- Email: [email protected]
A laser-induced fluorescence study of energy transfer between the symmetric stretching and bending modes of CO2
CHEMICAL PHYSICS LETI’ERS
Volttmr: 83, number 1
A LASER-iNDUCED
FLUO~~EN~E
1 October 1981
STUDY OF ENERGY TRANSFER
BETWEEN THE SYMMETRIC STRETCHING
AND BENDING MODES OF CO,
R.K. HUDDLESTON ’ and Eric WEITZ * Department of Chemistry, Northwestern University, Evanston, IIlinois 60201, USA Received 5 May 1981; in final form 16 June 1981
The equilibration of the lower laser levers in COz, loo0 and 02O0, has been studied via a laser-induced fluorescence technique. We conclude that the coupling between these leveis is rapid, >llOO ms-’ To& I and that these levels are also coupted though at a somewhat slower rate of 387 f 75 ms-* Torr-’ to the bending modes of C&.
or stepwise via
1. IntYoduction
energy transfer in gaseous CO, has been extensively studied [l-26]. While CO2 has come lo be regarded as a model compound for energy transfer studies, a number of vibration-vibration energy transfer rates in this system remain in dispute. The refaxation of the 001 state appears to be well established at a rate of 0.33 + 0.005 ms-l Torr-t [4-71 and a number of resonant vibration-vibration energy transVibrational
fer rates have recently been measured 1263. However, the rates for the process coupling 02OOand 1O"O, the
lower levels, CO,{ 1000) f C0,(0000) 2kb c02(0200) + C0,(0000), AE= 103 cm-l ,
(0
,hich due to Fermi mixing are a nearly equal mixture I &heunperturbed 02OOand I O”Ostates and the pro-
zss coupling the fund~ental of the bend to the fower I?‘:r levels and the 0220 state remain in question. Tf‘ %zrprocess may either proceed directljr via Cfizt_iO"O or 02OO)+ C02(OO”O)
* Presentaddress: Chemistry Division, Argonne National Laboratories Aqonne, Illinois 60439, USA. * Alfred. P. Sloan Fe&w.
174
CO~~Ol~O)+ ~02(01~0~ 2 CO2(0220) ~CO2{0~0) (3)
and CO,(O220) + co,@O*o) 2
CO(lOOOor 02OO)+ C02(OO”O).
(4)
Rates for process (1) range from a reported high value of IO3 ms” 1 Torr-l ffl] toaiowvalueof 140ms-t Torr-l [ 13J. In addition, the rate for the coupling of the fundamental of the bending mode to the lower laser levels is not well established. Rhodes et al. [ 1I ] report a value of 4 X 18 ms-1 Torr-1 while vdiues as low as 3.2 ms- t Torr-l 11’71or even l.Oms-t Torr-l [f 51 have been reported for this process. The apparent inconsistency of many of the above experimental results may, in part, be due to the variety of experimental conditions. Etectdcal discharges which were used in laser afterglow studies and gain measurements, may lead to unpredjctable effects of free electrons, ions, and dissociation products and uncertainties in temperature. Laser absorption and gain measurements are sensitive to popula~on d~eren~s between two states which are effected by changes in either state and to perturbations by the radiation tield. Discrepancies may also have resulted from the ambiguous assignment of specific kinetic steps to measured rates.
Volume83, number 1
CHEMICAL PHYSICSLETTERS
The present experiments employ the laser-induced fluorescence technique to directly observe the time evolution of population in CO, vibrationat states followhrg creation of a non~~~m d~t~ution of population via a pulsed infrared laser [24 1. This expcr. imental technique avoids many of the abovementioned diificulties,
1 October1981
averaged, and then plotted on an X-Y recorder and stored in digiti form for computer analysis. The response time of the &Ge detector loaded to 5 kf2 and the associated electronics was carefully measured to be 1.OPS [27].
