J . Phys. Chem. 1984, 88, 5167-5172
I
/ I
72
1
76
16 N(E-Eo)
k ( E ) = 2x10
I
I
N(E)
I
80
I
84
I
I
88
INTERNAL ENERGY, E ( k c a l mole-') Figure 6. Unimolecular decay rate constant obtained on using Forst's eq 1. See text and footnote 32 for details.
be produced, we find that an excess energy of at least 3.5 eV must be deposited in DTH, and fully utilized upon subsequent ionization, for observing CH3+ions upon vacuum-UV photoionization at 10.47 eV. From Figure 6 we find that with 3.5-eV internal energy (-81
5167
kcal/mol) the dissociation rate of the neutrals is about lo7 s-'. Thus, the fraction of molecules that will be dissociated during the 20-11s (fixed delay) time interval preceding the appearance of the vacuum-UV photoionizing pulse is between 15% (E, = 64 kcal/mol-I) and 70% (E, = 60 kcal mol-'). These large fractions mean that the first methyl ions observed in the system arise from radicals formed by neutral dissociation of DTH. Comparison with Previous Work. The major conclusion from this work is that in DTH energy redistribution is faster than the reaction rate induced by IRMPE. This result is in line with previous conclusions but is of more direct nature than previously published work. The paper of Farneth and Thomson" made the important observation that a reaction characterized by two separate but kinetically identical channels should be used. This work added the following features, to make the conclusion more unambiguous. (1) An attempt was made to place a barrier (in the form of the S C r C S group) between the two reaction site. The barrier evidently proved to be ineffective. (2) Yield measurements were made in real time, avoiding possible masking of the initial nonrandom reaction. (3) The pressure range was extended by several orders of magnitude. At the pressure used torr), very few collisions occur during the up-pumping process. This work thus constitutes a direct demonstration of intramolecular energy scrambling in a nearly isolated molecule undergoing IRMPE. The mechanism of the scrambling process is not yet clear-it may involve dipole-dipole interactions at low excitation energies, as well as anharmonic coupling in the quasicontinuum region. Realization of site-selective IRMPE reactions, if possible, must involve the design of a molecular structure that reduces the efficiency of these couplings by several orders of magnitude. Acknowledgment. We thank Prof. J. Blum, Dr. M. Weizberg, and Dr. S. Gershuni for their help in synthesizing DTH. Many discussions with Prof. C. Lifshitz are gratefully acknowledged, as well as her help in the MIKES measurements, together with Mrs. T. Peres. W e are indebted to Prof. T. Baer for communicating his photoionization results prior to publication. This work was supported by the US-Israel Binational Science Foundation, Jerusalem, Israel. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, FRG. Registry No. DTH, 91781-38-3;CH,, 2229-07-4; CD3, 2122-44-3.
Translational and Rotational Cooling in Supersonic Beams of OCS Seeded in Argon M. Maier,+ Henry S. Luftman,*and John S. Winn*g Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, California 94720 (Received: February 17, 1984) Translational and rotational relaxation in supersonic beams of OCS seeded in Ar was studied over a stagnation pressure-nozzle diameter product range of 5-140 tomcm at stagnation temperatures of 295,390, and 446 K. The relaxed translationaldistribution was measured by conventional time of flight (TOF) methods. The fraction of OCS molecules in the J = 1, MJ = 0 rotational state in that spatial and velocity group of the beam passed by electrostatic-state selectors was measured to probe rotational relaxation. These molecules were found to have an apparently greater J = 1, MJ = 0 population than that predicted by the full-beam translational temperature, indicativeof a possible state-specificenhancement of rotational relaxation for molecules at the longitudinal flow velocity. Introduction The supersonic molecular beam provides perhaps the most complex nonequilibrium distribution for the least amount of ex'Present address: IBM Research Center, San Jose, CA 95193. *Present address: Department of Chemistry, University of Texas, Austin, TX 78712. #Addresscorrespondence to this author at his present address: Department of Chemistry, Dartmouth College, Hanover, NH 03755. 0022-3654/84/2088-5167$01.50/0
perimental effort. A gross description of terminal energy distributions in such beams is that they are translationally very cold, rotationally nearly as cold, and vibrationally cold but considerably warmer than for rotations. Precise descriptions depend critically on the details of the supersonic expansion (nozzle size, source stagnation pressure and temperature, and gas compos~t~on), on the presence and position of collimating aperatures such as skimmers, on the position downstream where one interrogates the 0 1984 American Chemical Society
