting nitrous oxide by laser excitation at the resonant absorption frequency for the stretch mode of the N-O bond [6]. Intuition suggests that this bond must be excited of the NzO molecule is to decompose. However, it seems unlikely that the vibrational excitation was retained in the originally excited mode until the molecule reached the surface. Even though the mean free path was sufficiently long in these batch experiments to avoid collisional relaxation in the gas phase, it is probable that intramolecular transfer of vibrational energy into other modes did occur. In the experiments described in this paper a nozzle beam was used to study the effect of translational and vibrational energy of cyclopropane on the probability of isomerization to propylene upon collision with a mica surface. Because vibrational relaxation is slow in cyclopropane, the original vibrational energy does not relax during the free jet expansion. Consequently, the vibrational state is unchanged from the source value. However, because of a much faster relaxation rate the rotational energy of the beam molecules decreases to a small fraction of the source value. The translational energy of cyclopropane has a very narrow spread around the most probable value corresponding to the convective velocity. It can be varied by changing the nozzle temperature or by using the seeded beam technique [7]. A more complete discussion of the procedure used to investigate the effect of translational and vibrational energy on the reaction probability is given in the following section.

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apparatus and procedure

It is experimentally very difficult to distinguish between cyclopropane and propylene using a mass spectrometer, the usual detector employed in molecular beam work. On the other hand, the separation and quantitative detection of these two isomers by gas chromatography is a simple task. This realization along with a desire to increase our ability to detect small reaction probabilities led us to the development of a recycling molecular beam reactor (RMBR) previously described [8]. It is based on continuous recycling of gas molecules which in the form of an uncollimated molecular beam undergo a single collision with a target in the course of each cycle. The apparatus has been described in detail in ref. [8] but some important features will be repeated here. 2. I. The target surface The target surface was natural mica obtained from the Ruggles Mine, Grafton, New Hampshire. Only K, Al, Si, 0, and C could be detected in the surface of a freshly cleaved sample by means of X-ray photoelectron spectroscopy (HewlettPackard 5950A). Results with single crystal sapphire and quartz reference samples indicated that the aluminum to silicon ratio was about 0.98. This ratio and the infrared spectrum suggests that our sample was muscovite, KzO .3 A1203 . 6 SiOz . 2 H20. After use in our experiments the aluminum to silicon ratio decreased to 0.60. In some samples a decrease in potassium and an increase in carcon relative to their initial values were also detected. We also performed some experiments with mica which had undergone ion exchange with concentrated NH40H and was then calcined to give an “acid” surface. Results with this sample were the same as with untreated mica. Targets of two sizes and shapes were used. One was square with an area of 17.2 cm2. The other was round with an area of 3.8 cm’. In both cases the mica sheet was approximately 0.05 mm thick and was secured to the face of a molybdenum block by means of a peripheral flange of thin stainless steel or molybdenum. The block was heated by carridge resistance heaters, two for the square block, one for the round. The temperature of the round target was measured by an iron-constantan thermocouple spot-welded to the mica side of the retaining rim. The temperature of the square target was measured at a point 1.5 cm from the center by an iron-constantan thermocouple under the mica. A second small piece of mica was placed between the molybdenum and the thermocouple because it was found that a thermocouple in direct contact with the molybdenum surface always gave a high reading compared to a thermocouple resting on or cemented to the mica surface. The absolute surface temperatures are somewhat uncertain but it will be argued later that when the thermocouple temperatures for the two targets were the same the true surface temperatures differed by less than 20 K. Under otherwise similar conditions, the two targets gave concordant results but most of the measurements reported here were obtained with the round target.

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2.2. Nozzle sources The nozzles were fabricated from quartz tubing in the manner described previously [8]. Two different nozzles were used. With the square target, the diameter of the nozzle throat was 0.008 cm and the tube upstream of the throat was heated over a 4 cm length. For experiments with the round target the nozzle had a throat diameter of 0.009 cm and the upstreaum heated length was 10 cm. Temperature was monitored by a chromel-alumel thermocouple in a quartz sheath inserted from upstream in the nozzle tube so that the junction was about midway in the heated section. A “pneumatic-thermometry” technique indicated that the short heater length (4 cm) did not allow sufficient residence time for the gas to reach the thermocouple temperature, which because of radiant exchange was considered to be equal to the wall temperature [9]. Even with the longer heated length (10 cm) the effective gas temperature in the nozzle may not have been that indicated by the thermocouple. One approach to correcting the thermocouple reading is to use a form of pneumatic thermometry based on the measured recycle time [8]. A more precise and relevant “chemical” temperature can be calculated from the observed homogeneous isomerization rate of cyclopropane in the nozzle, i.e., what we refer to as the background rate measured when the target surface is cold. We make use of the following expression: -ln[(l

