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Vibrational relaxation of OCS(ν3)
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CHEMICAL PHYSICS LETTERS
29 July 1988
VIBRATIONAL RELAXATION OF OCS( v~) P.F. ZITTEL and M.A. SEDAM Chemistry and Physics Laboratory, The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009, USA Received 18 April 1988; in final form 18 May 1988
A laser-induced fluorescence method has been used to measure rate constants for relaxation of the u, (2062 cm-’ ) vibrational level of OCS. A frequency-doubled CO2 laser was used to pump OCS directly to the excited level. At 295 K the rate constants for relaxation by OCS, He, Ar, Kr, Hz, 02, NO2 and Hz0 were 144, 8.0, 8.0, 8.3, 27, 11, 61 and 675, respectively, in units of lo-r4 cm3/molecules.
1. Introduction The linear triatomic molecule OCS has been the of a number of studies of vibrational [ l-61 and rotational energy transfer. Vibrational energy flow in OCS is an important factor in various systems, including OCS molecular lasers [5,7,8] and the separation of isotopes by two-step laser photodissociation [ 9,101. Previous measurements of OCS vibrational relaxation have typically used a 9.6 pm CO1 laser to directly excite the 2 v2 (bending overtone) vibrational level and have analyzed fluorescence from other levels [ 3,4,6] or the absorption of laser energy [ 5 1, to obtain rate constants for various intra- and inter-mode vibrational relaxation processes. In the study of Mandich and Flynn [ 6 1, rate constants for intermode bend to stretch energy transfer and bend to translation/rotation relaxation were deduced from the solution of a simplified matrix of rate equations with the observed fluorescence decay eigenvalues. The deduced rate constants included a value for the near resonant intermode transfer from the 4vz bending level to the VI stretching level. The determination of rate constants for some energy transfer processes involving the OCS stretching vibrations can be simplified by initial excitation of the v, and v3 vibration stretching levels themselves. Direct laser excitation of the vI (S stretch) vibrational level with a 12 pm NH3 laser has been demonstrated [ lo], but has not been employed in energy transfer studies. Initial excitation of the V~(C-O stretch) visubject
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brational level has been achieved indirectly by near resonant, V-V energy transfer from vibrationally excited CO [ 21 and HBr [ 11. Rate constants for relaxation of OCS( v3) by a few gases have been reported in these studies. Except for self-relaxation, the OCS ( v3) relaxation rate constants determined in the studies involving initial laser excitation of the 2v2 level, energy transfer from CO, and energy transfer from HBr show large scatter where comparisons are possible, and in any event there is some complexity in the sequence of energy transfer processes which populate OCS ( v3) . In this paper we report rate constants for vibrational relaxation of OCS( v3) at 295 K. Direct laser excitation to the v3 vibrational level was achieved with a COz laser, frequency doubled in a AgGa$ crystal. Fluorescence on the v+O vibrational transition was observed through a monochromator. The experiments provide straightforward measurements of OCS ( v3) relaxation rate constants for several collision partners.
2. Experimental A laser-induced fluorescence method was used to measure the relaxation rate constants. The frequency-doubled, 9.6 pm CO2 P(30) laser line is nearly coincident (AE= 199 MHz) with the R( 34) line of the 16012C3zSO-+v3vibrational baud [ 11,121. A grating-tuned, CO2 TEA laser (Lumonics 203-2)
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was operated with a C02/He gas mixture, a standard multimode output optic, and a 15 mm diameter knife-edge aperture in the laser cavity near the output optic. The laser configuration produced a short ( x 70 ns), linearly polarized laser pulse with a fairly uniform fluence profile in the far field (*4.2 m), approximated by a Gaussian function with a full width at half maximum (fwhm) of 6.2 mm. The far field laser spot was compressed by a x2 telescope and attenuated with CaF2 flats to achieve a desired intensity. The CO* laser pulse was frequency doubled in a AgGaSz crystal with PbF anti-reflection coatings (Cleveland Crystals). The crystal was 8 x 10 mm in cross section, 15 mm long, and was cut at 57.0” to the optic axis. The crystal was angle tuned to achieve the proper internal angle (measured to be 56.6” f 0.4” ) between the optic axis and the ordinary CO2 laser beam for type-1 second harmonic generation [ 131 #I. The incident CO* pulse energy was adjusted to 68 mJ, providing a fluence and peak intensity at the center of the laser spot of ~0.62 J/ cm2 and w 8.9 MW/cm’, respectively. The doubled pulse energy was 0.27 mJ with a spot diameter of 2.3 mm fwhm, corresponding to a pulse energy conversion of 0.40%. Doubled pulse energies as large as 5.7 mJ, corresponding to conversion efficiencies of 2.0%, were achieved with larger CO2 laser pulse energies and a spot with a slightly different fluence profile; however, damage to the entrance and exit faces of the crystal occurred with the higher laser intensities. The COz laser radiation was separated from the frequency-doubled radiation by a 45’ multilayer dielectric mirror on a ZnSe substrate (CVI Corp. ) which reflected 9.6 pm radiation ( > 99% reflection) and transmitted 4.8 pm radiation ( > 95% transmission) and also by a MgF2 flat at Brewster’s angle to the doubled radiation. Fluorescence experiments were conducted in a Pyrex cell 25 mm in diameter by 30 mm long with MgF2 windows for the laser entrance and exit and for observation of fluorescence perpendicular to the laser beam. The cell had an isolatable cold finger to facilitate sample preparation and to allow some experiments to be run with the cold finger immersed ” The refractive indices given for the “RRE” crystal [ 13 ] best reproduced our observed phase matching angles for SHG with the P( 18)-P(44) lines of the 9.6 pm CO1 laser.