5168 The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
beam, and on the method of interrogation itself. The concept of temperature (or even terms such as hot and cold) must be applied with care to nonequilibrium distributions. At its most complete meaning, a temperature implies a unique distribution of population (an equilibrium one) among all states. At its simplest, a temperature may mean no more than a ratio of populations in two different states. This simplest application is the one most often applied to supersonic expansions. Since internal excitations are greatly reduced by the expansion, one frequently has only a few vibrational levels with sufficient population for observation, and these populations are usually fit within experimental error to a single Boltzmann factor (and thus to a single vibrational temperature). Translational distributions are generally measured by fitting time of flight spectra to assumed velocity distributions (discussed in detail later) which presuppose a Maxwellian form (and thus single translational temperatures). The question we address in this paper is most directly related to the rotational distribution. Consider an equilibrium sample of a polyatomic gas. If one could select molecules in an arbitrary velocity group in this gas and interrogate their internal states, one would find equal rotational-vibrational temperatures for every velocity group, and these temperatures would all be the same, i.e. the equilibrium temperature. To what extent is this true for the nonequilibrium distribution of a supersonic beam? In particular, are different velocity groups described by different internal-state population distributions? We have used time of flight measurements, rotational-state focusing, and electric resonance spectroscopy to examine these questions. Time of flight distributions yield translational temperatures characteristic of all the molecules in the unobstructed solid angle subtended by the beam detector. Electrostatic focusing probes the rotational-state distribution of that spatial and velocity group transmitted by the electrostatic-state filters. Our results indicate that the rotational distribution may not be uniform at all velocities. We are not the first to suggest or to observe nonuniformities in internal-state distributions. Bergmann, Hefter, and Hering' used sub-Doppler laser-induced fluorescence to probe the velocity profile of selected vibration-rotation levels of Na2 in a supersonic beam. These authors found significantly different velocity distributions for Naz in various internal quantum states, with low-energy quantum states correlating with the narrowest (coldest) velocity distributions. Similarly, Bennewitz and Buess2 found that CsF seeded in Ar exhibited a vibrational temperature which increased as the CsF velocity was increased or decreased from the most probable value. Their technique was similar to ours in that electrostatic focusing and electric resonance spectroscopy were used to deduce the CsF internal temperatures. Our experiments used OCS seeded in Ar. OCS has been studied by other groups, using similar methods. Kukolich, Oates, and Wang3 found large deviations from a Boltzmann distribution of rotational population ratios using a beam maser spectrometer to probe the OCS ( J = 0-2) populations. Zivi, Bauder and Giinthard4 observed the OCS ( J = 1 0) transition by injecting a supersonic molecular beam into a microwave Stark cell and found the signal to correspond to emission, indicative of a gasdynamic population inversion. Double-resonance experiments confirmed that the J = 1 population was not in thermal equilibrium. Meerts, Ter Horst, Reinartz, and Dymanus5 combined time of flight and electric resonance spectroscopies to examine the translational and rotational temperatures of OCS, in both pure OCS and OCS/Ar beams. A variety of other techniques have probed molecular beams with rotational-state resolution: various electrostatic focusing methods:,' laser-induced fluores~ence,"~ electron-impact fluorescence,I0
-
(1) Bergmann, K.; Hefter, U.; Hering, P. J . Chem. Phys. 1976, 65, 488. (2) Bennewitz, H. G.; Buess, G. Chem. Phys. 1978, 28, 175. (3) Kukolich, S. G.; Oates, D. E.; Wang, J. H. S. J . Chem. Phys. 1974, 61, 4686. (4) Zivi, H. S.; Bauder, A.; Giinthard, Hs. H. Chem. Phys. Left.1981,83, 469: Chem. Phvs. 1984. 83. 1. ( 5 ) Meerts, W. L.; Ter Horst, G.; Reinartz, J. J. L. J.; Dymanus, A. Chem. Phys. 1978, 35, 253.
