J . Phys. Chem. 1987, 91, 1778-1785
1778
levels are unable to reproduce the experimental findings, suggesting that the trans form is slightly more s\able. In the gas phase we find no evidence of the presence of a second conformer, and we know that the cis form is both present (from the microwave spectrum)19 and predominant (from the electron diffraction study),’ but we still cannot exclude the possibility that a small proportion of a second conformer is also present in the gas phase.
Acknowledgment. The authors gratefully acknowledge financial support of this research by the National Science Foundation by Grant CHE-83-11279 and the NATO Scientific Affairs Division through their collaborative research program under Grant No. 140/82. Registry No. CH,CH,NCO, 109-90-0.
Vibrational Relaxation Rates of CO,(OOl) with Various Collision Partners for T < 300 K S. H. Bauer,* J. F. Caballero, R. Curtis, and J. R. Wiesenfeld Department of Chemistry, Cornell University, Ithaca, New York 14853-1 301 (Received: July 8, 1986; In Final Form: October 29, 1986)
Population decay rates of C02(001) due to self-collisionsand to encounters with ten other species [(CH,),N, (CHJ20, H20, CS2,HC1, N20,OCS, NO, 02,and N2] were measured as a function of temperature by recording the decay in fluorescence of C 0 2 ((001) (000)). The (001) level was overpopulated by exposing mixtures of C 0 2 with various collision partners to narrow pulses of 9.4-pm radiation from a mechanically chopped C 0 2 CW laser which selectively pumped the thermal populations of C 0 2 {(loo) + (020)). The lowest attained temperatures ranged from 190 to 240 K and were limited mostly by the population of C 0 2 {(loo)+ (020)). While, in general, the log of the probability for collisional deactivation is linear when plotted against for T > 400 K, significant departures appear at lower temperatures. In a substantial fraction of cases, the probability rises with decreasing temperature after passing through a minimum. In general, the probability for collisional deactivation is higher for polyatomics compared to diatomcs and is lowest for those molecules which possess no dipole moment.
-
Introduction The relaxation of an assembly of molecules to thermal equilibrium after having been exposed to a perturbation which overpopulates a specific vibrational state clearly involves collisional redistribution of the excess vibrational energy to lower vibrational states, to rotation, and to translational motion shared by the collision partners. The molecular dynamics of such processes have been experimentally investigated for over half a century; the results have been extensively reviewed,l and numerous models have been proposed and analyzed.* The relaxation rates were found to be not only temperature dependent, but also highly sensitive to the structure of the collision partner. Indeed, there was hope that the experimentally determined probabilities for energy transfer, when resolved for state-to-state transitions, could provide insight into the interaction potentials of the molecular pairs. Regrettably, the basic description of the dynamics of such encounters, which are based on simple molecular models involving three or four atoms, apparently cannot be extended to larger molecules because of the complexity of the potential energy surfaces and the unavoidable averaging over collision parameters (impact parameters; angles of attack; phases of the relative rotations and vibrations, etc.). Nonetheless, the proposed models (which in time became (1) For recent reviews see: (a) Lambert, J. D. Vibrational and Rotational Relaxation in Gases; Clarendon Press: Oxford, 1977. (b) Bailey, R. T.; Cruickshank, F. R. Gas Kinetics and Energy Transfer, Vol. 3; The Chemical Society: London, 1978. (c) Buchwald, M.; Bauer, S . H. J. Phys. Chem. 1972, 76, 3108. (d) Walsh, P.; Bauer, S. H. J . Phys. Chem. 1973, 77, 1078. (e) Weitz, E.; Flynn, G. W. Annu. Rev. Phys. Chem. 1978, 25, 275. (f) Yardley, J. T. Introduction to Molecular Energy Transfer; Academic: New York, 1980. (2) (a) Landau, L.; Teller, E. Phys. Sowietunion 1936, 10, 34. (b) Schwartz, R. N.; Slawsky, 2.I.; Herzfeld, K. F. J . Chem. Phys. 1952, 20, 1591. (c) Sharma, R. D.; Bau, C. A. J. Chem. Phys. 1969.50.924. (d) Shin, H. D. J . Am. Chem. SOC.1968, 90, 3029. (e) Widom, B.; Bauer, S . H. J . Chem. Phys. 1953,21,1670. (f) Pack, R. T. J . Chem. Phys. 1980,72,6140. (g) Clary, D. C. J. Chem. Phys. 1981, 75, 209. (h) Price, R.J.; Clary, D. C.; Billing, G. D. Chem. Phys. Lett. 1983, 101, 269. (i) Clary, D. C. J. Chem. Phys. 1984,81,4466. (j)Maricq, M. M.; Gregory, E. A.; Simpson, C. J. S. M. Chem. Phys. 1985, 95, 43. (k) Bacic, Z.; Schinke, R.; Diercksen, G. H. F. J Chem. Phys. 1985,82, 336.