3. Results 2. Experimental A detailed description of the experimental procedure used in this study has been previously presented [27]. Briefly the experiment consisted of monitoring the ffuorescence emission from the bending and symmetric stretching modes of CO, following excitation of CO, with a Q-switched CO2 laser. The CO, infrared laser consisted of a 2.5 m water-cooled tube with Brewster angle NaCl windows mounted at each end. A longitudinal discharge at approximately 20 kV and 15 mA was maintained throu8h a flowing mixture of CO2, N2, and He. The laser was Q-switched with a 10 m radius of curvature gold mirror rotating at I00 HZ. The output of the laser could be tuned over the 9.6 and 10.6 lun vibrational bands of CO2 by a diffraction grating blazed for 10.0 WII,yielding 2 mJ in 2 MS pulses (full width at base) on a single rotational line. The laser beam was directed through an aluminum cell closed with NaCl windows. Fluorescence in the 15 m region was detected perpendicular to the beam with a liquid He cooled GeCu detector looking through a 5 mm thick KBr window. Interference filters were used to isolate certain wavelength regions. Available were 13.48, 13.97, and 15.475 E.cmlong-pass filters (5% points) with average tr~~itt~~s of 6070% and a 14.00-16.53 lun bandpass falter (50% points), The bandpass falter could be cooled inside the detector dewar to limit room-temperature blackbody radiation and increase the s~n~-t~no~e ratio. Typically, a combination of the cooled bandpass filter and long-passWters was used. For most long-wavelength measurements, both the 13.48 and the 15.475 pm long-passWters were used in conjunction with the cooled fdter. These filters produced an effective bandpass filter with a bandpass of 15.48-16.92 pm (5% pts). The three filters were able to almost completely eliminate laser scatter. The si8nalswere ~pl~ed, d&itized with a model 610B Biomation transient recorder,
Following absorption of the CO2 &switched laser pulse on either the 9.6 or 10.6 elm branch, the fhrorescence intensity of the signal observed through the combination of 14.00-16.53 pm bandpass and 13.97 @n long-pass filters is seen to decrease. Fig. 1 shows a typical signal taken on a long-time base. While the details of the energy transfer processes governing the time evolution of the entire fluorescence signal will not be discussed here, the overall interpretation of this signal is straightforward [28]. As will be discussed, on the time scale of the recovery and subsequent fall of the signalin fig. 1, the lower laser levels in CO,, the Fermi mixed states 1000 and 0200, are rapidly collisionally coupled. These levefs are also rap idly coupled on this timescale to the fundamental of the bending mode. The CO2 laser pulse depletes these levels causing a decrease in intensity of fluorescence emission from this system at the wavelengths corresponding to transitions of the type
I
0.0
0.2
0.4
0.6 Time
0.6
II0
I
12
(msec)
Fig. 1. Averagedfluorescence@ml from CO2 observed through a 14.00- 16.53 gm optical window followi?@sxcitntion of 25 Ton of C02. Tbe prep&c bamline is IndicHedby the zero position on the ordinate,The fastdropinsignathitens& which occursat time t = 0 is not expltdUYvisible.
175
Volume 83, number 1
CHEMICAL PHYSICS LL-!XERS
co~(1ooo)
+ CO~(O1’0)
+ hv,
@a)
co2(0200)
+ CO,(O110)
+ tzv’,
(5b)
CO,(O110)
+ co,(ooOo)
+ Izv”,
(SC)
C07(0220)
+ CO,(O110)
+ hv”‘.
(5d)
These states are gradually refried from neighbormg states and the asymmetnc stretch. The mtensrty of emission from the transitrons m eqs. (5) gradually mcreases, as does the populatron. to somewhat above the pre-laser pulse level. This mrght be expected smce the laser mtroduces addrtional vrbrational energy mto the system whrch at vrbrational equrhbnum results m an elevated vibratronal temperature and therefore more exerted-state molecules and a larger fluorescence srgnal than at the ambient prepulse vibratronal temperature_ The populatron then decays back to the imtral pre-pulse equihbnum value due to V + T/R and heat and mass transport processes [3_9] _ The observed V + T/R rate agrees weU wrth ultrasoruc results for co, [28]. Additronal mformatron IS available d thus signal is observed on a much faster timescale. Usmg the three filters m combinatron, when pumpmg the 10.6 pm transrtron, the imtral drop m fluorescence mtensrty was observed to be very fast. Due to the finite detector response time and laser pulse wrdth the fastest rate that could be accurately measured in these expenments was 900 ms-I. At a pressure of 0.8 Torr of CO, the initral drop m fluorescence intenstty was
clearly rate limited by the comomatron of these factors. Thus a mirumum rate for this fast fall could be estabhshed as being in excess of 1100 ms-1 Torr-I_ When pumping the 10.6 E.cmtransttion, rf the pressure IS decreased to 0.5 Torr, the mitral decrease in fluorescence intensrty appears to sIow up. However, at this pressure the signal-to-noise ratio has degraded sufficrentiy so that an actual measurement of the rate of the decrease in fluorescence intennty versus pressure was not possrble. Followmg the rapid fall, the signal etibits a slow recovery for the reasons drscussed above. A fast recovery is observable on some signals but due to the poor signal-to-noise ratro of the unaveraged srgnal the rate cannot be measured even after extensive averaging. When pumping the 9.6 pm transition, rmmediately 176
1 October
198 1
a
Frg 2 Averaged fluorescence signal from CO2 observed through a 15.48-16 92 pm ophcal wmdow following 9.6 pm pumping of 0.75 Torr of COz. The prepuke basehne is indrcated by the zero posrtion on the ordmate. (a), (b) and (c) indmate the important features in the sgnaL The peak mdicared by (a) rs due to laser scatter and thus mdicates the position of the laser pulse relative to the start of the pretriggered trace which occurs at t=O. @) mdicates the response of the observed state to remoral of populatron via laser pumpmg, (c) mdrcates the refii of the observed state from other states m the system. Process (c) has a rate, as discussed m the telt, of 387 ms-r Torr-‘. Followmg process (c) 1sa much slower flow of populatron mto the observed state. Thrs ts shown, on a much longer tunescale, m fg. 1.