Maier et al. Raman scattering,"J2 and bolometer-detected IR beam absorpt i ~ n . ' ~ - Most ' ~ of these experiments have been insensitive to the velocity distribution of molecules in a given quantum state. Experimental Section The apparatus used was a supersonic molecular beam electric resonance spectrometer. This spectrometer will be described in detail in a subsequent publication.16 Briefly, the apparatus consists of differentially pumped chambers which function as beam generation, buffer, spectroscopy, and detection chambers. The beam source chamber is directly pumped by a 1600 cfm blower pump, allowing beams to be generated at very high source pressurenozzle diameter products. Nozzles of 0.1-, 0.2-, and 0.4-mm diameter were used in these experiments. The nozzle source could be varied in temperature from 77 to >500 K. At a variable distance downstream from the nozzle, the beam was intercepted by a highly polished skimmer (opening diameter of 0.48 mm) which passed the central portion of the beam into a buffer chamber. The beam emerged through a 0.5-mm diameter collimator from the buffer chamber into a third chamber housing the components of an electric resonance spectrometer. Quadrupole A and B fields (36.1 and 25.4 cm long, respectivelye, which could be operated at dc potentials of 30 kV or less, served as the rotational-state selector and analyzer, respectively. The C field consisted of two gold-coated optically flat pieces of Pyrex 20.5 X 10 cm2 in size and accurately separated by precision spacers. A movable stopwire, 0.119 cm in diameter, served as an obstacle to the central portion of the beam between the A and C fields. This arrangement is the standard flop-out scheme, wherein molecules undergoing an appropriate transition in the C field are not focused into the detector by the analyzing B field. The beam, on leaving the spectrometer chamber, enters a chamber housing a rotatable mass spectrometer beam detector. Two stages of differential pumping, one of which houses the quadrupole mass filter and particle detector, surround the electron bombardment beam ionizer. This ionizer and the mass filterdetector are pumped by separate 110 L-s-' ion pumps and by liquid-nitrogen cryosurfaces. For time of flight experiments, the A field was replaced with a motor-driven slotted disk, 4.9 cm in radium, with two opposed slits 1 mm wide turning at 120 Hz. The flight length from this disk to the ionizer region was 104 cm, All experiments reported here were with mixtures of OCS (0.1 mole fraction) in Ar, and all data were recorded by monitoring the OCS parent ion peak in the mass spectrometer.
-
Results
Time of Flight Anatysis. Experiments were performed using all three nozzle diameters at source temperatures, To,of 295, 390, and 446 K and at a variety of stagnation pressures. Data were accumulated in a 4096-channel signal averager with a time resolution of 1 ys per channel. Calibration runs with pure Ar at room temperature were made to establish accurate values for the ionizer response time. These runs were necessary because our ionizer operates in the space charge limited mode. Rather than estimating the residence time of the ionizer, these preliminary experiments served to measure ~
( 6 ) Borkenhagen, U.;Malthan, H.; Toennies, J. P. J . Chem. Phys. 1975, 63, 3173. (7) Keil, D.; Lubbert, A,; Schugerl, K. J . Chem. Phys. 1983, 7 9 , 3845. (8) Hansen, S . G.; Thompson, J. D.; Kennedy, R. A,; Howard, B. J. J . Chem. Soc., Faraday Trans 2 1982, 78, 1293. (9) McClelland, G. M.; Saenger, K . L.; Valentini, J. J.; Herschbach, D. R.; J . Phys. Chem. 1979, 83, 947. (10) Faubel, M.; Weiner, E. R. J . Chem. Phys. 1981, 7 5 , 641. (11) Godfried, H. P.; Silvera, I. F. Phys. Rev. A 1983, 27, 3008, 3019. (12) Valentini, J. J.; Esherick, P.; Owyoung, A. Chem. Phys. Leu. 1980, 75, 590. (13) Gough, T. E.; Miller, R. E. J . Chem. Phys. 1983, 7 8 , 4486. (14) Gough, T. E.; Miller, R. E.; Scoles, G. J, Phys. Chem. 1981,85,4041. (15) Douketis, C.; Gough, T. E.; Scoles, G.; Wang, H., submitted for publication. (16) Luftman, H. S.Ph.D. Thesis, University of California, Berkeley, CA, 1982. Luftman, H. S.; Maier, M.; Sherrow, S. A,; Winn, J. S., to be submitted for publication.