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in a dry ice/acetone bath. The fluorescence cell was placed at the entrance slit of an f /4 grating monochromator operated with wide slits (2 mm) and tuned to a center wavelength of 4.869 pm with a measured bandpass of 0.028 pm fwhm. Thus, the monochromator passed most of the P-branch of the OCS Y~-+Oemission band and blocked nearly all scattered laser lighi. A small amount of scattered laser light and electrical noise was removed by subtracting a cell-empty, background run from each fluorescence record. Fluorescence was detected at the exit slit of the monochromator by a liquid-N,-cooled, 2 mm diameter, InSb detector with matched preamp followed by a wideband voltage amplifier. In response to a short scattered laser light pulse, the detector/ amplifier combination produced a signal with an exponential decay time of 320 ns. In all cases fluorescence decay times were at least a factor of 10 longer than the detector response time. The signals were digitized by a Transiac 2008 transient recorder (25 MHz maximum sample rate, 8K record) controlled through a CAMAC interface by an IBM AT computer. Signal averaging of x: 1000 laser shots produced fluorescence decay curves with an initial signal to noise > 12 in the worst case. The computer was also used to make least-squares tits of decay times to the single exponential fluorescence decay curves. The He, Ar, Hz and O2 gases (Air Products, research grade) used in the experiments were removed from bulbs with a cold finger immersed in liquid N2. Kr (Air Products, research grade) was removed from a bulb in a dry ice/acetone bath. OCS (Matheson, >97.5Oh), NO2 (Air Products, ~99.5%) and H20 (distilled, deionized) were frozen at liquid-N* temperature and pumped on several times before use. OCS was further purified by distillation from a dry ice/acetone bath. NO* was further purified by being frozen in a dry ice/acetone bath and briefly pumped on.
3. Results and discussion In all experiments the observed OCS( v3) fluorescence was fit very well by a simple, single exponential decay. The results of measurements in pure OCS at 295 K are shown in fig. 1. The least-squares linear fit of the OCS( v3) fluorescence decay rate against 487
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0
0
0.05
0.10
0.15
0.20
0.25
xocs
POCS (TM Fig. 1. Relaxation rate of OCS ( uj) in pure OCS. The line is a least-squares linear fit to the data.
OCS pressure gives a self-relaxation rate constant of ~os=(47k5)x103 s-l Torr-‘. Measurements made in OCS/Ar mixtures are shown in fig_ 2. In a few experiments at low OCS mole fractions, measurements were made with the cold finger of the fluorescence cell immersed in a dry ice/acetone bath for > 1 h to remave any traces of H,O from the gas sample. After a small ( z 4%) correction for the decrease in pressure due to the cold region of the cell, the measured fluorescence decay times were identical to those obtained with the cold finger warm. The intercept and slope of the least-squares linear fit in fig. 2 determine the rate constant kAr= (2.6+ 0.4) x 10’ s- ’ Torr- ’ for relaxation of OCS( y3) by Ar and a value for kocs which is identical to the result obtained in pure OCS. Similar sets of experiments were done with mixtures of OCS in He, Kr, Hz and Oz. The resulting relaxation rate constants are listed
Fig. 2. Relaxation rate constant of OCS( ~1) in OCS/Ar mixtures, The solid line is a least-squares linear tit to the data. The dashed line is the calculated rate constant for self-equilibration of the OCS bending levels [ 5,6] which are probably produced by the relaxation of OCS( v3); see text.
in table 1. The final value in table 1 for the self-relaxation rate constant kocs is the average of the results obtained in pure OCS and in each of the sets of mixture experiments. The rate constant for relaxation of OCS( us) by NOz was measured in mixtures of OCS and NO2 (0.36~Xocs~0.09) and mixtures of OCS, NOz and Kr (0.029~Xocs>O.O20, 0.333>XNoz>0.056). The Ihs of l/~-~ocskocs-~~~~~r=~~oz~~o~
(1)
is plotted in fig. 3 against NO* pressure, where t is the experimental fluorescence decay time, PA is the pressure of gas A, and /coosand km are the relaxation rate constants determined in previous experiments.