after the uutial ialI of the signal a raped increase in
fluorescence mtensity IS seen. Thrs is shown in fig. 2. After thrs process is complete, the level of fluorescence mtensity is still below the baseline, and the rest of the recovery process appears on this timescale as a very slow rise. Thrs is the slow rise that is shown on an even longer tune scale in fig. l_ The fact that the pressure range over which the signals corresponding to the aforementioned fast recovery can be observed is small, being limited on the high srde by the response time of the apparatus and on the low side by the pressure at which reasonable signal-to-noise ratros can be obtained, leads to somewhat larger than desrrable error brackets on the measured pressure dependent rate of this process. However, as shown in fig. 3, the rate has been measured over the pressure range from 0.4 to 1.5 Torr and IS reported
as 387 f 75 ms-1
Torr-1.
With a 9.6 Drn pump and observation of the signal through the three-filter combination, on addition of up to 9.00 Torr of argon, the fast recovery rate of
Volume 83. number 1
CHEhIICAL
700
. ?-:,A WO-
.
500-
2
l
5
.
D
cs30
.
Slope
rcec
.
: 387
: 7i
’ 1c.r. ’
.
200
loo
OO
05
IO
15
3. Rate of rise of the fast recorery signalin CO2 versus pressure.The data were obtamed from fluorescence signals observedthror@r a 15.48-16.92 pm optical windowfollowing9.6 pm pumpmg of COa. Fg.
the signal shown m fig. 2 did not change for a constant CO, pressure. The imphcations of this will be discussed m the next section. 4. Discussion The fact that more than one CO2 vibrational state contributes to the fluorescence signal complicates the mterpretation of the results of this study. The wide band-pass filter used in these expernnents passes the emission from 02O0,0220,and 01 1 0 and a small part of the lOoO-01 l0 band (~3% of the total 1s loo0 + 01 IO emission). This and other estimates are based on room-temperature bandpasses whrch change slightly on cooling of filters *_ Even with the three-filter combination there is some emission from transitions SC and 5d, but the majority of the fluorescence comes from Sb (02OO). With this filter combination a very fast initial fall of the signal is observed pumping either the 10.6 or 9.6 pm CO2 laser transition. ‘lks drop in amplitude has a rate of > 1100 ms-1 Torr-l .The most significant observation is that pumping the IO00 state casues a
* Optical Coating Laboratory, Inc, Santa Rosa, California Stock Film Catalog.