0022-3654/87/2091-1778$01.50/0
increasingly more involved) do indicate which molecular parameters play dominant roles and how each of these affects the dependence of relaxation rate upon temperature. The relative probabilities for energy transfer are state-specific, and the rate constants measured at the lowest temperatures best reflect the specific features of the interaction potentials. Interest in C 0 2 extends beyond its being a suitable test species; it is directly involved in the heat balance of the earth’s atmosphere and is a significant constituent of the atmospheres of the other planets. It is the active medium of the most efficient and widely used infrared laser (which is solely dependent on balancing rates of excitation and deexcitation of populations in selected vibrational states) and is the major product of combustion of hydrocarbon fuels. Measurements of vibrational relaxation rates of C 0 2 were among the first to be undertaken in the mid-l930s, with sound dispersion technique^.^ Later more extended data were obtained by recording density profiles past shock fronts in suitable mixtures.lc,d Since these techniques determine lags in the equilibration of heat capacity, the measured rates applied primarily to the populations of the lowest vibrational state (010). Time-resolved fluorescence measurements are now the standard method for determining collisional efficiencies for vibrational state deex~itations.~The availability of high-powered lasers provides new routes for creating vibrationally excited m o l e c ~ l e s . ~While laser optimization depends upon high-temperature energy-transfer data, almost no information was available regarding relaxation rates below 300 IC, until the mid- and l a t e - 1 9 7 0 ~ ~Previous experiments have already indicated that extrapolation of relaxation rates from high-temperature measurements to obtain estimates (3) Cotrell, T. L.; McCoubrey, J. C. Molecular Energy Transfer in Gases; Butterworths: London, 1961, and references therein. (4) Hocker, L. 0.; Kovacs, M. A,; Rhodes, C. K.; Flynn, G. W.; Javan, A. Phys. Rev. Lett. 1966, 17, 233. (5) Photodissociation and Photoionization, Vol. LX, Prigogine, I., Rice, S., Ed.; Wiley: New York, 1985; Adv. Chem. Phys. (6) (a) Inoue, G.; Tsuchiya, S.J . Phys. SOC.Jpn. 1975, 38, 870. (b) Geuguen, H. G.; Yzambart, F.; Chakroun, A,; Margottin-Maclou, M.; Doyennette, L.; Henry, L. Chem. Phys. Lett. 1975, 35, 198
0 1987 American Chemical Society
Vibrational Relaxation Rates of CO2(O01) of rates even at room temperature does not give reliable results. Although early theories, Landau-Teller (LT)& and Schwartz, Slawsky, and Herzfeld (SSH),2badequately accounted for the high-temperature data, they failed when the temperature fell below 4 0 0 K,' because they considered only the repulsive part of the interaction potential. LT and SSH predict that a plot of the logarithm of the transfer probability vs. should be linear. They also predict that the rate should increase as the reduced mass of colliders decreases, and increase as AEvibdecreases. Both of plots these trends were observed, but the failure of In k vs. to be linear at low temperatures led to other theories in which the attractive parts of the potential were taken into consideration.,- In the Sharma-Brau model (SB),2Cmultipolar forces are incorporated to represent the long-range part of the interaction potential. This concept was further extended by Shin.2d The calculations for C02-N2 relaxation are in good agreement with experiment for the I4N2isotope but underestimate the rate for the 15N, isotope.6b Recent calculations for COz-hydrocarbon mixtures with slightly modified models8 show only a modest qualitative agreement with experimental values. Theories based on distorted wave and infinite-order sudden approximations for calculating relaxation rates for diatom-atom, diatom-diatom, and triatom-atom systems do account for the observed temperature dependence of some relaxation but have not yet been extended to binary systems with more degrees of freedom. Reliable theoretical treatments require accurate, multidimensional potential energy surfaces. The molecular beam electricresonance experiments of Klemperer et aL9 provide structural parameters of van der Waals complexes of C02with HCI, H20, NH,, and CO,; however, the well depths for only H20 and NH, are k n o ~ n . Tsuchiya ~ ~ , ~ et a1.I0 reported energy-transfer probabilities at low temperatures for C02-Nz and CO,-CO pairs. They fitted their values to a Sharma-Brau model which gave satisfactory agreement with experiment for resonant energy transfers. For these mixtures, this was found to be the case by other experimenters, reported at about that time.6b The present experiments were undertaken to measure accurate rates for C02(O01) relaxation under conditions where the attractive region of the potential plays a dominant role.
Experimental Section Vibrational relaxation rates of COz were determined by using a variant of laser fluorescencelb in which the (001) level was pumped by irradiating CO,/quencher mixtures with a mechanically chopped CO, laser operating on the P(20) line of the 9.4-pm band. The spontaneous fluorescence from the (001) state is a measure of its population, and its temporal behavior reflects collisional deactivation by the M quencher. Thus, we obtained the temperature dependence of relaxation rates induced by the atmospheric species C 0 2 , H 2 0 , 02,and N,, as well as (CH3)2O, (CH,),N, HCl, OCS, NO, N 2 0 , and CS2. The C 0 2 laser was operated in the continuous mode, but the beam was mechanically chopped by a rotating slotted aluminum disk onto which it was focussed. A single 0.040-in. slot allowed passage of the beam for each rotation of the disk (at ~ 2 0 Hz). 0 Pulse lengths ranged from 5 to 20 ps; the incident energies were 100 to 400 pJ per pulse. Pulse shapes and intensities were monitored with a lithium tantalate pyroelectric detector (New England Research, Model LTO-1.25-BT). (7) (a) Stephenson, J. C.; Moore, C. B. J . Chem. Phys. 1970, 52, 2332. (b) Stephenson, J. C.; Wood, R. E.; Moore, C. B. J. Chem. Phys. 1971, 54, 3097. (8) (a) Manzanares, C.; Pinzon, I. H.; Fumero, J.; Gonzalez, C.; Sanchez, E. J. Chem. Phys. 1983, 78, 5971. (b) Manzanares, C.; Carraza, I.; Carraza, J. J. Chem. Phys. 1983, 79, 2212. (9) (a) Nelson, Jr., D. D.; Fraser, G. T.; Klemperer, W. J . Chem. Phys. 1985, 83, 6201, and references therein. (b) Altman, R. S.; Marshall, M. D.; Klemperer, W. J. Chem. Phys. 1982, 77, 4344. (c) Peterson, K. I.; Klemperer, W. J . Chem. Phys. 1984, 80, 2439. (d) Fraser, G. T.; Nelson, Jr., D. D.; Charo, A,; Klemperer, W. J. Chem. Phys. 1985,82, 2535. (e) Fraser, G. T.; Leopold, K. R.; Klemperer, W. J . Chem. Phys. 1984, 81, 2577. (0 Novick, S. E.; Davies, P.B.; Dybe, T. R.; Klemperer, W. J . Am. Chem. SOC.1973, 95, 8547. (10) Inoue, G.; Tsuchiya, S. J . Phys. SOC.Jpn. 1975, 39, 479.