Table 1 Rate constants for relaxation of OCS( vs) at 295 K M
ocs He Ar Kr H2 02 NO2 Hz0
kM (10’s_’ Torr-‘)
b
41 * 4 2.6* 0.4 2.6& 0.4 2.7+ 0.4 8.9? 1.3 3.6? 0.5 20 t 3 220 +40
144 8.0 8.0 8.3 27 11 61 615
( lo-r4 cm3 molecule-’ s-r) 6.0x 1.8x 3.5x 4.2x 3.8x 4.4x 2.3x 2.7x
1O-3 1O-4 1o-4 1OW lo+ lo-4 lO-3 1O-2
=’Phc=b.,lklt,mwhere JQ, is the hard sphere, gas kinetic collision rate constant for OCS and collision partner M. The collision diameters used in the calculation of /car+,were 4.1, 2.57, 3.4, 3.6, 2.96, 3.5, 4.2 and 2.8 A for OCS, He, Ar, Kr, HZ, 02, NO2 and HzO, respectively.
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The slope of the least-squares linear fit to the data forced through the origin gives kNol = ( 20 &3 ) X 10’ s-l Tot-r- ‘. At the highest NOz pressure used in the experiments, the equilibrium fraction of Nz04 dimer is calculated to be 4.8%. The small amount of dimerization and the linearity of the plot in fig. 3 indicate that relaxation by N204 is not a significant factor. It should be noted that the experiments were not generally done at constant mole fraction, and therefore a non-linearity not related to the presence of N204 could in principle be introduced into therate versus NOz pressure plot by a systematic variation in the sample mole fractions coupled with a particular sequence of relaxation steps and rates. Several of the data points spanning, the range of NOz pressure (i.e. at PNo2= 1.57, 3.67 and 4.42 Torr) were, however, obtained with a constant mole fraction OCS/NO&r sample and tit very well on the linear plot. Relaxation of OCS ( v3) by Hz0 was measured in mixtures of OCS and Hz0 (0.68&Xocs~0.54) and mixtures of OCS, Hz0 and Ar (0.029 2 X,,~O.025, 0.054aXHzo 30.016). The results are shown in fig. 3 and give the rate constant kHzo= (220540)x lo3 s-’ Torr-‘. The relaxation of OCS ( v3) can occur by a number
PM (Torr) Fig. 3. Relaxation of OCS( v,) in OCS/NOZ/Kr and OCS/H,O/ Ar mixtures. The data are for OCS/NO&r mixtures (circles) and OCS/H,O/Ar mixtures (squares) with untilled symbols for mixtures with I’s?, or PA,,= 0. See eq. ( 1) and the text for an explanation of the ordinate. The lines are least-squares linear fits forced through the origin.
of pathways, including the near resonant intramolecular V-PV processes, OCS(OO1) tM kl,M
OCS(O40) tM-43
-
cm-‘,
(2)
km -
OCS(120)+Mt170cm-‘,
(3)
OCS(200)+Mt351
(4)
km -
cm-‘.
The vibrational angular momentum quantum number 2 of the OCS bend is suppressed here for simplicity, and energy discrepancies are given for the I= 0 sublevel. The energy discrepancies for the processes involving the sublevels with larger 1are only slightly different from those given. In the case of OCS seifrelaxation, the intramolecular processes in eqs. (2)(4) have various intermolecular energy transfer and energy sharing analogs, where the vibrational quanta on the rhs of eqs. (2)-( 4) can be distributed in a variety of ways between the two OCS collision partners. For relaxation of OCS( y3) by M=He, Ar, Kr, H2 and OCS, the intramolecular relaxation processes in eqs. (2)-(4) and the OCS self-relaxation intermolecular analogs are the most likely relaxation pathways because of the minimal energy discrepancies. For relaxation by 02, NO1 and H20, a variety of near resonant intermolecular V-V processes which result in vibrational excitation of the collision partner are also possible. It is evident that the rate constants measured here for relaxation of OCS ( v,) are the total forward relaxation rate constants and are not distorted by the reverse of the possible near resonant VAV relaxation processes. The experimental fluorescence decay curves were single exponentials in all cases and were not the double exponent& expected from rapid equilibration between OCS ( v3) and another near resonant level followed by slower relaxation of the equilibrated levels. No faster fluorescence decay component with a rate constant less than 10 times the reported rate constant, or no slower decay component with an amplitude greater than 0.05 times the amplitude of the primary single exponential decay, was evident for any collision partner. The limits are set by the signal to noise constraints of the experiments. In the case of the intramolecular processes (and self-relaxation intermolecular analogs) 489
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described by eqs. (2 )- (4)) the reverse processes can also be shown to be unimportant because of the rapid self-relaxation of the overtone and combination levels on the rhs of the equations. It has been shown [ 5,6] that equilibration of the bending vibrational levels of OCS through resonant processes such as OCS(0, m, O)fOCS(O, +OCS(O, m-x,
n, 0)
O)+OCS(O, nSx, 0)
(5)