-x)/(1

-x0)]

= kfu,

where k = 1015.5 exp(--65,600/M+) see-‘, the rate constant which has been well established from previous studies. [lo]. Thus, x - x0 is the change in mole fraction of propylene in t seconds, where u is the volume fraction of total gas charged which is in the heated portion of the nozzle. For a thermocouple reading of 800 K the calculated correction is -80 K for the 4 cm heater and -30 K for the 10 cm heater. It should be noted that because of the high activation energy the value of x -XC, is very sensitive to the maximum gas temperature which is presumably the same as the effective stagnation temperature in the nozzle. 2.3. Energy states of the reactant molecules In an ideal isentropic expansion of a gas the total equilibrium enthalpy difference between initial and final temperatures is converted to convective kinetic energy. However, for molecules in which a large number of collisions are required to convert internal energy to translational energy the relaxation of internal energy may be incomplete. By time-of-flight analysis of beams from free jets of cyclopropane Gallagher found that rotational energy remained almost in equilibrium with translational energy but that vibrational energy did not relax at all during the expansion [ Ill. Thus, the vibrational energy of the molecules after expansion was essentially characterized by the source temperature. The nozzle Renyolds numbers in our experiments were always less than in Gallagher’s experiments. Therefore, there

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should have been no more vibrational relaxation than he observed. Consequently, we felt safe in assuming that the vibrational state of the molecules incident on the target was the same as in the source gas before expansion. It is clear that variations in the source temperature will change the translational energy of the reactant molecules as well as their vibrational energy. However, it is possible to vary the translational energy of the molecules independently of the source temperature by introducing an inert gas having a sonic velocity higher or lower than that of the cyclopropane [7]. In principle, by this so-called seeding technique we could have maintained the translational energy of the cyclopropane molecules constant while varying the vibrational energy by changing the source temperature. In practice we found, as will be described, that in accelerating the cyclopropane with helium and decelerating it with argon, there wasvery little dependence of reaction probability upon translational energy. Consequently, we did not attempt to maintain a constant translational velocity while we covered a fairly wide range of vibrational energy in the molecules incident upon the surface. 2.4. Analysis of reactants and products The cyclopropane was Matheson CP grade (98.0 mole%) with a typical composition of 99.8% cyclopropane, 0.18% propylene and 0.02% propane. Carrier gases for the seeding experiments were helium, Air Products CP grade (99.995 mole%) and argon, Matheson UHP grade (99.999 mole%). To determine the extent of isomerization as a function of time we analyzed periodic samples of 0.2-0.4 cm3 withdrawn with a gas syringe at the stagnation pressure (410-430 Torr) through two septa in series. The space between the septa was continuously flushed during sampling with helium at one atmosphere so that the contents of the syringe was brought up to one atmosphere with diluent helium, the carrier gas used in the chromatograph. 2.5. Determination of reaction probability The reaction probability is calculated from a plot against time of the natural logarithm of reactant mole fraction in the gas samples. Of course, the observed overall depletion of reactant cyclopropane includes the contribution from homogeneous reaction in the nozzle stagnation region. In each experiment this background rate was determined for given nozzle conditions with the target surface cold and was subtracted from the overall rate to obtain the net conversion due to collision of molecules with the target. For a first order reaction the slope of the resulting straight line is related to the reaction probability by the following expression p = slopelfr , where f is the fraction per pass of molecules intercepted by the target and r is the recycle frequency. The recycle frequency is measured directly by injecting a small

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quantity of tracer (0.1 cm3 helium) into the sampling port and with a mass spectrometer monitoring the concentration of helium in the reaction chamber as a function time. About three cycles can be followed before the tracer concentration becomes too dispersed in the gas stream to provide a well-defined peak [S]. The fraction intercepted by the round target can be readily calculated from target dimension, nozzle-target distance, and the radial density distribution in the jet [8]. For the square target, we estimated the fraction intercepted from a calculation which assumed a round target of equivalent area.