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 1779
q 5mm
'yJ-L Gri
Figure 1. Detailed view of the apparatus used to monitor the infrared fluorescence from CO2(O01): 1, cryogenic support; 2, thermocouples; 3, filling tubes, to glass helices; 4, mirror; 5 , NaCl or KBr windows; 6, sapphire windows; 7, optical filter; 8, detector element; 9, top plate of shroud.
TABLE I: Gas Compositions Matheson
MG Scientific Fisher Scientific Airco Eastman Kodak Mallinckrodt
-
>99% >99% >99% >97.5% >99.8% >99.999% >99.8% >99.995% redistilled 99.94%
The time-resolved C 0 2 (001 000) infrared fluorescence emitted perpendicular to the laser beam axis was monitored with a liquid-He-cooled Hg:Ge infrared detector (0.16 cm2, 80-11s rise time, with a matching A320 preamplifier) equipped with a 4.3-pm infrared interference filter (OCLI, 0.2 pm fwhm). The signals were filtered, digitized (Biomation 8 loo), averaged over thousands of shots (Nicolet SD-78), and analyzed by standard fitting procedures (IBM-AT computer, ASYST software, nonlinear leastsquares routine [NLLS]). The electronics were triggered by a signal from the pyroelectric detector. To avoid CO,(OOl) selfabsorption," the distance between the viewing window and the emission region was set to be as small as possible (Figure 1). Cell temperatures below 300 K were achieved by attaching the cell to a cryostat (Air Products Model LT3-110A Heli-Tran) controlled by an temperature indicator-controller (Air Products APD-E Series 3700). The variable-temperature cell was made of an aluminum block; it has three windows; two were fitted with NaCl plates, set at the Brewster angle for passage of the laser beam, and the third with a sapphire window, to transmit the fluorescence radiation. The windows were attached to the cell with a low-temperature epoxy (Ecosil 1777). To avoid heat losses, the cell was connected to a gas-handling system through two Pyrex helices, 0.2 cm in diameter and 20 cm long. Condensation of moisture on the windows was prevented and good temperature control was maintained by placing the cell and glass helices inside a vacuum chamber maintained at lo-, Torr. The chamber was equipped with two side arms for NaCl windows, and a sapphire window perpendicular to the beam axis to allow observation of the fluorescence radiation. Chromel-alumel thermocouples were attached to each end of the AI cell and used to check the accuracy of the temperature controller unit. Temperature differences were less than A 2 K; stability was f l K. (11) Huddleston, R. K.; Fujimoto, G. F.; Weitz, E. J . Chem. Phys. 1982, 76, 3839.
1780 The Journal of Physical Chemistry, Vol. 91, No. 7 , I987
We found that minor impurities (especially water) greatly affected the quality of the data.7a Care was taken to purify the gases used (Table I). All gases (other than O2 and N2) were treated by freezing to liquid N2 temperatures and pumping, followed by several trap-to-trap distillations to remove impurities. The sample cell and gas handling system were pumped down to Torr before admitting any gas into the cell. less than An MKS Baratron gauge (0-100 Torr) was attached directly to the cell to monitor sample pressures during runs. In some cases it was necessary to make measurements with flowing samples because a pressure drop was noted for those collision partners due to wall adsorptions. Flow adjustments were made with two needle valves outside the chamber connected to the glass helices. Mixtures were prepared at room temperature and stored in a 5-L glass bulb attached by a short copper line to the cell. Prior to use, the mixtures were stored for 30 min or longer to obtain uniform distribution of components. Several runs were made at each pressure; no significant differences were found between the earlier and later runs. Specific pressures were selected for each system so that the decay time was considerably longer than the laser pulse width. Also, mixture compositions were optimized so that the observed decay rates were due mainly to the C02-M collisions, and not to CO2-CO, collisions. Samples were admitted to the cell after it had cooled to the desired temperature. Pressure and temperature readings remained constant during the course of the experiments. In cases where wall adsorption was noted, the gas mixture was passed through the cell for approximately 20 min until the fluorescence signals stabilized. In previous s t u d i e ~ ~ concern J ~ - ~ ~was expressed for changes in sample composition, pressure and temperature during the experiments. We monitored directly both the pressure and temperature, and although we could not monitor the composition, we did compare our data with published values reported at room temperature and used this comparison to check on changes in composition. In all cases, excellent agreement with previous work was obtained. Two or three runs were made at each temperature to provide error estimates. The lowest temperature for which relaxation data could be obtained was limited by the thermal population of the C0,(020) level. The population of CO2(O20) at temperature, T, relative to that at 300 K is given by the ratio [NT/N,oo]= 649 exp(-1943/T). At 200 K that ratio is 0.039. Hence at low temperatures, the signal levels were substantially smaller than at room temperature. The minimum temperatures attained for the various mixtures ranged from 230 to 190 K. The high repetition rate of the CO, laser pulses allowed us to use low incident energies ( X2:
XI = keW1 + k-e[CO21 +f{k11[CO21 + k12[MI + k17J + (1 -f)(k21[C021 + k22[MI + k2rJ (14)
= (k-e/ke)f [MI-'(k11[C0212 + [(ke/k-e)k21 + k12I X [CO2I [MI + (ke/k-e)k22[M12 + kl,[CO21 + (ke/k-e)k2T[MI1 (15)
A2
f = ke[MI/{ke[MI
+ k-e[CO211
(16)
Since the A term in (13) decays more rapidly, experiments at high total pressures can be used to determine X2 directly. Tu estimate XI, data must be obtained at low pressures and the contribution of the slow decay term subtracted from the measured intensities. A exp(-Xlt) = I(t) - B exp(-X2)
(17)
The rate of change of X2 with pressure is related to the desired rate constant, k12 dX2/d[MI = (k-e/ke)f(kl,(X12/X,2) + [(ke/k-e)k21 + k12I X (x1/x2) + (ke/k-e)k221 (18)
'
where XI is the mole fraction of C 0 2 and X2 is the mole fraction of M. The ratio k , / k , is given by the Boltzmann factor, exp(AEIkT), where AE is the vibrational energy of the products minus the vibrational energy of the reactants (the vibrational defect). A linear least-squares fit to a plot of the pressure of M vs. X2 gives dX2/d[M]. Then values for [(ke/k-e)k21+ kI2]can be calculated if k22is known from other experiments. In previous work,I5it was found that kI2>> k21(ke/k-e)for the C02-N2 system; kI2was calculated on the basis of this approximation, which is not valid for all the systemsI5 discussed in this report. For double exponential systems, dX2/d[M] depends on the mole fractions of components, while for single exponential decays, the derivative is insensitive to composition. Thus one may determine if rapid equilibria are involved for a specific quencher by varying the mole fraction of [MI while monitoring dX2/d[M]. Additionaly, one can record fluorescence at low pressures and look directly for the fast and slow components. The values obtained for the rate constants are in units of Torr-' s-l. Expressed in these units k depends on the relative molecular speeds. To remove this dependence the following relation converts k into a probability of vibrational relaxation per collision:18 P = 2.31
X
10-8(pT)1/2k/d2
' 0.00
0.25
0.50
0.73
1.00
'
1.25
1.50
1.75
2.06
Time (marc)
Figure 3. Infrared signal from 1.25 Torr of COzin 3.75 Torr of NZ. The fluorescence profile is a double exponential.
mass of the colliding pair in amu. Results C02-CO,; C02-N2 The C0,-CO, and C02-N2 systems were measured to check the reliability and accuracy of our experimental and data reduction procedures. To determine C 0 2 - C 0 2relaxation rates, pressures from 10 to 80 Torr were used while for C02-N2 mixtures, the slow V-V transfers were examined for ratios P(C02)/P(N2) = 0.2-0.3. Total pressures for the C02-N2 slow decay experiments ranged from 20 to 130 Torr. Lower pressures (1-7 Torr) were used to check the fast V-V decay at room temperature. Fluorescence following excitation of pure C 0 2 shows single exponential behavior whereas that from C02-N2 mixtures follow a double exponential decay. Figure 3 is a typical profile of a 1:3 mixture of C 0 2 in N2. We extracted rate constants from this type of trace, on the basis of eq 17-1815 using the approximation of Gerry et a1.I2 Thus the contribution of the slow process was separated from the fast V-V process. In Figure 4 our data for C02-C02 and C02-N2 are compared with previously published ~ a l ~ e ~ . ~ ~ .The ~ ~agreement , ~ ~ , ~is ~quite , ~ satisfactory. ~ , ~ ~ , ~Our ~ attempts to determine the temperature dependence of the fast V-V rate were frustrated because of the low signal levels at the low pressures required to make these measurements. C02-02. Relaxation rates were measured by using static mixtures, P(C02)/P(02) = 0.1-0.6, for total pressures ranging from 10 to 90 Torr. In all cases a single exponential decay was observed. The probability for quenching vs. T1/3 is displayed in Figure 5; our data are combined with previously measured values at higher temperature^.'^.'^ It is clear that extrapolation of relaxation rates obtained above 400 K to estimate values below 400 K would give seriously misleading values. C02-N20. Static samples of C 0 2 and N 2 0 were used [P(C02)/P(N20)= 0.5 and 1.01 at pressures from 5 to 60 Torr. A double exponential decay of C 0 2 fluorescence was observed. As in the case of N2, our calculation of the slow decay included correction for the fast decay by following the procedure discussed in the Analysis section. We were able to record the fast decay but were not able to extract ke, since the relaxation time15v20and laser pulse duration were of similar length. Our observation of the fast component of the decay was made with a 2:l C02:N20 mixture at room temperature and is shown in Figure 6. Figure 7 is a plot of the slow V-V energy transfer probability for C 0 2 / N 2 0 mixtures. Corrections were made to the slow V-V data using published values of the fast decay.15 The striking
(19)
d is the hard-sphere collision diameter (A) and p is the reduced (18) Starr, D. F.; Hancock, J. K. J . Chem. Phys. 1975, 63, 4730.
1
0 1
(19) (a) Chakroon,A.; Margottin-Maclou, M.; Gueguen, H.; Doyennette, L.; Hency, L. C. R . Acad. Sci., Ser. B 1975, 281B, 29. (b) Bass, H. E.; Hottman, S. D. J. Chem. Phys. 1977, 67, 5966. (20) Gueguen, H.; Arditi, I.; Margottin-Maclou, M.; Doyennette, L.; Henry, L. C. R . Acad. Sci. Ser. B 1971, 272B, 1139.