is extremely fast with an overall bending equilibration rate constant of ky2eq = (800 + 400) x 103 s- ’ Torr- ‘. Therefore, the OCS produced in excited bending levels by the processes in eqs. (2) and ( 3 ) can be rapidly relaxed in subsequent collisions with OCS. A similar rapid equilibration of vI stretching levels would also quickly relax the vibrationally excited product of the process in eq. (4). In this work the sample compositions used in the determination of rate constants for all collision partners were chosen such that the observed fludrescence decay rate 1/T was less than, and in most cases many times smaller than, the rate of bending self-equilibrium (i.e. l/~
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brationally excited HBr have been reported by Hopkins et al. [ 11. The reported OCS self-relaxation rate constant is close to the result of the present study; however, the rate constants reported for relaxation by He, Ar and H2 are l-2 orders of magnitude smaller than the values determined in the present study and are smaller than the rate constants reported for V+T, R relaxation of the lowest energy vibrational level of OCS [6]. There is some question whether the OCS( v3) vibrational level is cleanly populated by energy transfer from HBr in these experiments, since much more nearly resonant processes exist for the population of other combination and overtone vibrational levels of OCS. The results of the present study may also be compared with the results of Mandich and Flynn [ 61 derived from observations of the fluorescence from several vibrational levels of OCS following laser excitation of OCS(2v,) in pure OCS, our measured eigenvalue for v3 fluorescence decay is identical to the eigenvalue measured by Mandich and Flynn for the rise in v3 fluorescence following laser excitation of the bending manifold (i.e. 47 x 1O3s- ’ Torr- 1) . Approximately the same “v3 filling” eigenvalue has been reported by Hui and Cool [ 4 ] following either laser excitation of 2 v2, or energy transfer to the OCS bending manifold from vibrationally excited ozone. By considering the amplitudes of the eigenvalue components of the fluorescence from several different vibrational levels, Mandich and Flynn deduced that the v3 level was populated predominantly by the process OCS(O40) +ocs k;,ocs -
OCS(OOl)+OCS+43
cm-‘.
Solution of a simplified rate matrix gave the rate constant k’,,,,, = (12+2)x103 s-’ Torr-‘. By detailed balance the rate constant for the reverse relaxation process described by eq. (2) would be k l,ocsx47~103s-‘Torr-‘whichisthesameasour measured total self-relaxation rate constant for OCS( v3). It appears that OCS( v3) is self-relaxed predominantly by the process in eq. (2 ) to the 4 v2 vibrational level, rather than to lower bending levels, or to levels involving the v, stretching vibration. The specific pathways for relaxation of OCS ( v3) by other collision partners have not been determined. The
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shallow dependence of relaxation probability on reduced collision mass for the “vibrationally inert” collision partners Hz, He, Ar and Kr does suggest, however, that relaxation of OCS( v3) by these partners is a near resonant, intramolecular process releasing less than a few hundred cm-’ of vibrational energy to translation/rotation [ 14,15 ] (i.e. the processes in eqs. (2)-(4)); however, the dominant relaxation path is not necessarily the same as for OCS self-relaxation. In the case of the analogous linear triatomic molecules CO2 and N20, it has been suggested from a comparison of experimental results with theoretical energy transfer calculations that for those molecules relaxation of the v3vibration by the rare gases results in excitation of a combination of the vI (stretch) and v2 (bend) vibrational modes [14,15].
Acknowledgement This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Offrce of Energy Research, US Department of Energy.
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References [ 1] B.M. Hopkins, A. Baronavski and H.-L. Chen, J. Chem. Phys. 59 (1973) 836. [2] J.K. Hancock, D.F. Starr and W.H. Green, J. Chem. Phys. 61 (1974) 3017. [ 31 D.R. Siebert and G.W. Flynn, J. Chem. Phys. 64 (1976) 4973. [4] K-K. HuiandT.A. Cool, J. Chem. Phys. 65 (1976) 3536. [ 51Yu.R. Kolomiiskii, VS. Letokhov and O.A. Tumanov, Soviet J. Quantum Electron. 6 (1976) 959. [ 61 M.L. Mandich and G.W. Flynn, J. Chem. Phys. 73 (1980) 1265,3679. [7] H.R. Schlossberg and H.R. Fetterman, Appl. Phys. Letters 26 (1975) 316. [ 81 B.M. Landsberg, IEEE J. Quantum Electron. QE-16 (1980) 704. [9] P.F. Zittel, L.A. Damton and D.D. Little, J. Chem. Phys. 79 (1983) 5991. [ 101 P.F. Zittel and D.E. Mastuno, J. Chem. Phys. 85 (1986) 4362. [ 111G. Guelachvili, Opt. Commun. 30 (1979) 361. [ 121 N. Hunt, SC. Foster, J.W.C. Johns and A.R.W. McKellar, J. Mol. Spectry. 111 (1985) 42. [ 131 G.C. Bahr and R.C. Smith, IEEE J. Quantum Electron. QE10 ( 1974) 546, and references therein. [ 141J.T. Yardley and C.B. Moore, J. Chem. Phys. 46 ( 1967) 4491. [ 151 J.T. Yardley, J. Chem. Phys. 49 (1968) 2816.