The Journal of Physical Chemistry, Vol. 88, No. 22, 1984 5169 0
Bot
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ameter (Pa) products for each source temperature investigated. All data pertain to OCS (0.1 mole fraction) in Ar. The lines are the predictions of eq 1.
the detector response function. Correction procedures were then used for converting OCS time of flight spectra to true velocity distributions, as follows. For each OCS scan, an iterative procedure was used in which the measured first arrival time (the onset of the rapidly rising TOF signal) and the geometric flight length were used to calculate a flow velocity from which a terminal beam temperature could be inferred. This temperature was used to generate a predicted arrival time and hence a corrected flight length, which was then used iteratively. This process converged rapidly and gave an effective flight length of 117 cm (compared to a mean geometric length of 104 cm). To show that this correction was principally due to detector response, comparisons were made with the Ar data. Semilogarithmic plots of the TOF signal tail vs. arrival time were made and found to be consistent with the flight length difference expectations described by Young." A slit function correction'* was applied to remove the effects of the finite TOF disk aperature width, and a very slight correction was made for the differences in time between openings of the beam aperature slot and the trigger aperature. Figure 1 shows the measured speed ratios for OCS at various source temperatures, To,and various stagnation pressure (Po)nozzle diameter ( D ) products. The speed ratio is given by ( m ~ ~ ~ / 2 k T , ,where ) ' / ~ ,so is the longitudinal flow velocity, T,, is the beam translational temperature, m is the mass, and k is Boltzmann's constant. The data are differentiated by source temperature only, since speed ratios were found to follow the same trend with P& for all three values of D at any one temperature. The standard treatment of translational +axation in a supersonic e x p a n ~ i o npredicts '~ a speed ratio, S, given by 3 = F ( y )(y/ 2 ) ' / 2 ( K n * ) - ( + ) / y (1) where y = Cp/Cu,Kn* is the effective Knudsen number (defined below), and F ( y ) is given by McClelland et al.9 The effective Knudsen number is the ratio of an effective stagnation mean free path to the nozzle diameter: K,,* = k T o / ( 2 ' / 2 P o D a t ) (2) where u is the usual hard-sphere cross section for the mean free path and is a parameter less than unity which accounts for the maximum fractional change in the mean random velocity per collision. (17) Young, W. S. Rev. Sci. Instrum. 1973, 44, 715. (18) Hagena, 0. F.; Varma, A. K . Reu. Sci. Instrum. 1968, 39, 47. (19) Anderson, J. €3.; Fenn, J. B. Phys. Fluids 1965, 8, 780. Anderson, J. B. In "Molecular Beams and Low Density Gasdynarnics"; Wegener, P. P., Ed.; Marcel Dekker: New York, 1974; p 1.
To the extent that 7,a, and t are independent of temperature, the speed ratio given by eq 1 is a universal function of the source parameter combination T o / ( P o D ) .The data in Figure 1 are in disagreement with this expectation. Previous m e a s ~ r e m e n t s ' ~ confirmed eq 1, but only at P& products smaller than (or Knudsen numbers larger than) those of the majority of the data in Figure 1. In fact, our low PODdata do follow eq 1 resonably well, as is shown by the three curves drawn on the figure. Each curve is of eq 1 with u* = at = 5 AZand y = 1.625, a mole fraction weighted equivalent y for our gas mixture. Departures from eq 1 occur at each To as sudden increases. These increases occur at a common value of the Knudsen number given by To/(P&) E 11 K-torr-l-crn-'. We believe that this effect is related to the fact that the transition from continuum to molecular flow is occurring upstream of our skimmer at low P& values, as required by the derivation of eq 1, but that continuum flow is continuing at and beyond the skimmer at the higher P$, values. Our results indicate that it is possible to extend the region of continuum flow through and beyond the skimmer orifice, raising the speed ratio further, without adversely affecting the beam intensity. (Each measurement was made at that nozzleskimmer separation which maximized the beam intensity.) Our combination of skimmer geometry, pumping system, and source. Knudsen number range is shown, by these measurements, to provide a cleanly attached shock wave, protecting the core of the beam from background gas intervention (at pressures as high as 0.1 torr in the source chamber) and from a turbulent nozzle-skimmer interaction. The formation of molecular clusters was observed in the beam mass spectrum throughout these experiments. By operating at elevated source temperatures (all above room temperature), we minimized the formation of such clusters. The most serious effect such cluster formation could have would be the release of the enthalpy of cluster formation. The fate of this enthalpy poses interesting questions. Is it disposed as an increase in the bulk flow velocity? Does it contribute to a preferential increase in the transverse speed? None of these questions can be addressed here, since cluster formation was kept at levels low enough to preclude the observation of such effects, but other m e a s ~ r e m e n t s ' ~tend J~ to indicate that this enthalpy does raise the translational temperature. To convert speed distributions to translational temperatures, we have used the standard form for the velocity distribution function wherein the probability of a transverse speed in the range u to u + du and a longitudinal speed in the range s to s ds is proportional to