Bauer et al.
1782 The Journal of Physical Chemistry, Vol. 91, No. 7 , I987 T (deglres Kelvin) 578.7
4552
364.4
2963
2441
2035
1715
1458
1250
C02-N20
Fluorescence Profile
C o p - CO2 Collis onal Dew: v o l ~ o iProbability c
I
c 0
N
O12mo
Qlxxl
01400
01500
01600
01700
01800
01900
'0 OOO
02000
0.050
0 100
0 150
T (degrees Kelvin) 5787
"
4768
COS
3975
- N2
3349
2848
0.300
0.250
0.200
0.350
0.400
Time (msec)
T- 1/3
244 1
2109
1834
1605
Figure 6. Infrared fluorescence signal at room temperature for C02-N20 mixture. Samples pressure was 1.2 Torr with 0.57 Torr of N20. 902.8
1OOO.10
Collisional Deactivation Probability
805.6
T (dw'lo) 708.5 611P 3 514.1
Ja¶.8
4169
2226
7
Temperature Dependence of t h e Collisianol Oeoctivatian Probobility
u u
.-
0
0
c1
0
I
0
8
....
COm - M i a
0
0
0
a 0
o 1200
0 1280
o
1360
0 1440
0 1520
o
1600
01680
31760
0~810
T-l/3
Figure 4. Collisional deactivation probability (CDP) vs. T1I3for (a, top) C02-C02 (B) and (b, bottom) C02-N2 (B). Other high- and low-temfor C02-C02 and C02-N2 are shown in perature data6a~7a~8a,10,12,1~~1*~19 this figure (0). T (degrees Kelvin) 7118
5787
4768
3975
3349
2848
2441
2109
1834
0
0 m
o.iooo
0.1081
01163
0.1244
0.1325 T-Vs
0.1406
miim
0 . 1 ~0.1650 ~
Figure 7. Temperaturedependence of CDP vs. for a [C02]/[N20] = 2 mixture (B) and C02-NO mixtures ( 0 ) .The high-temperature data for C02-N20 is from ref 15 (0)and for C02-N0 from Gerry et (0). T (degrees K)
COz - 02 Collisior?al Deacttvation Probability
600.0
'
553.7
507 5
461.2
415 0
368.7
322.5
276 2
230.0
Temperature Dependence of t h e Collisional Deactivation Probability 0
.
.
CO2-HCI
0
I 01120
0.1200
0 1280
0.1360 0 1 4 4 0
0 1520
0.1600
0 1680
0.1760
T - W
Figure 5. Measured CDP vs. T1I3 for C02-0, mixtures (B). Data from Gerry" and Moorei5complete the plot at high temperatures (0).
feature is the increase in probability with declining temperature, similar to that shown for C 0 2 - C 0 2 relaxation. CO2-NO. Static samples with P ( C 0 2 ) / P ( N O )= 0.1 and 1 .O were investigated at total pressures from 5 to 60 Torr. At room temperature the observed rate agrees with previously reported values.21 For a range of low total pressures and high dilutions
-
in
01186
01241
01297
01353
01404
0 1465
0 1521
01576
01632
for C0,-OCS (X) and C0,-HCl (m)systems. High-temperaturedata for C02-HCl mixturesz3 (0)are shown in the figure.
Figure 8. CDP vs.
of COz in NO, the signals always followed a single exponential decay. While static samples were used to obtain the temperature
The Journal of Physical Chemistry, Vol. 91, No. 7. 1987
Vibrational Relaxation Rates of CO2(O01) 1ooO.O
902 5
8050
T (degrees K) 707.5 610.0 512.5
415.0
317.5
220.0
608.6
1783
T (degrees K) 2738 230.9
196.5
168.6
145.8
0.1630
01720
0.1810
0.1900
406.2
397.5
328.0
0.1270
0.1360
0.1450
t Temperature Dependence of the Collisianol Deactivotion Probability
.
COz-HzO o 0
m
0
0
0
0.1180
0.1540 T-v3
Figure 10. CDP vs. H 2 0 and HCI).
01000
01082
01164
01246
01328
01410
01492
01574
0.1657
,-v3
Figure 9. CDP vs. C02-H20 (m) and C02-CS2 (X) mixtures. Plot is completed with the high-temperaturedata for C02-H20after Moore and Gerry et a l l 3 (0). et
dependence, we checked the value a t room temperature with flowing samples and found excellent agreement (Figure 7). C02-OCS. Single exponential decays were observed in static experiments for 1:l mixtures of C 0 2 - O C S , with total pressures ranging from 3 to 40 Torr. There is little published information on this system.22 A slight rise with declining temperature was observed (Figure 8). We used both static and flowing samples at room temperature; there was good agreement between the two experimental procedures. C02-HCl. Flowing samples of mixtures P ( C O , ) / P ( H C I )= 0.1, 1.O, and 2.0 were tested at total pressures from 4 to 40 Torr. At 0.1 dilution, using Pt,,, = 0.5 and 2 Torr, we were unable to detect the fast V-V decay previously reported.23 Our data fit well a single exponential decay which is independent of the mixture composition. Note that the probability increases dramatically with decreasing temperature below 300 K (Figure 8). CO2-H2O. It is well-known that water is strongly adsorbed onto glass or metal surfaces.24 We found that it was not possible to obtain reproducible relaxation data with static samples due to the pressure drop in the sample cell. However, reproducible values were obtained for C02-H20 mixture under flowing conditions. Relaxation rates were obtained as a function of both flow rates and time. Both the cell and the flow train had to be well conditioned before accurate values could be recorded. Adequate conditioning was reached when we found that our data, obtained after suitable cell preparation, remained invariant with time; these checked with previously measured relaxation rates at room temperature.I3pz4Typically, flow rates were >0.3 Torr/s; 20 min was required for cell conditioning. Because of the rapid decay rates, large dilution ratios of C 0 2 / H 2 0 were used (40, 100, 400) with total pressures from 10 to 70 Torr. The C 0 2 - H 2 0system has been extensively investigated in the past; more recently, the structure of the collision complex was determined.9c Figure 9 shows that within the range of experimental variations there is almost no temperature dependence of the probability of relaxation over this temperature range. CU2-CS2. For this collision partner, we followed the same precautions in sample handling which were used in the H 2 0 experiments. Signals from flowing samples of 1 part in CS2 to (21) (a) Rosser, W. A.;Gerry, E. R. J . Chem. Phys. 1971.54, 4131. (b) Stephenson, J. C.; Wood, R.E.; Moore, C. B. J. Chem. Phys. 1968,48,4790. (22) Stephenson, J. C.; Wood, R. E.; Moore, C. B. J . Chem. Phys. 1972, 56, 4813. (23) Stephenson, J. C.; Finzi, J.; Moore, C. B. 1.Chem. Phys. 1972, 56,
5214.