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VIBRATIONAL RELAXATION OF OCS( v~) P.F. ZITTEL and M.A. SEDAM Chemistry and Physics Laboratory, The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009, USA Received 18 April 1988; in final form 18 May 1988
A laser-induced fluorescence method has been used to measure rate constants for relaxation of the u, (2062 cm-’ ) vibrational level of OCS. A frequency-doubled CO2 laser was used to pump OCS directly to the excited level. At 295 K the rate constants for relaxation by OCS, He, Ar, Kr, Hz, 02, NO2 and Hz0 were 144, 8.0, 8.0, 8.3, 27, 11, 61 and 675, respectively, in units of lo-r4 cm3/molecules.
1. Introduction The linear triatomic molecule OCS has been the of a number of studies of vibrational [ l-61 and rotational energy transfer. Vibrational energy flow in OCS is an important factor in various systems, including OCS molecular lasers [5,7,8] and the separation of isotopes by two-step laser photodissociation [ 9,101. Previous measurements of OCS vibrational relaxation have typically used a 9.6 pm CO1 laser to directly excite the 2 v2 (bending overtone) vibrational level and have analyzed fluorescence from other levels [ 3,4,6] or the absorption of laser energy [ 5 1, to obtain rate constants for various intra- and inter-mode vibrational relaxation processes. In the study of Mandich and Flynn [ 6 1, rate constants for intermode bend to stretch energy transfer and bend to translation/rotation relaxation were deduced from the solution of a simplified matrix of rate equations with the observed fluorescence decay eigenvalues. The deduced rate constants included a value for the near resonant intermode transfer from the 4vz bending level to the VI stretching level. The determination of rate constants for some energy transfer processes involving the OCS stretching vibrations can be simplified by initial excitation of the v, and v3 vibration stretching levels themselves. Direct laser excitation of the vI (S stretch) vibrational level with a 12 pm NH3 laser has been demonstrated [ lo], but has not been employed in energy transfer studies. Initial excitation of the V~(C-O stretch) visubject
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brational level has been achieved indirectly by near resonant, V-V energy transfer from vibrationally excited CO [ 21 and HBr [ 11. Rate constants for relaxation of OCS( v3) by a few gases have been reported in these studies. Except for self-relaxation, the OCS ( v3) relaxation rate constants determined in the studies involving initial laser excitation of the 2v2 level, energy transfer from CO, and energy transfer from HBr show large scatter where comparisons are possible, and in any event there is some complexity in the sequence of energy transfer processes which populate OCS ( v3) . In this paper we report rate constants for vibrational relaxation of OCS( v3) at 295 K. Direct laser excitation to the v3 vibrational level was achieved with a COz laser, frequency doubled in a AgGa$ crystal. Fluorescence on the v+O vibrational transition was observed through a monochromator. The experiments provide straightforward measurements of OCS ( v3) relaxation rate constants for several collision partners.
2. Experimental A laser-induced fluorescence method was used to measure the relaxation rate constants. The frequency-doubled, 9.6 pm CO2 P(30) laser line is nearly coincident (AE= 199 MHz) with the R( 34) line of the 16012C3zSO-+v3vibrational baud [ 11,121. A grating-tuned, CO2 TEA laser (Lumonics 203-2)
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
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was operated with a C02/He gas mixture, a standard multimode output optic, and a 15 mm diameter knife-edge aperture in the laser cavity near the output optic. The laser configuration produced a short ( x 70 ns), linearly polarized laser pulse with a fairly uniform fluence profile in the far field (*4.2 m), approximated by a Gaussian function with a full width at half maximum (fwhm) of 6.2 mm. The far field laser spot was compressed by a x2 telescope and attenuated with CaF2 flats to achieve a desired intensity. The CO* laser pulse was frequency doubled in a AgGaSz crystal with PbF anti-reflection coatings (Cleveland Crystals). The crystal was 8 x 10 mm in cross section, 15 mm long, and was cut at 57.0” to the optic axis. The crystal was angle tuned to achieve the proper internal angle (measured to be 56.6” f 0.4” ) between the optic axis and the ordinary CO2 laser beam for type-1 second harmonic generation [ 131 #I. The incident CO* pulse energy was adjusted to 68 mJ, providing a fluence and peak intensity at the center of the laser spot of ~0.62 J/ cm2 and w 8.9 MW/cm’, respectively. The doubled pulse energy was 0.27 mJ with a spot diameter of 2.3 mm fwhm, corresponding to a pulse energy conversion of 0.40%. Doubled pulse energies as large as 5.7 mJ, corresponding to conversion efficiencies of 2.0%, were achieved with larger CO2 laser pulse energies and a spot with a slightly different fluence profile; however, damage to the entrance and exit faces of the crystal occurred with the higher laser intensities. The COz laser radiation was separated from the frequency-doubled radiation by a 45’ multilayer dielectric mirror on a ZnSe substrate (CVI Corp. ) which reflected 9.6 pm radiation ( > 99% reflection) and transmitted 4.8 pm radiation ( > 95% transmission) and also by a MgF2 flat at Brewster’s angle to the doubled radiation. Fluorescence experiments were conducted in a Pyrex cell 25 mm in diameter by 30 mm long with MgF2 windows for the laser entrance and exit and for observation of fluorescence perpendicular to the laser beam. The cell had an isolatable cold finger to facilitate sample preparation and to allow some experiments to be run with the cold finger immersed ” The refractive indices given for the “RRE” crystal [ 13 ] best reproduced our observed phase matching angles for SHG with the P( 18)-P(44) lines of the 9.6 pm CO1 laser.