+
exp{-[(s - so)2+ u2]/ab2)u du ds
(3)
where ab2= 2kT,,/m. The beam translational temperature is computed from the speed ratio by
(4) The speed ratios of Figure 1 span T,, values from 7.3 to 0.1 K or bb values from 4500 to 530 cm-s-'. Refocusing Analysis. The rotational-state population was probed by using the quadrupole A and B fields. The refocusing pattern as a function of A and B field potentials (to be discussed in detail in a later publication) showed a cleanly resolved maximum corresponding to selection of molecules in the (J,M,) = (1,O) state. It is the variation of transmitted intensity in this state with varying source conditions which we have measured. For each measurement, the percent refocusing of the beam, defined as (refocused signal, stopwire in place) X 100 (beam intensity, fields off, stopwire removed) was measured as a function of A and B field voltages. The J = 1, MJ = 1 0 radio-frequency transition of OCS was monitored as well, and the maximum transition intensity was found to occur at the same A and B field voltages which gave the maximum +-
5170 The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
Maier et al.
180
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Po ( t o r r ) Figure 2. Refocusing curves for To = 446 K. The dashed lines are explained in the text.
percent refocusing. This check ensures that the refocused intensity was faithfully monitoring the ( 1 , O ) state only. In Figure 2, we show the variation in the maximum percent refocusing with source pressure at the highest source temperature (446 K) for each of the three nozzle diameters. Data at the lower temperatures were similar to these, except the maximum in each curve occurred at lower Po values for the lower temperatures. The interpretation of these curves is straightforward. As Po is increased from zero, the final translational and rotational motions are more and more relaxed. If the gas were at equilibrium, there would be a unique temperature which would maximize the (1,O) state population; for OCS, this temperature is 0.682 K. The refocusing curves simply reflect the initial growth of (1,O) population to a maximum value followed by a decline as rotation is relaxed further. We also show in Figure 2, as dashed lines, the expected refocusing behavior on the assumption that an equilibrated rotational temperature equal to the translational temperature yould apply at each measurement. Each dashed line is normalized to yield the observed maximum refocusing of each set of data. The heights of these lines are of less significance than their shapes, which reflect the decrease in translational temperature with increasing source pressure. The measured (1,O)population is found to vary much more rapidly than the translational temperature variation alone would suggest, indicating a supercooling of the observed (1,O) population below the full-beam translational temperature prediction. Before interpreting these population changes, we emphasize exactly what we have measured. First, the A and B fields pass a selected rotational state, ( l , O ) , from a selected spatial and velocity band of the entire beam.20*21Careful computer simulations of beam trajectories in these experiments16 show that, in a typical case, those molecules with transverse velocity components greater than roughly 200 cms-' will not be focused by our apparatus. Thus, only the central portion of the full velocity distribution is sampled. (Recall that q,,the standard deviation of the transverse velocity component, ranged from 530 to 4500 cms-'. The geometry of our apparatus precludes molecules with transverse velocity components greater than -40 c m d from reaching the detector in the unobstructed, zero-focusing field voltage, TOF experiments.) Second, since these measurements pertain only to the (1,O) state, we are left in the position of not having a second state's population with which we can form a population ratio.22 (20) Dyke, T.; Tomasevich, G.; Klemperer, W.; Falconer, W. J . Chem. Phys. 1972,57, 2211. ( 2 1 ) Wicke, B. G . J . Chem. Phys. 1975, 63, 1035. (22) In principle, we could also have probed the J = 2 state, which focuses at the voltage limits of our fields. We chose not to, however, since the refocused intensity is not cleanly due to J = 2, being overlapped by other states and by residual (1,O) intensity from higher harmonic focusing trajectories.