(24) (a) Bass, H. E.; Hottman, S . D.; Bauer, H. J. J . Chem. Phys. 1980, 72, 21 13. (b) Heller, D. F.; Moore, C. B. J. Chem. Phys. 1970, 52, 1005. (c) Cheo, P. K. Bull. Am. Phys. SOC.1968, 13, 207.
for C02with DME and TMA (compared with
TABLE II: Rates (Torr-' s-') at Room Temperature our previous mixture values work CO2-CO2 337 345 330 350 329
385 346 330 335 329 34 1
19a 24a 10 26
366 C02-N2 (fast decay)
1.7 x 104
1.6 x 104 1.9 x 104 1.7 x 104 1.4 x 104
(slow decay)
120
co2-02
125
90- 106 112 120 110 125 140
(1.3-1.9)
ref 8b 12 14 25 4 7a 7b
X
lo4
6a 14 12 19b 6b 14 6a 15 12 15 13
CO2-N2O (slow decay)
4600
C02-NO
795
c0,-ocs
2780
C02-HZO
3.27 x 104
co2-cs2
2.6 x 104 4800
CO2-HC1
4400 3200 740 715 2400 3 x 104 4.2 x 104 3.1 x 104 2 x 104 2.83 x 104 4400
15
20 21b 21a 22 13 24c 24b 24a 22 23, 20
3 parts of C 0 2 follow a single exponential decay, for pressures ranging from 5 to 30 Torr. Figure 9 shows a dramatic increase of collisional deactivation probability with decreasing temperature, even more striking than do C 0 2 - C 0 2 and C02-NO. Unfortunately, no data are available at higher temperatures to indicate where the relaxation rates begin to increase with rising temperature, as they must. CO2-(CH3),Oand CO2-(CH3),N. Fluorescence decay measurements were made with dimethyl ether (DME) and trimethylamine (TMA) as collision partners, over the temperature range 300-230 K (Figure lo). These showed single exponential decays, and, as anticipated, both are very efficient relaxers, comparable to H 2 0 . Ammonia could not be tested because it reacts rapidly with C 0 2 to generate the carbamate. Discussion Rate constants measured at room temperature are listed in Table 11, along with values reported by previous investigators. Since we could not monitor the final states of the products, the
Bauer et al.
1784 The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987 TABLE 111: Possible V-V Transfers, with Low AE’s reaction AE. cm”
+ c0,(000)
CO,(OOl) C02(001) C02(001)
CO,(OOl) C02(001)
--------+
C02(001) C02(001) CO,(OOl)
+
+
+
+
+
C02(001)
+ +
CO2(llO) c 0 2 ( 0 0 0 ) CO2(03O) CO2(OOO) + NI(0) C02(000) N2(1) C02(110) N2(0) + H20(000) C02(010) H20(010) C02(110) H20(000) CO(0) c0,(000) CO(1) CO2(11O) CO(0) + 0 2 ( 0 ) CO2(O10) 02(1) C0,(110) 02(0) + NO(0) C02(110) NO(0) C02(000) NO( 1) + HCI(0) C02(000) HCI(1) C02(110) HCI(0) + o c s ( o o o ) C02(100) OCS(O0l) c0,(000) OCS(lO0) C02(110) ocs(ooo) + N2O(OOO) C02(000) N20(100) CO2(OOO) N,O(O40) C02(110) N20(000) + CS2(0O0) CO2(01O) CS2(0O1) c o 2 ( o o o ) CS2(101) C 0 2 ( 110) CS2(O0O)
+
CO,(OOl)
--
+ + + + + + + +
+ +
+ + + +
+ + +
+ +
272 470 19 272 87 272 207 272 127 272 272 474 -537 272 100 287 272 125 -7 212 149 156 272
no
20 21 22 23 24 25 26 27 28 29 30
32 31
assignment of the measured relaxation processes to specific transitions is somewhat ambiguous. All predict that processes with the fewest changes in quantum numbers and the smallest AE‘s occur most readily, provided the reduced masses and dipole moments are about equal. For an increase of either 200 cm-’ in AE or an additional quantum to transfer, the relaxation rates decrease by a factor of =1O.ld Table 111 is a list of possible product states for each of the collision partners. C02-CO transfers, which were studied by other workers, were also included. For the C02-C02,C02-N2, C02-H20, and C 0 2 - C 0 systems, there are few accessible states and the observed rates can be matched to specific processes. Indeed for C0,-CO, collisions the products have been identified25in states which correspond to small AE‘s. Since the levels in the vicinity of 2000 cm-I are strongly coupled and these levels rapidly relax to lower levels via the bending mode, the populations of co2(030) and C 0 2 (110) remain small throughout the experiment. Although not directly demonstrated it is reasonable to assign the observed relaxation rate (1 lo), since that has the smallest AE to the transition (001) and involves the fewest changes in quantum numbers. For the C02-N2 system, two relaxation rates have been measured. These correspond to a single quantum intermolecular transfer (fast), and to an intramolecular (slow) process.