3. Results

No conversion of cyclopropane to propylene could be detected when all surfaces were cold and the reactant was recycled through the hot mercury pumps for several hours. A measurable conversion was detected when the Bayard-Alpert ionization gauge was on. The rate of conversion due to the gauge was two orders of magmtude smaller than the lowest rate reported here for the hot mica surface. AI1 reported results are with the gauge off either most or all of the time during the run. Blank experiments were performed with three surfaces which represent materials of construction of the reactor. Stainless steel and freshly abraded molybdenum surfaces did not effect the conversion of cyclopropane to propylene. A midly oxidized molybdenum surface had an activity about half that of the mica at all temperatures and showed a surface activation energy of 19 kcal/mol, about the same as mica [12]. At a cyclopropane background pressure of 5 X lo4 Torr reaction on the molybdenum target-heater block could not account for more than 5% of the overall conversion even if the effective temperature of the cyclopropane molecules was the same as that of the source. The actual cyclopropane background pressure was less than 10m4 Torr and because the temperature was probably the same as for the walls of the vacuum chamber, and because the heater block was surrounded by a stainless steel heat shield, the contribution to conversion from reaction on the heater block was, in fact, negligible. The peripheral molybdenum flange used to secure the mica to the heater block did contribute a few per cent to the observed conversion. Results obtained with a stainless steel flange, which was insert, indicated that the contribution from the molybdenum flange was within the 6% uncertainty in the overall reproducibility of consecutive runs. The molybdenum flange was preferred because the higher coefficient of expansion of stainless steel resulted in poor thermal contact between the mica surface and the heater block. 3.2. E#&.-t of surface temperature oy1reaction probability An arrhenius plot of the logarithm of reaction probability versus reciprocal surface temperature is shown in fig. 1. The nozzle temperature was constant and equal

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3.0

1.1

1.2

1.3

1.4

l/Ts X lo', K-l

Fig. 1. Arrhenius plot of reaction probability against reciprocal surface temperature at a constant source (vibrational) temperature. The solid triangles and squares relate respectively to nozzle target distances of 200 and 400 nozzle diameters. The semi-open squares relate to a nozzle target distance of 100 nozzle diameters. The apparent activation energy in each case is 21 kcal/mol.

to 745 K for these experiments. The experimental points fall on a straight line whose slope corresponds to an activation energy of 21 f. 1.5 kcal/mol. As indicated, three different nozzle-target distances were used. The reaction probabilities for the points referring to target distances of 200 and 400 nozzle diameters from the nozzle, are in just the ratio which would be expected for the calculated values off, the fraction of jet gas intercepted by the target. #en the target is only 100 nozzle diameters from the target, i.e., 1 cm, there is an apparent increase in the reaction probability relative to f. These results were obtained with the square target. The apparent sixfold increase in rate is much too large to be accounted for by faulty approximation of the fraction f.There are two alternative possibilities: (1) The temperature profile across the target is not uniform and at short nozzle-to-target distances a larger portion of molecules intercepted strike the center which might be hotter than other portions of the target, or (2) at very short nozzle-to-target distances essentially all molecules leaving the nozzle are intercepted by the target and a fair fraction of those rebounding from the target will also be intercepted by the hot nozzle and its heater. In fact, some molecules could undergo several bounces on

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each cycle. The multiple bounce explanation of high reaction probability appears reasonable, but we have not performed enough experiments to prove it. In experiments discussed in the following two sections, the nozzle-target distances were large enough so that the mean free path in the jet gas was of the same order as the target diameter which itself was large relative to the frontal dimension of the nozzle assembly. Under these conditions, complications due to multiple bounces were minimal. A thermal radiation shield was used along with the round target. It comprised a thin stainless steel sheet with a small hole placed against the nozzle face. The thermocouples on the target indicated that the shield effectively eliminated radiation heating of the target surface by the nozzle and its heaters. 3.3. Effect

of translational energy on reaction probability

To determine the effect of translational energy on the reaction probability the surface temperature was held constant at 830 K and the nozzle temperature (vibrational temperature) was maintained at 745 K. The translational energy was changed by seeding about 20% cyclopropane in helium and in argon. With pure cyclopropane the reproducibility in the measured reaction probability was usually better than *4%. When the reactant was diluted by carrier gas the analysis became more difficult. Moreover, the process of preparing the gas mixtures increased the possibility of contamination by traces of atmospheric oxygen in the reactant stream, which lowers the reproducibility for the seeded beam experiments to about +20%. We have found that small amounts of oxygen promote the complete destruction of product propylene with a concomitant formation of methane and ethylene in approximately equal quantities. It should be noted that these products cannot be due to simple cracking of either cyclopropane or propylene which would produce methane and acetylene. The oxygen presumbaly oxidizes some hydrocarbon to CO? (and perhaps HzO) to supply the hydrogen needed for the ethylene since photoelectron spectroscopy shows that a continued build-up of carbon residue does not occur. Results on duplicate runs of various translational energies of incident cyclopropane molecules are shown in table 1. The indicated kinetic energies relate to the most probable velocities. Because of the high degree of expansion the local (static) temperature is quite low so that the energy spread around the indicated value is only ten percent. Values in the column labeled Teff correspond to the source temperature that would be required to provide with pure cyclopropane the most probable kinetic energy in the fourth column, assuming no vibrational relaxation during the expansion. They do not reflect what the situation would be if the target were exposed to quiescent reactant gas at T,ff. In thet case, the much broader velocity spread around the most probable value would encompass translational energies in its Boltzmann distribution much higher and lower than in the free jet after expansion. It is clear from the results presented in table 1 that the reaction probability does