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in a dry ice/acetone bath. The fluorescence cell was placed at the entrance slit of an f /4 grating monochromator operated with wide slits (2 mm) and tuned to a center wavelength of 4.869 pm with a measured bandpass of 0.028 pm fwhm. Thus, the monochromator passed most of the P-branch of the OCS Y~-+Oemission band and blocked nearly all scattered laser lighi. A small amount of scattered laser light and electrical noise was removed by subtracting a cell-empty, background run from each fluorescence record. Fluorescence was detected at the exit slit of the monochromator by a liquid-N,-cooled, 2 mm diameter, InSb detector with matched preamp followed by a wideband voltage amplifier. In response to a short scattered laser light pulse, the detector/ amplifier combination produced a signal with an exponential decay time of 320 ns. In all cases fluorescence decay times were at least a factor of 10 longer than the detector response time. The signals were digitized by a Transiac 2008 transient recorder (25 MHz maximum sample rate, 8K record) controlled through a CAMAC interface by an IBM AT computer. Signal averaging of x: 1000 laser shots produced fluorescence decay curves with an initial signal to noise > 12 in the worst case. The computer was also used to make least-squares tits of decay times to the single exponential fluorescence decay curves. The He, Ar, Hz and O2 gases (Air Products, research grade) used in the experiments were removed from bulbs with a cold finger immersed in liquid N2. Kr (Air Products, research grade) was removed from a bulb in a dry ice/acetone bath. OCS (Matheson, >97.5Oh), NO2 (Air Products, ~99.5%) and H20 (distilled, deionized) were frozen at liquid-N* temperature and pumped on several times before use. OCS was further purified by distillation from a dry ice/acetone bath. NO* was further purified by being frozen in a dry ice/acetone bath and briefly pumped on.
3. Results and discussion In all experiments the observed OCS( v3) fluorescence was fit very well by a simple, single exponential decay. The results of measurements in pure OCS at 295 K are shown in fig. 1. The least-squares linear fit of the OCS( v3) fluorescence decay rate against 487
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0
0
0.05
0.10
0.15
0.20
0.25
xocs
POCS (TM Fig. 1. Relaxation rate of OCS ( uj) in pure OCS. The line is a least-squares linear fit to the data.
OCS pressure gives a self-relaxation rate constant of ~os=(47k5)x103 s-l Torr-‘. Measurements made in OCS/Ar mixtures are shown in fig_ 2. In a few experiments at low OCS mole fractions, measurements were made with the cold finger of the fluorescence cell immersed in a dry ice/acetone bath for > 1 h to remave any traces of H,O from the gas sample. After a small ( z 4%) correction for the decrease in pressure due to the cold region of the cell, the measured fluorescence decay times were identical to those obtained with the cold finger warm. The intercept and slope of the least-squares linear fit in fig. 2 determine the rate constant kAr= (2.6+ 0.4) x 10’ s- ’ Torr- ’ for relaxation of OCS( y3) by Ar and a value for kocs which is identical to the result obtained in pure OCS. Similar sets of experiments were done with mixtures of OCS in He, Kr, Hz and Oz. The resulting relaxation rate constants are listed
Fig. 2. Relaxation rate constant of OCS( ~1) in OCS/Ar mixtures, The solid line is a least-squares linear tit to the data. The dashed line is the calculated rate constant for self-equilibration of the OCS bending levels [ 5,6] which are probably produced by the relaxation of OCS( v3); see text.
in table 1. The final value in table 1 for the self-relaxation rate constant kocs is the average of the results obtained in pure OCS and in each of the sets of mixture experiments. The rate constant for relaxation of OCS( us) by NOz was measured in mixtures of OCS and NO2 (0.36~Xocs~0.09) and mixtures of OCS, NOz and Kr (0.029~Xocs>O.O20, 0.333>XNoz>0.056). The Ihs of l/~-~ocskocs-~~~~~r=~~oz~~o~
(1)
is plotted in fig. 3 against NO* pressure, where t is the experimental fluorescence decay time, PA is the pressure of gas A, and /coosand km are the relaxation rate constants determined in previous experiments.