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We therefore express the (1,O) population by assuming that an equilibrium rotational distribution exists in the velocity band transmitted by the fields. Points on the measured refocusing curves were expresed as fractions of the maximum refocusing for each Toand D. These points were assigned rotational temperatures according to the expression
(5)
where OrOt = B / k (0.2919 K for OCS), T,,, is the temperature which maximizes the (1,O) population (0.682 K), and Z ( T ) is the rotational partition function. In Figures 3-5, we show the ratio of T,, (computed from eq 4) to Tra (eq 5 ) plotted vs. P@ for each of the source temperatures studied. The data show similar trends. The Ttr/Trotratio is greatest for the lowest To, and the rise and fall are more pronounced for the lowest To. This method of assigning a rotational temperature (i.e. by following the population of one non-ground state from a hot to a cold distribution through a population maximum) can yield the same temperature as that deduced from the populations of several states at any one nozzle condition. Douketis, Gough, Scoles, and Wang'* measured rotational temperatures for CH,F using bolometer-detected IR absorptions in the v3 mode. At POD= 3.2 tormm, these authors found a J-dependent Boltzmann distribution
The Journal of Physical Chemistry, Vol. 88, No. 22, 1984 5171
Supersonic Beams of OCS Seeded in Ar
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for states with K = 2 which was fit by a temperature of 9.4 K. By following23the pressure dependence of their Q(2,2) transition’s signal alone, which reaches a maximum near 1.3 torr-cm, one can inferz4a temperature of 10 K at 3.2 torrcm, in good agreement with the 9.4 K value quoted above.
Discussion To summarize our data, we have plotted TI,, vs. T,,for all our data in Figure 6. Each point represents a different Po, To,D combination, differentiated in the graph only by To. The data show a correlation which is slightly sensitive to To,and perhaps sensitive to D, although our accuracy causes us to be hesitant to claim more than the qualitative trend exhibited in the figure. While we have used a temperature to characterize the rotational population, we have no measurements which pertain directly to any but the (1,O) state. We thus cannot conclude from these measurements alone that the populations of other states in the velocity and spatial groups represented by our refocusing data on (1,O) would be predicted by these Tro{s and a Boltzmann expression. Qualitatively, however, the behavior of the entire refocusing pattern is consistent with changes in the J = 0-2 populations which reflect the (1,O) trend. It would also be instructive to measure directly the velocity distribution of the refocused (23) Scoles, G., private communication. (24) The J = 2, K = 2 population of CH3F is a maximum at an equilibrium temperature of 20.7 K. The observed Q(2,2) signal (ref 15 and 23) attained a maximum at P f l N 1.3 torr-cm.
state-selected beam. Unfortunately, the time of flight disk and motor occupied the space taken by the A field during these measurements, precluding such measurements. Modifications to the apparatus in the future will allow this type of measurement to be made. The variety of results reported in the literature on rotational relaxation reflects, we feel, not only differences in molecular systems (i.e. varying rotational constants, collision partners, etc.) but also differences in the measurements themselves. Faubel and Weiner’O appear to be the only authors to have found a rotational temperature, deduced from a Boltzmann fit to several levels, which is less than the corresponding translational temperature. This was observed in N,/He expansions but not in N 2 / N e or N2/Ar expansions. As mentioned earlier, Bergmann, Hefter, and Hering’ found velocity-dependent internal-state distributions in Na2, yet a study of C 0 2 / H e expansions,1° which used a Doppler shift technique to obtain velocity distributions, found no difference in velocity distributions for various C 0 2 rotational states. The gas-dynamic rotational inversion reported by Zivi et aL4 in OCS/Ar, OCS/He, and pure OCS expansions is consistent with our observations to the extent that our (unknown) J = 0 population could be lagging behind the growth in J = 1 population, especially at P$ values less than those which maximize J = 1 (Le. on the “hot” side of the peaks in Figure 2 , at low Po). In other words, our results are consistent with their observation that the J = 1 population exceeds the J = 0 and J = 2 populations. The experiments closest to our own are those of Meerts et a1.5 These authors made their measurements on OCS/Ar and pure OCS expansions at P$ = 3.3 torrcm and To = room temperature. This P$ product is at the lower end of our range of values; degradation of beam intensity due to scattering by background gas precluded them from using higher P$ products. They report translational temperatures (deduced from TOF measurements) which we find surprisingly low. Under their experimental nozzle parameters, eq 1 and 2 would predict T,, = 4.2 K for a pure Ar expansion; Meerts et al. report T,, = 1.5 (3) K for such a beam. Put another way, their reported range of T,, can be converted into a range of e values (see eq 2) from 0.72 to 1.2. We, and others>19 find e 0.25 for pure Ar. Meerts et al. arrived at rotational temperatures by measuring intensities of AJ = 0 1-doubling