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Table 1 Effect of translational energy on reaction probability Mole% inert carrier

Teff (K)

0 0 78% 79% 77% 80%

745 745 1791 1838 550 543

He He Ar AI

a

Velocity (cm/set) 10.7 10.5 16.84 17.06 9.33 9.27

X

lo4

Kinetic energy @al/mol)

Reaction probability x104

5.93 5.93 14.23 14.60 4.36 4.31

2.83 2.93 1.99 1.82 3.04 2.49

a This is the effective nozzle temperature required to obtain the indicated kinetic energy by expansion of pure cyclopropane in which no vibrational relaxation occurs.

not increase with increasing translational energy. In fact, there is a 30% decrease in reaction probability when the kinetic energy is more than doubled by seeding with helium. We think this decrease is real and is due to the decreased contact time between target surface and reactant molecule at high incident velocities. It is worth emphasizing at this point that the distribution in translational energy is sharply peaked at the indicated velocity. Superposed on the convective velocity indicated in table 1 is a Boltzmann distribution which corresponds to a local temperature (measured by a thermometer moving with the beam) of only a few degrees above absolute zero. The vibrational energy as we have pointed out is characterized by a Boltzmann distribution at the source temperature of 845 K. 3.4. Effect of vibrational energy on reaction probability An arrhenius plot of the homogeneous background reaction rate in the nozzle gives an activation energy of 66 kcal/mol, in good agreement with gas phase bulk experiments [lo]. The reaction probability on the surface, corrected for background reaction in the nozzle, is plotted against reciprocal nozzle temperature in fig. 2. The results were obtained with both square and round targets, a larger temperaturc range of 120 K having been covered in the latter case. In both cases the apparent activation energy is lower than for the homogeneous reaction and is approximately equal to 56 kcal/mol. For the data shown the surface temperature was 830 and 756 K, respectively, for the square and round targets. When the reaction probabilities on the square target are corrected to a surface temperature of 756 K (dashed line in fig. 2), there remains a difference in reaction probability equivalent to a difference of approximately 15 K in surface temperature, well within the uncertainty of the surface temperature determination. 3.5. Isotope effects on the reaction probability The isomerization of cyclopropane and perdeuterocyclopropane were performed in separate experiments under conditions as nearly identical as possible. The ratio

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2.5

\ 3.0

SQUARE TARGET

3.5

a ," 4.0 5 I 4.5

ROUND TARGET

5.0

5.5 1.2

1.3

1.4

l/T, X 103, K-l

Fig. 2. Arrhenius plot of reaction probability against reciprocal source temperature showing the effect of vibrational temperature on isomerization rate at a fixed surface temperature. The slope indicates an apparent activation energy of 56 kcal/mol.

of reaction probabilities (kH/kD) in the nozzle (homogeneous reaction 805 K) was 1.7 + 0.2, in good agreement with the value of 1.85 obtained by Blades [ 131. The ratio of reaction probabilities at the mica surface (T = 734 K) was 0.9 f 0.1. This value is in reasonable accord with the low pressure data of Rabinovitch et al. which probably reflected walI effects [14]. The rather large uncertainty in our values for this ratio stems from the large activation energy and the consequent large temperature dependence. We had to determine the bulk rate for each isomer in separate experiments subject to uncertainties in nozzle temperature of +3 K. While this uncertainty in temperature is only 0.2%, it gives rise to an uncertainty of about 10% in the probability ratios. Uncertainty in the value of the rate ratio for reaction at the surface was further compounded by uncertainty in the target temperature.