-
C02(001)
-
+ N~(u=O)
-
C02(110)
C02(000)
+ N2(u=O)
+ N,(u=l) AE = 19 cm-’ (20) AE = 272 cm-’
(21)
The near resonance (eq 20) is responsible for the rapid equilibrium which is observed. The slow process (reaction 21) is comparable to the corresponding C02-C02 rate; the AE’s are the same for both systems and neither N2 nor C 0 2 has a dipole moment.27 Since the C02-C02 system has a deeper well ( e l k = 213)28than C0,-N2 ( e / k = 132), differences in the slope of the potential of interaction at the turning point of the interaction potential may explain the differences in relaxation rates. The well depths for the intermolecular potentials were estimated from the geometric (25) Bailey, R. T.; Cruickshank, F. R.; Pugh, D.; Middleton, K. M. J . Chem. Soc., Faraday Trans. 2 1985, 818, 255. (26) Alexander, P.; Houghton, A,; McKnight. C. Proc. Phys. Soc. 1968, 1, 1225. (27) Handbook of Chemistry and Physics; The Chemical Rubber Co.: Cleveland, 1985. (28) Hirschfelder, J. 0.; Curtis, C . F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964.
mean of the molecular wells of the colliding partners wherever the tabulated values were not available.28 The C 0 2 - H 2 0 system has a large relaxation rate, which can be explained in part by the dipole moment of H 2 0 and in part by the possibility of its associating with C 0 2 to produce a relatively long-lived complex. The small AE (reaction 22, Table 111) may also contribute to the efficiency of the collisional vibrational energy transfer. Collisional deexcitation of C 0 2 by C O was studied previously; fast and slow rates were m e a ~ ~ r e d . These ~ ~ ~can ~ ~be~ ’ ~ , ~ ~ ~ assigned to reactions 23 and 24. As indicated in Table 111, two processes may occur during C02-02 collisions leading to relaxations 25 and 26. Since the measured rate is only slightly higher than that for the “slow” C0,-N2 process, similar AE‘s may be involved, which suggests that the second reaction may dominate. During C 0 2 - N 0 interactions there are also two possible transfer mechanisms, (27) and (28); the route which involves the smaller AE probably dominates. Moore et al.23investigated the C02-HCI system. They proposed reactions 29 and 30 to account for their observation of a of energy is double exponential decay. Since only ~ 2 0 cm-I 0 available in rotation and translation at room temperature, the first reaction has a low probability. In agreement with the permitted energetics, a single exponential decay was observed in our experiments. The measured rate agrees with the slow rate reported by Moore et al.,23which we ascribe to reaction 30. Calculations indicate that, under our experimental conditions, the second exponential decay listed by Moore should have been observed. For each of the remaining systems, several processes are possible. The C 0 2 - N 2 0 system is particularly intriguing. The N20(040) state is closer to resonance (reaction 31) than is the N,0(100) level [nominally the N-N stretch] (reaction 32), but populating this state requires a multiple quantum transfer which decreases its probability. If the N20(040) level is populated as a result of the fast decay (1 X lo5 Torr-’ SI), then cascading may proceed through the following mainfold: N20(040) + N20(000)
-
2N20(020)
AE
N
N20(020) + N20(000)
-
2N20(010)
AE
N
N20(010)
+ NZO(000)
---*
-45 cm-* (33a) -10 cm-’ (33b)
2N20(OOO)(V-R,T) AE N 589 cm-’ (33c)
The rate for (33b) has been estimated29at 1 X lo5. The rate for (33a) should be smaller but within an order of magnitude of that for (33b). However, this sequence is not consistent with the observed relative amplitudes of the fast and slow decays (Figure 6). Huddleston and we it^^^ reported that excitation of N 2 0 by vibrationally excited CH3Fgenerates products in the N20(100) level even though this level is farther from resonance than the N20(020) level. This suggests that, in vibrational energy transfer to N20,the number of quanta transferred may be more important than closeness to resonance. In CO2-N2O mixtures, the formation of N20(001) may dominate. If the fast decay leaves N 2 0 in this level and reaction 3 1 is unimportant, the following equilibrium may apply: Keq
= “(100)l
t
~
~
2
~
~
~[C02(00l)ll ~ ~ l
(34) /
= exp(125/kn = 1.83 (at 300 K)
The general trend for transfer rates is to increase as AE decreases. In Figure l l the measured relaxation rates, converted to collisional deactivation probabilities (CDP), were plotted against LIE.^'^ For each of the collision partners which deviates significantly from the general trend, a distinctive feature is present, such (29) Huddleston, R. K.: Weitz, E. J . Chem. Phys. 1981, 7 4 , 2879
~
t
~
2
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 1785
&
1
Relaxation Rates Versus Slope of the Potential aH20
1 1
HC'
ocs
a
s
15
a
N20
a
.