transitions in the (01’0) bending state for J = 1-5. Their ability to see these transitions implies a much wider aperature for accepting transverse velocity components than we have. (Just how much wider is a complex function of field and detector aperature geometries which cannot be readily discerned from their published work.) This implication is also evident by the relatively flat normalized state selector efficiencies for J = 2-5 which they reported. Since the full-beam intensity of Meerts et al. declined with increasing pressure at roughly the same PODvalues as their individually focused state intensities declined, due to scattering, they could unfortunately not operate in the regime for which our results are most dramatic. We, however, are confident that background scattering was negliglble throughout our experiments; at large P$ values for which the refocused intensity was virtually nil, the full-beam intensity was continuing to increase. Although we are hesitant to endorse the translational temperatures of Meerts et al., suspecting them to be somewhat low, we reconcile our results with theirs (which was that the rotational and translational temperatures were equal within experimental uncertainties) by concluding that one is most likely to find a rotational temperature close ta (but probably above) the translational temperature i f measurements are made on only the lowest few rotational levels, without velocity discrimination, and with low to modest expansion conditions. Our results are not at odds with theirs, since different measurements were made on different expansions in these two sets of experiments, and we again emphasize that TI,,in Figures 3-6 does not represent a Boltzmann average equilibrium temperature which would apply to every velocity group in the beam or to every rotational state. On a molecular level, the decreasing density of an expanding supersonic molecular beam leads to the familiar view that the
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J . Phys. Chem. 1984, 88, 5172-5176
translational distribution will become invariant when velocitychanging collisions cease, and similarly for rotational and vibrational distributions. The relative degrees of relaxation, in the broadest sense, reflect the ratios of inelastic collision cross sections for the appropriate degrees of freedom. For rotations, the unequal spacing in energy from level to level provides a natural mechanism for non-Boltzmann relaxation, in the sense that collisions affecting any given level will cease at a point in the expansion which is different for each level. This mechanism is, respectively, more or less strongly coupled to the translational relaxation as the local translational energy (Le. the translational energy in a reference frame moving at the flow velocity, or 3kT,,/2) is larger or smaller than rotational level spacings from a given level to neighboring levels. Such coupling can account not only for a non-Boltzmann distribution but also for the observation of Douketis et al.I5 that the terminal rotational temperature of the lowest levels of a molecule is a monotonic (and apparently linear) function of rotational constant at any fixed PODexpansion condition. More to the point of the measurements reported here, however, is the possibility that molecules with velocities closest to so (Le. those which can be said to have undergone the greatest degree of translational relaxation) could be able to display nonequilibrium internal relaxation. Should the cross section for rotational relaxation exceed that for translational relaxation, the rotational distribution in a particular velocity group would continue to relax after the translational temperature has become fixed. This continued relaxation would be most dramatic for a molecule with a small rotational constant (so that inelastic collisions would not
significantly alter the translational distribution), and the effect would be most readily observed if experimental constraints limited the range of interrogated velocities. An equivalent conclusion is reached if one takes the point of view that so is the “goal” velocity of all the molecules in the beam. Those with velocities nearest so in any arrested expansion have achieved that state as the result of experiencing a greater number of relaxing collisions than their neighbors. It does not seem unreasonable to expect these molecules to be the more highly relaxed internally as well. There is no a priori reason why the distribution of velocities and internal energies in a supersonic expansion should follow Boltzmann-like equilibrium forms. An interesting, but difficult, calculation of the terminal distribution function would seem to be possible starting from the Boltzmann transport equation and various assumptions about state-to-state collision cross sections. Such a calculation should show if reasonable assumptions for these cross sections are capable of yielding not only nonequilibrium distributions but also distributions which show coupling among various degrees of freedom. Acknowledgment. We thank Professor G. Scoles for communicating results on his CH,F/He expansions. This research was supported by the National Science Foundation, by the donors of the Petroleum Research Fund, administered by the America1 Chemical Society, and by the Division of Chemical Sciences, Office of Basic Energy Sciences, US.Department of Energy, under Contract No. DE-AC03-765F00098. Registry No. Ar, 7440-37-1; OCS,463-58-1.