4. Discussion 4.1. Introduction By this time it should be clear that the unique feature of the experiments reported here consists in their ability to distinguish between effects on reaction

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probability due to surface temperature, the velocity of the incident molecules and their vibrational energy state when they strike the target. The hope is, of course, that this separation of variables will be helpful in elucidating the mechanism by which isomerization of cyclopropane occurs. Our measurements relate primarily to the surface induced reaction but they may also reflect some light on the pathway by which the homogeneous gas phase process occurs. The process of unimolecular isomerization has been intensively studied by many investigators and has been recently reviewed by Berson [ 1.51. We will briefly outline the essential features which seem to relate to our results. It has been experimentally established that the Arrhenius activation energy for isomerization of cyclopropane to propylene is 65.6 kcal/mol and that the pre-exponential frequency factor is about 10’5.5. In the classical Rice-Ramsperger-Kassel approximation these results imply a value of 12 or 13 for s, the number of vibrational modes which participate in intramolecular exchange of the energy required to surmount the activation barrier, e.g., to rupture a C-H and C-C bond in the cyclopropane molecule * [ 161. Benson and his colleagues have argued persuasively that the mechanism most consistent with these experimental observations comprises the formation of a trimethylene biradical intermediate by rupture of a C-C bond [17-191. As discussed by Benson, the experimental frequency factors are quite consistent with what might be expected for the trimethylene mechanism making the overall picture quite inviting. However,i3erson points out that a number of apparent deficiencies arise in the concept of a stereorandom biradical intermediate when it is applied to experimental results obtained for stereomutation of cyclopropanes in which the H atoms have been replaced by groups of varying complexity [ 151. We will not attempt to explore and analyze the arguments but we will note for future reference than one weakness of the biradical hypothesis is the lack of any independent evidence for the existence of a metastable trimethylene biradical intermediate. Increasingly elaborate quantum mechanical calculations have thus far failed to confirm its existence. Moreover, all experimental attempts to identify it by use of radical scavengers have been fruitless although it is obvious from the predicted equilibrium concentration that this is a difficult task [ 171. There has also been some previous work on the heterogeneous isomerization of cyclopropane which is relevant to our results. Kennedy and Pritchard found that the activation energy for thermal isomerization to propylene on a Pyrex surface is 57.2 f 2 kcal in the temperature range from 750 to 790 K [20]. They conclude that in the low pressure first order (wall-dominated) region “the nature of the isomerization of cyclopropane is unchanged, the only difference being that energization takes place predominantly on the walls instead of in the gas phase.” This * We do not suggest that the classical RRK model is a valid representation of the real process. Here and later we will use it only as an empirical description of actual rates with s as an adjustable parameter chosen to give the best fit to experimental data.

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interpretation was echoed by ~binovitsch et al. and strongly endorsed by Thomas et al. when they referred to cyclopropane results in a discussion of their own work on methyl cyclobutane [ 14,211. The only direct evidence against a surface catalyzed reaction appears to be the observation in the case of cyclobutane that at low pressures the rate constant is not increased in proportion to the surface-tovolume ratio [21]. In the case of cyclopropane there is a similar observation in that the rate was only increased by a factor of 2.5 when the surface-to-volume ratio was increased by one order of magnitude [20]. These experiments do not exclude the possibility of parallel reaction in the gas phase and on the surface after surface collision activation in both cases. There are well known examples of surface reaction at low temperatures where the high activation process (gas phase decomposition of collision activated molecules) cannot compete. For example, Hall et al. found that over silica-alumina at a temperature of 423 K the isomerization of cyclopropane was clearly catalytic and characterized by an activation energy ranging from 1.5to 35 kcal, depending upon the catalyst treatment. To explain their results they invoke a mechanism which involves formation of a carbonium ion intermediate after the cyclopropane molecule becomes hydrogen-bonded to an acidic hydrogen atom on the surface [23]. 4.2. Effect of ~~br~tio~l

energy at constant temperature

It is now appropriate to examine our results in the light of these past studies. We first note that the seeding experiments summarized in table 1 clearly indicate that the translational energy with which a ~yclopropa~e molecule hits the target surface has very little effect upon reaction probability. Indeed, the result with helium suggests that at a high velocity of incidence the reaction probability decreases slightly. This evidence is not unequivocal because of the possibility (unlikely, we think) that helium atoms might be more effective than cyelopropane molecules in lowering the vibrational temperature of cyclopropane during expansion. There is both experimental and theoretical support for the position that inert gas-~y~loprop~e collisions are less effective than bimolecular cyclopropane collisions [10,24]. Of much more interest and significance is the effect of vibrational temperature on reaction probability. As is shown in fig. 2 an Arrhenius plot of reaction probability against reciprocal source temperature gives a straight line with a slope corresponding to an activation energy of 56.4 kcallmol. As we have already noted, the homogeneous gas phase reaction has an activation energy of 65.6 kcal/mol. If the mechanistic path in the two cases is to be presumed similar, we must in some way explain how the surface provides a reaction pathway which requires 9 kcal less energy than the gas phase reaction. A similar problem emerges in any attempt to make the previous heterogeneous results conform with the homogeneous pattern. Recall that Kennedy and Pritchard found an activation energy of 5’7kcal for reaction on a Pyrex surface, very close to our value [20]. They and Rabinovitch et al. attach no particular significance to the apparent deficit of 9 kcal [ 141. One can un-