Table 1 Rate constants for relaxation of OCS( vs) at 295 K M
ocs He Ar Kr H2 02 NO2 Hz0
kM (10’s_’ Torr-‘)
b
41 * 4 2.6* 0.4 2.6& 0.4 2.7+ 0.4 8.9? 1.3 3.6? 0.5 20 t 3 220 +40
144 8.0 8.0 8.3 27 11 61 615
( lo-r4 cm3 molecule-’ s-r) 6.0x 1.8x 3.5x 4.2x 3.8x 4.4x 2.3x 2.7x
1O-3 1O-4 1o-4 1OW lo+ lo-4 lO-3 1O-2
=’Phc=b.,lklt,mwhere JQ, is the hard sphere, gas kinetic collision rate constant for OCS and collision partner M. The collision diameters used in the calculation of /car+,were 4.1, 2.57, 3.4, 3.6, 2.96, 3.5, 4.2 and 2.8 A for OCS, He, Ar, Kr, HZ, 02, NO2 and HzO, respectively.
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The slope of the least-squares linear fit to the data forced through the origin gives kNol = ( 20 &3 ) X 10’ s-l Tot-r- ‘. At the highest NOz pressure used in the experiments, the equilibrium fraction of Nz04 dimer is calculated to be 4.8%. The small amount of dimerization and the linearity of the plot in fig. 3 indicate that relaxation by N204 is not a significant factor. It should be noted that the experiments were not generally done at constant mole fraction, and therefore a non-linearity not related to the presence of N204 could in principle be introduced into therate versus NOz pressure plot by a systematic variation in the sample mole fractions coupled with a particular sequence of relaxation steps and rates. Several of the data points spanning, the range of NOz pressure (i.e. at PNo2= 1.57, 3.67 and 4.42 Torr) were, however, obtained with a constant mole fraction OCS/NO&r sample and tit very well on the linear plot. Relaxation of OCS ( v3) by Hz0 was measured in mixtures of OCS and Hz0 (0.68&Xocs~0.54) and mixtures of OCS, Hz0 and Ar (0.029 2 X,,~O.025, 0.054aXHzo 30.016). The results are shown in fig. 3 and give the rate constant kHzo= (220540)x lo3 s-’ Torr-‘. The relaxation of OCS ( v3) can occur by a number
PM (Torr) Fig. 3. Relaxation of OCS( v,) in OCS/NOZ/Kr and OCS/H,O/ Ar mixtures. The data are for OCS/NO&r mixtures (circles) and OCS/H,O/Ar mixtures (squares) with untilled symbols for mixtures with I’s?, or PA,,= 0. See eq. ( 1) and the text for an explanation of the ordinate. The lines are least-squares linear fits forced through the origin.
of pathways, including the near resonant intramolecular V-PV processes, OCS(OO1) tM kl,M
OCS(O40) tM-43
-
cm-‘,
(2)
km -
OCS(120)+Mt170cm-‘,
(3)
OCS(200)+Mt351
(4)
km -
cm-‘.
The vibrational angular momentum quantum number 2 of the OCS bend is suppressed here for simplicity, and energy discrepancies are given for the I= 0 sublevel. The energy discrepancies for the processes involving the sublevels with larger 1are only slightly different from those given. In the case of OCS seifrelaxation, the intramolecular processes in eqs. (2)(4) have various intermolecular energy transfer and energy sharing analogs, where the vibrational quanta on the rhs of eqs. (2)-( 4) can be distributed in a variety of ways between the two OCS collision partners. For relaxation of OCS( y3) by M=He, Ar, Kr, H2 and OCS, the intramolecular relaxation processes in eqs. (2)-(4) and the OCS self-relaxation intermolecular analogs are the most likely relaxation pathways because of the minimal energy discrepancies. For relaxation by 02, NO1 and H20, a variety of near resonant intermolecular V-V processes which result in vibrational excitation of the collision partner are also possible. It is evident that the rate constants measured here for relaxation of OCS ( v,) are the total forward relaxation rate constants and are not distorted by the reverse of the possible near resonant VAV relaxation processes. The experimental fluorescence decay curves were single exponentials in all cases and were not the double exponent& expected from rapid equilibration between OCS ( v3) and another near resonant level followed by slower relaxation of the equilibrated levels. No faster fluorescence decay component with a rate constant less than 10 times the reported rate constant, or no slower decay component with an amplitude greater than 0.05 times the amplitude of the primary single exponential decay, was evident for any collision partner. The limits are set by the signal to noise constraints of the experiments. In the case of the intramolecular processes (and self-relaxation intermolecular analogs) 489
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described by eqs. (2 )- (4)) the reverse processes can also be shown to be unimportant because of the rapid self-relaxation of the overtone and combination levels on the rhs of the equations. It has been shown [ 5,6] that equilibration of the bending vibrational levels of OCS through resonant processes such as OCS(0, m, O)fOCS(O, +OCS(O, m-x,
n, 0)
O)+OCS(O, nSx, 0)
(5)