NO
a
COP
a
co
14
a
a
N2
a
02
d I
0 1 r
00
375
750
1125
1500
1875
2250
2825
3000
A E (cm-')
Figure 11. CDP of energy transfer (intra- or intermolecular) at room temperature from CO2(O01) to other molecules (see text). Our data: (9) 14N2,(10) 12c32S2, (1 1) I6O2,(1 2) I4N2, (13) H2160,(14) 16012C32S, (1 5) I4N2l6O,(16) H W l , (17) I4Nl6O,(18) 12C1602. (0)indicates species with no permanent dipole moment, ( 0 )with permanent dipole moment. Data from other report^^^.^^,^^,^^,^^^^,^^ complete the plot: (1) 12C2D4,(2) 'Y!12,(3) 12CL60180, (4) 13C1602, (5) I4N2l6O,( 6 3 ) I2Cl6O,(7) l3CI6O. (X) indicates species with no permanent dipole moment, (a) with permanent dipole moment.
as a large dipole moment or the possible formation of a long-lived transient complex. The following observations were made by Yardley" and Lambedla regarding general principles which control vibrational energy transfers. (1) V-V relaxation in plyatomics is more efficient than V-R, T processes. (2) V-R,T relaxations generally proceeds through the lowest excited vibrational level. (3) V-V processes are more efficient for small AE's and when minimal numbers of quanta are changed. (4) When large dipole matrix elements are present, long-range interactions become important. ( 5 ) The attractive part of the potential is important at low temperatures for all molecules, and at all temperatures for polar molecules. Recently, there have been attempts to use current models to quantitatively fit the relaxation rates of CO, excited by collisions with "hot atoms".30 As in the case of CO, excited by laser radiation,s only modest success was found in fitting the experimental results. All the models (SSH, Sharma-Brau, infinite order sudden approximation) developed for calculating relaxation rates require knowledge of the intermolecular potential. At present the theoretical models provide only qualitative accounts of the experiments. Study of the data presented above raises two questions: What molecular parameters determine the relative magnitudes of the probability of energy transfers per collision, at some reference temperature-say at 300 K, and what intermolecular process leads to increasing probability for energy transfer with decreasing temperature, which apparently applies to all collisional partners but with different magnitudes? The decline of the probability with Til3follows from the classical Landau-Teller theory, and all the variants thereof. The magnitude of the high-frequency component of the perturbation field to which the excited species are subjected by the approach of the collision partner is directly proportional to the slope of the interaction potential at the turn-around point, r*, of collisions with the smallest impact parameters. As expected, this slope decreases when the temperature is reduced and scales with elk. This ac(30) (a) O'Neill, J. A.; Cai, .I.Y . ; Flynn, F. W.; Weston, Jr., R. E. J . Chem. Phys. 1986,84, 50, and references therein. (b) McGee, T. H.; Weston Jr., R. E.; Flynn, G . W. J. Chem. Phys. 1985, 83, 145, and references therein. (c) MacDonald, R. G.; Sopchyshyn, F. S. Chem. Phys. 1985, 94, 455.
'-2160
-2080
-2000
-1920
-1840
dV(r')/dr
-1760
-1680
-1600
-1520
at 300 K
Figure 12. Ln (CDP) vs. [dV(r*)/dr] at 300 K (see text) for the systems
studied. TABLE I V Correlations of Molecular Parameters
[aviari,. COPNY
co,-o2 co2-co
C02-CO2 C02-NO
c0,-ocs C02-N20
COZ-HCl
co,-cs2
C02-H20
at 300 K -1542 -1664 -1 620 -1734 -1642 -1967 -1821 -1910 -2105 -2 127
probability elk 132 147 145 190 (146) (252) 204 (203.5) (304) (209)
T,.A. K 160 210 270 258 325 >300 296 349 >310 >500
at T-;" 7 x 10" 1.5 x 10-5 2.5 x 10-5 4.5 x 10-5 8.7 x 10-5 3.8 X lo4 5 x 10-4 5.5 x 10-4 2.8 x 10-3 2.8 x 10-3
counts for the good correlation (Figure 12) we found between the logarithm of the probability (at 300 K) and [dV(r)/drIr., calculated on the basis of Lennard-Jones interaction potentials with elk values listed in Table IV at 300 K. In the absence of a dipole moment for COz the only model which provides a physical basis for generating a stronger intermolecular interaction with decreasing temperature is the formation of a transient complex, due to induced dipole-dipole or valencetype attractive forces. The appearance of minima in the probareflects the effects of these two opposing trends. bility vs. T1I3 The increasing probability should correlate with the density of deexciting molecules in the immediate vicinity of the vibrationally excited species. A measure of the "equilibrium constant" for these transient complexes in the general case is given by
(35) which for a Lennard-Jones (6-12) potential reduces to a T5/6 dependen~e.~'Shin's formulationa expresses this effect in greater detail. His final expression has the form In P(T) = A - B T ' t 3 4- C T 2 I 34- D T ] (36) Whilemost of our data can be fitted to ( 3 6 ) , the magnitudes of the constants so derived appear to bear no relation to the magnitudes calculated from Shin's expressions. At this stage it appears that an accumulation of energy transfer probabilities at low temperatures is needed to test whether the trends found for CO,(OOl) are typical, and to provide data for uncovering correlations between these probabilities and the molecular parameters which characterize various collision partners. Registry No. CO,, 124-38-9; NMe,, 75-50-3; acetone, 67-64-1; H@, 7732-18-5; CS2, 75-15-0; HCI, 7647-01-0; NZO, 10024-97-2; COS, 46358-1; NO, 10183-43-9; 0 2 , 7782-44-7; N2, 1545-47-4. (31) Smith, I . W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980.