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derstand their lack of concern because the observed activation energy for these heterogeneous experiments falls between the limiting values of 65.6 kcal/mol at high pressure and 48.5 kcal/mol at low pressure for the homogeneous gas phase reaction. By simply assuming that the wall is a more efficient collision partner than a gas molecule, they can dismiss any possibility of surface participation involving adsorbed species [ 14,201. As noted by Benson, the activation energy for gas phase isomerization at the low pressure limit does not imply an activation energy below the critical 65.6 kcal/mol [ 111. The lower value is an experimental consequence. The time between collisions has become long compared to the time for unimolecular decomposition of those molecules with energy above the critical energy E*. The experimental activation will be the difference in the average energy between reacting and the average molecule which has energy skT. At very low pressure most molecules that react will not attain an energy above E* t kT because of the relatively long time between collisions relative to the decomposition time. The difference between the reacting and average molecule is thus E*-(s-

l)kT,

which becomes the theoretical

low pressure limit of

E*-(s-;)kT,

after correcting for the temperature dependence of the coliision frequency. Assuming a value of 13 for s and a temperature of 750 K, the low pressure limit is 48.5 kcal/mol. As we will show below, cyclopropane molecules in our experiment have certainly reached the low pressure limit in the sense that molecules that exit the nozzle with energy in excess of E* will have had sufficient time to react before they collide with a surface as was the case in the experiments of Kennedy and Pritchard or Rabinovitch et al. [14,20]. Our experiments differ from the previous experiments in that the gas and wall temperatures need not be the same and we can measure the probability of reaction following a single surface collision. Thus, we can calculate the probability of reaction due to a single non-sticking collision using the classical RRK model and compare it to experiment. First we show that all of the molecules which acquired in the source the activation energy necessary for gas phase reaction have reacted by the time they reach the target. The RRK classical model predicts a mean lifetime for such a vibrationally excited molecule of: r,,, = V-‘(1 t E*/skT)-’

,

(1)

where E’ is the activation energy, k is the Boltzmann constant, 3 is the kinetic frequency factor for unimolecular reaction and s is the number of vibrational modes in the molecule which can contribute to the activation energy needed in some critical mode in order for reaction to occur [ 161. There are 21 possible vibra-

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tional modes in cyclopropane but it turns out that a good fit to experimental data on the pressure dependence of the gas phase isomerization rate is obtained if s is taken as 13 for a collision diameter of 3.9 A [25]. It follows that only 13 of the possible vibrational modes can participate in the reaction process. Using the high pressure rate constant k = 10 ‘5~5exp(-65,500/RT) to evaluate V and E*, we find r, = to 3.0 X lo-* set at 700 K and 8.8 X low9 set at 800 K. For the minimum nozzle target distance of 1 cm, the respective minimum flight times for these two temperatures in our experiments were 9.6 and 8.9 X 10m6 sec. Thus, the flight times were very long relative to the reaction times in every case so that all the molecules with energy above E* should have reacted by the time they reached the target. The most likely candidates for reaction al the surface, therefore, are those molecules which lacked only one quantum of energy in one of the 13 active vibrational modes. We suppose that we can characterize the surface as an array of oscillators such as Si = 0 which typically have vibrational energy levels about 1000 cm-’ apart [26]. At 750 K about 15% of these oscillators would be excited to the first or second vibrational level. If the most probable transfers are assumed to be near-resonant, then we are concerned with those vibrational modes in the incident cyclopropane molecules which have an energy level around 1000 cm-’ above the ground state. When the source temperature is the same as the surface temperature, 750 K in the case we are considering, the incident cyclopropane molecules will also have about 15% of these modes excited. The remaining 85% will be in the ground state. We can thus conclude that the transfer of a vibrational quantum, from the surface to an unexcited, near resonant mode of the incident molecules, will have a maximum probability of about (0.15) X (0.85). Similarly, the probability that one of the initially excited modes will be further excited from the first to the second vibrational level will be about (0.15)* X (0.5). (The factor 0.5 is due to the fact that in this second kind of encounter the transfer can occur with equal probability in either direction.) If energy exchange occurs on every collision, the maximum reaction probability will thus be: P= 0.15 (0.85 + O.l5/2)[F(E