is extremely fast with an overall bending equilibration rate constant of ky2eq = (800 + 400) x 103 s- ’ Torr- ‘. Therefore, the OCS produced in excited bending levels by the processes in eqs. (2) and ( 3 ) can be rapidly relaxed in subsequent collisions with OCS. A similar rapid equilibration of vI stretching levels would also quickly relax the vibrationally excited product of the process in eq. (4). In this work the sample compositions used in the determination of rate constants for all collision partners were chosen such that the observed fludrescence decay rate 1/T was less than, and in most cases many times smaller than, the rate of bending self-equilibrium (i.e. l/~
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brationally excited HBr have been reported by Hopkins et al. [ 11. The reported OCS self-relaxation rate constant is close to the result of the present study; however, the rate constants reported for relaxation by He, Ar and H2 are l-2 orders of magnitude smaller than the values determined in the present study and are smaller than the rate constants reported for V+T, R relaxation of the lowest energy vibrational level of OCS [6]. There is some question whether the OCS( v3) vibrational level is cleanly populated by energy transfer from HBr in these experiments, since much more nearly resonant processes exist for the population of other combination and overtone vibrational levels of OCS. The results of the present study may also be compared with the results of Mandich and Flynn [ 61 derived from observations of the fluorescence from several vibrational levels of OCS following laser excitation of OCS(2v,) in pure OCS, our measured eigenvalue for v3 fluorescence decay is identical to the eigenvalue measured by Mandich and Flynn for the rise in v3 fluorescence following laser excitation of the bending manifold (i.e. 47 x 1O3s- ’ Torr- 1) . Approximately the same “v3 filling” eigenvalue has been reported by Hui and Cool [ 4 ] following either laser excitation of 2 v2, or energy transfer to the OCS bending manifold from vibrationally excited ozone. By considering the amplitudes of the eigenvalue components of the fluorescence from several different vibrational levels, Mandich and Flynn deduced that the v3 level was populated predominantly by the process OCS(O40) +ocs k;,ocs -
OCS(OOl)+OCS+43
cm-‘.
Solution of a simplified rate matrix gave the rate constant k’,,,,, = (12+2)x103 s-’ Torr-‘. By detailed balance the rate constant for the reverse relaxation process described by eq. (2) would be k l,ocsx47~103s-‘Torr-‘whichisthesameasour measured total self-relaxation rate constant for OCS( v3). It appears that OCS( v3) is self-relaxed predominantly by the process in eq. (2 ) to the 4 v2 vibrational level, rather than to lower bending levels, or to levels involving the v, stretching vibration. The specific pathways for relaxation of OCS ( v3) by other collision partners have not been determined. The
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shallow dependence of relaxation probability on reduced collision mass for the “vibrationally inert” collision partners Hz, He, Ar and Kr does suggest, however, that relaxation of OCS( v3) by these partners is a near resonant, intramolecular process releasing less than a few hundred cm-’ of vibrational energy to translation/rotation [ 14,15 ] (i.e. the processes in eqs. (2)-(4)); however, the dominant relaxation path is not necessarily the same as for OCS self-relaxation. In the case of the analogous linear triatomic molecules CO2 and N20, it has been suggested from a comparison of experimental results with theoretical energy transfer calculations that for those molecules relaxation of the v3vibration by the rare gases results in excitation of a combination of the vI (stretch) and v2 (bend) vibrational modes [14,15].
Acknowledgement This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Offrce of Energy Research, US Department of Energy.
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References [ 1] B.M. Hopkins, A. Baronavski and H.-L. Chen, J. Chem. Phys. 59 (1973) 836. [2] J.K. Hancock, D.F. Starr and W.H. Green, J. Chem. Phys. 61 (1974) 3017. [ 31 D.R. Siebert and G.W. Flynn, J. Chem. Phys. 64 (1976) 4973. [4] K-K. HuiandT.A. Cool, J. Chem. Phys. 65 (1976) 3536. [ 51Yu.R. Kolomiiskii, VS. Letokhov and O.A. Tumanov, Soviet J. Quantum Electron. 6 (1976) 959. [ 61 M.L. Mandich and G.W. Flynn, J. Chem. Phys. 73 (1980) 1265,3679. [7] H.R. Schlossberg and H.R. Fetterman, Appl. Phys. Letters 26 (1975) 316. [ 81 B.M. Landsberg, IEEE J. Quantum Electron. QE-16 (1980) 704. [9] P.F. Zittel, L.A. Damton and D.D. Little, J. Chem. Phys. 79 (1983) 5991. [ 101 P.F. Zittel and D.E. Mastuno, J. Chem. Phys. 85 (1986) 4362. [ 111G. Guelachvili, Opt. Commun. 30 (1979) 361. [ 121 N. Hunt, SC. Foster, J.W.C. Johns and A.R.W. McKellar, J. Mol. Spectry. 111 (1985) 42. [ 131 G.C. Bahr and R.C. Smith, IEEE J. Quantum Electron. QE10 ( 1974) 546, and references therein. [ 141J.T. Yardley and C.B. Moore, J. Chem. Phys. 46 ( 1967) 4491. [ 151 J.T. Yardley, J. Chem. Phys. 49 (1968) 2816.
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