Metal-Support Interactions on Rh and Pt/T102 Model Catalysts D. N. Belton, Y.-M. Sun, and J. M. White* Department of Chemistry, University of Texas, Austin, Texas 78712 (Received: March 14, 1984)
Model catalysts comprised of Pt and Rh films on oxidized Ti were studied with static secondary ion mass spectrometry to observe their temperature-dependent structural characteristics. Encapsulation of the metal overlayers by the support material is observed and correlated with thermal desorption spectra. The results suggest that encapsulation and electronic interactions occur simultaneously to alter the behavior of these model catalysts.
Introduction Since the report Of strong metal-support interactions (SMS1) in 1978 by Tauster et a1.’a2 the source of this interesting effect has been an area of active debate in the surface science-catalysis Oxide community. Many studies On a variety Of systems have been carried Out in an attempt to discover the underlying causes for the suppressed H2 and CO chemisorption which is characteristic of these SMSI system^.^-'^ The inherent com(1) S.J. Tauster, S. C. Fung, and R. L. Garten, J . Am. Chem. Soc., 100, 170 (1978). (2) S.J. Tauster and S. C. Fung, J . Catal., 55, 29 (1978). (3) “Metal-Support and Metal Additive Effects in Catalysis”, B. Imelik et al., Ed., Elvesier, Amsterdam, 1982, and references cited therein. (4) T. Huizinga, Dissertation, Eindhoven University of Technology, 1983. (5) X.-Z. Jiang, T.F. Hayden, and J. A. Dumesic, J. Catal., 83,68 (1983). (6) D. E. Reasco and G. L. Haller, J . Catal., 82, 279 (1983). (7) M. A. Vannice and C. C. Twu, J. Catal., 82, 213 (1983). (8) D. R. Short, A. N. Mansour, J. W. Cook, Jr., D. E. Sayers, and J. R. Katzen, J . Catal., 82, 299 (1983). (9) S.-M. Fang and J. M. White, J . Catal., 83, 1 (1983).
0022-3654/84/2088-5172$01.50/0
plications of powder catalysts make application of most modern surface analisis techniquks very diffi<. Hence, information gained from studies of this type have been unable to clearly demonstrate the of SMSI, In order to separate and characterize the possible effects, thin film models of the actual catalysts are helpful,13-18 Someof the first studies concentrated on photoelectron spectroscopy, both X-ray (XPS) and ultraviolet (UPS), in an attempt to observe changes in the electronic structure of metals deposited on oxide (10) K. Tanaka and J. M. White, J. Catal., 79, 81 (1983). (11) R. T. K. Baker, J . Catal., 63, 523 (1980). (12) S.C. Fung, J . Catal., 76, 225 (1982). (13) M. K. Bahl, S. C. Tsai, and Y. W. Chung. Phys. Rev.B, 21, 1344
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(14) J. E. E. Baglin, G. J. Clark, J. F. Ziegler, and J. A. Cairns, J . Mol. Catal., 20, 299 (1983). (15) B. R. Powell and S.E. Whittington, J . Catal., 81, 382 (1983). (16) Y.-W. Chung, G. Siong, and C.-C. Kao, J . Catal., 85,237 (1984). (17) J. A. Schriefels, D. N. Belton, J. M. White, and R. L. Hance, Chem. Phys. Lett., 90, 261 (1982). (18) D. N. Belton, Y.-M. Sun, and J. M. White, JPhys. Chem., 88, 1690 (1984).
0 1984 American Chemical Society