* -/IV)]

,

(2)

where F(E* - hv) is the fraction of incoming molecules having vibrational energy in the 13 iarticipating modes which is just one quantum short of the amount necessary to pass over the activation barrier. Note that identical probabilities apply to the transfer of energy from the molecules to the surface. Consequently, as the Second Law requires, there is no net transfer in either direction. Moreover, even when the surface temperature is lower than the source temperature, and there is overall a net flow of energy to the surface, some of the incident molecules can be excited to reaction. That this may happen is clearly indicated in fig. 2 where the arrow indicates the vibrational. (nozzle) temperature which is equal to the surface temperature. We now require an estimate of F(E* - hv). Treating the vibrational modes of

G. Prada-Silva et al. /Role

cyclopropane

once again as classical harmonic

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467

oscillators we may write: (3)

Numerical integration with 1000 cm-’ as a value for hu and 13 as a value for s we obtain the fraction of molecules within one quantum of E* to be 3.7 X lo-’ at 700 K and 2.1 X lo-’ at 800 K. The observed reaction probabilities at these temperatures were respectively 3.4 X 10e6 and 5.4 X 10V4. In short, eq. (2) in conjunction with eq. (3) predicts a maximum reaction probability which is too small by almost 4 orders of magnitude. We thus find highly unlikely any mechanism based on the transfer during a non-sticking collision of a vibrational quantum from the surface to one of the participating modes in the incident molecule. We can bring the calculated reaction probability much nearer to the observed value if we include all the molecules having energy within one quantum of the requirement and remove the restriction that this energy be found in the modes which appear to participate in surmounting the energy barrier to reaction, i.e., if we let s = 21 rather than 12 or 13. In this case eq. (3) gives values for F(E* - hv) of 1.55 X lo-’ at 700 K and 2.95 X 10m4 at 800 K. If we adhere to the reasonable assumption that the energy required for activation must find its way into one of the modes which participate in the gas phase reaction, then a lot must happen during a non-sticking collision with the surface. The incident molecules must pick up a quantum of energy from the surface and, in addition, at least one quantum, and more often several, must be shuffled within the molecule from non-participating to participating modes. All this must happen with unit probability during a single nonsticking collision for every molecule lacking only one quantum of total vibrational energy. We can improve the reaction odds a bit more by including those molecules whose total energy before collision is sufficient for activation but is not in the proper modes. A much bigger effect could be obtained by assuming physical adsorption. For example, the heat of adsorption of cyclopropane on silica-alumina was reported to be 5.2 and 5.5 kcal/mol by Hall et al. and Hightower and Hall [23,27]. From this one can estimate an adsorption lifetime of about lo-” set at 750 K assuming a vibrational frequency of 3.3 X 10-l 3. This would be equivalent to approximately 30 surface collisions per molecule if a sticking coefficient of one was invoked. Even so, the complexity of the energy redistribution which would seem to be required in either case dilutes the credibility of this approach. Furthermore, the mechanisms we have been considering in no way explain the experimentally observed dependence of reaction probability on surface temperature, a dependence which corresponds to an apparent activation energy of only 21 kcal/mol. There is no theoretical or experimental precedent for such a strong temperature dependence of a physical adsorption sticking coefficient [28]. These considerations persuade us that the surface cannot be convincingly cast in the relatively simple role of an unreactive partner in an inelastic but non-sticking collision. Accordingly, we examine the other reasonable alternative, namely that

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the overall process involves true surface chemisorption of an incident cyclopropane molecule. Such adsorption must be activated in the sense that only those molecules with 56 kcal/mol of vibrational energy can achieve the surface state which ultimately leads to propylene formation. This energy requirement is provocatively close to the value of 54 kcal/mol which thermochemical calculations indicate is the energy difference between a ground state trimethylene biradical and a ground state cyclopropane [ 181, The fact that the apparent activation energy and enthalpy of formation of a trimethylene radical are nearly identical suggests the possibility of a mechanism involving the irreversible chemisorption of the trimethylene radical. Assuming the heat of physical adsorption of cyclopropane is about 5 kcal and the forward and reverse rate constants for the formation of the trimethylene radical from cyclopropane that were estimated by O’Neal and Benson, one can estimate an upper limit for the reaction probability. Since the estimated reaction probability is much lower than measured, we conclude that the apparent activation energy of 56 kcal/mol represents the barrier to direct chemisorption upon collision with the surface. It still may be argued that the internally activated cyclopropane species that chemisorbs has much in common with a radical since (1) it appears to readily chemisorb on what are usually considered inert surfaces (Pyrex and mica) and (2) possesses energy in excess of the enthalpy of formation of trimethylene radical. The isotope ratio (kH/kD) of about one might as first suggest that the formation of the chemisobred species does not involve the breaking of a C-H bond. However, the vibrational frequencies of the deuterated molecule leads to a higher population of vibrational modes which would increase the rate while the usual kinetic isotope effects would lower the rate. Thus, an equivocal interpretation is not possible. 4.3. Effect of surface temperature at constant vibrational energy The essential features in the scenario we have just constructed are that a cyclopropane molecule incident upon a surface will be strongly adsorbed if it is activated by possessing 56 kcal/mol of internal energy. It will then be transformed into an adsorbed propylene which is desorbed to become a product molecule. We have had to call on the substantial amount of adsorption energy which must be released during adsorption of the biradical in order to justify a lower activation energy than observed in the gas phase. This strong interaction with the surface can offer an explanation for the rate dependence on surface temperature that would not be possible assuming a non-sticking surface collision. The apparent activation energy for the surface process, which we infer from the surface temperature dependence of the rate, is 21 kcal/mol. It is noteworthy that we found a comparable value in some early preliminary experiments on a molybdenum oxide surface. It is within the range from 15 to 35 kcal/mol found by Hall et al. and by Bassett and Habgood for the activation energy of the truly catalytic process on silica-alumina [23,29]. Krivanek et al. found that the heat of irreverisble chemisorption of propylene on a

G. Prada-Silvaet al. /Role of vibrationalenergy

469

bismuth-molybdenum oxide catalyst averaged about 22.5 kcal/mol [30]. The adsorption was irreversible because there was enough oxygen present to oxidize the propylene to acrolein which was the major desorbed product. We found during our study that if even traces of oxygen were deliberately or inadvertently admitted to the system, the formation of propylene ceased and the production of methane and ethylene markedly increased. We did not look for acrolein. Even so, the prevention of propylene formation by oxygen in our experiments is entirely consistent with the idea that one stage in the surface isomerization of cyclopropane to propylene involves chemisorbed propylene which is extremely vulnerable to oxidation. Taken all together these observations suggest that the apparent activation energy of the surface process may be entirely attributable to the desorption of chemisorbed propylene and that this step may be rate determining in the surface catalyzed reaction. This low activation energy step could not, of course, be observed in those experiments where the gas was in thermal equilibrium with the wall and the activation energy for adsorption is high, e.g., the Kennedy-Pritchard experiments. It can be observed on better catalysts where the adsorption is less activated and in our experiments where the wall and gas temperature can be varied independently. Our reflections on mechanism have been preoccupied with the tacit assumption that both homogeneous and heterogeneous (but non-catalytic) isomerization processes occur via a transition state somehow related to some sort of a trimethylene biradical. As we earlier pointed out this mechanism has become somewhat suspect, experimentally because no independent evidence of a biradical intermediate has been found and theoretically because quantum mechanical calculations have not revealed any energy minima which could be associated with a biradical configuration. In reviewing these calculations Greenberg and Liebman conclude that no substantial energy preference exists for any particular structure which can reasonably be associated with a biradical reaction intermediate [31]. They also point out the possibility that a trimethylene zwitterion +CH,CH,CH; may be an equally viable candidate as a reaction intermediate , pith many of the same capabilities and shortcomings of the biradical model. Their overall conclusion may be an appropriate note upon which to conclude: “Indeed, the whole idea of well-defined structural intermediates appears suspect. One must seemingly consider dynamics and modes of internal energy . . . . It would appear that the simple ideas of molecular structure and reaction coordinates have seemingly been replaced by potential-energy surfaces and trajectories. While profound understanding and even intuition may be achievable at this newer level of complexity, it is nonetheless distressing to us that such complexity is necessary to understand such a seemingly simple and long-studied reaction.” Acknowledgments Acknowledgment is made to the Donors of the Petroleum administered by the American Chemical Society, for partial

Research Fund, support of this

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research. Partial support by the National 37074 is also acknowledged.

of vibrational energy

Science Foundation

under Grant No. GK

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