PHYSICS LETTERS
1 October 198 L
response m the 02OO state with the rate cited above. This defimtely shows that these states are coupled on this times&e. With the three-filter combination and a 9.6 can pump, a significant amplitude fast recovery of population is observed. The rate of this recovery is inertgas pressure independent. Thus, the population must be coming from a state with significant ambient population and vra a pathway for which the rate hmiting step would be expected to be inert-gas pressure independent [30].Thiswould fingerprint this process as being the transfer of population from the 0110 state to 02OO erther drrectly or through an intermediate state such as 02’0 or even 10°O. The population of the bending mode fundamental is expected to decrease as it comes into equilibrium with the depleted lower laser levels. The rate of this population decrease would be the same as the rate of the increase in the lower laser IeveIs if ret%ng the lower laser levels involves a single rate limiting step within the bending mode manifold. Thus, if ail states were observed sunultaneously and with the same emission intensity, the signal corresponding to the fall of population in 01 l0 would cancel the population rise in the upper states, and under these hypothetical circumstances no fast depletion or fast recovery signal would be observed. In the actual case, observed emisraon intensities are tiected by the filter bandpass, the ernissron band strengths, and by the degree of self-trapping of a given state. Self-trapping can be significant m these circumstances. When radiation is emitted and absorbed over the same Doppler line shape, the degree of self-trapping can be evaluated from the integral given by Holstein 1311 which for this case can be expressed as the infiite series. T(kol) =
m$o (-ko’y”lm!(m
f
1)1’2,
where 1 is the pathlength, and kg istheabsorption coefficient at line center. Ihe r2sult of a cakulation using eq. (6) and the individual rotational linestrengths is that for the 01’0 + OO”Oemission band in CO, at a pressure of 1 Torr and a path length of 1.5 cm (our cell radius), 89% of the fluorescence emission will be self-trapped! Hot bands terminating in the 01 IO state will be absorbed only about one-fourth as much with 02*0 + 0110 emission expected to be absorbed more strongly than 02OO + 0 1 l0 emission since the former 177
Volume 83. number 1
CHEMICALPHSYICSLEITERS
transition ahnost exactly overlaps the fundamental 0110 + 0000 transition. The assumption of an average path length will lead to an overestimate of the amount of fluorescence reabsorbed but will not change the conclusion that reabsorption can be s~~c~t. As would be predicted from the above discussion, the relative contribution of the fast recovery to the total signal amplitude decreases when the signal corresponding to a 9.6 pm pump is viewed with the wide bandpass falter versus the three-falter combination. This is due to the observation of relatively more 0 1i 0 + 0000 emission in the former case which will cancel some of the amplitude of the recovery signal from the upper states (principally, 02OOand 10°O, though 0220 may also be involved if it is an intermediate state in the transfer of energy from 01 l0 to the lower laser levels). This cancellation of amplitude is mitigated by the more efficient self-trapping of the 01 IO + 0000 transition versus transitions terminating in 01 10 and, of course, by our selection of falters which transmit mostly emission from 02OO. It is now of interest to relate the observed rates to elemental rate constants for ~dividu~ steps. In the case of V-V equilibration of the two lower laser leveIs, the observed rate will be the sum of the forward and reverse rates of process (I), under the assumption that these levels can be considered isolated from other states in the system on the timescale of equilibration between them. Thus, a lower limit of 700 ms-l Torr-1 can be placed on the forward rate (exothermic direction) of process (1). The remaining question is assignment of the recovery rate of 387 ms- ’ Torr-l to a specific process. If coupling between 1000 and 02OOis rapid and if these states are also rapidly coupled to 0220, for purposes of assignment of a rate process to the 387 ms-1 ‘I’orr-t rate, the system can be considered as a threerevel system with the levels being the ground state, 01’0 and the combined 02O0, @O and 1000 states. I- this case, the measured rate of 387 ms-1 Torr-1 :ire lower laser level * bend equ~ibration process L I responds to a good approximate to the backward rate of ~.12(0110j + COz(oi~oj 2
~0~(02~0/02~0/~0~0)+ ~O~(OO~Oj.
(7)
Though our data are consistent with this mechanism,
178
1 October 1981
0220 does not have to be rapidly coupled to 02OO and 1000 if 02OOand/or 10”O are directly filled from 01 10 by a near resonant process. In this case, the rate of 387 ms- 1 Torr-lwill stlll be assigned to the back rate of process (7) with the fast species on the right being indicated as C~~(~~O/I~O). The assignment of the observed rates of 387 ms-1 Torr-i to kb @Ieq. (7) can be most easily understood by considering a hypothetical situation in which the lower laser levels had initial excess population. As is generally true, a change in the initially perturbed state wifi not change the rates in a kinetic system, only the ampiitude of the rates. Thus the observed rates for the hypothetical situation corresponding to excess population in the lower laser levels would be identical to the actual experiment described here since only the initial conditions for the kinetic equation are different. In this hypo~etic~ case, energy rransferred from the lower laser levels to 0220 is rapidly equilibrated with 0110 so that on the average the lifetime of a molecule in 0220 is short and the reverse process, tE20 + (lOuO/ 02OO)is unlikely. Thus in the present experiments the rapid filing of the lower laser levels is also contro~ed by the backward rate constant kb in eq. (7). The only experimental feature that poses a question about our analysis is that with a 10.6 pm pump and observation with the three-filter combination, though a fast drop in intensity is observed, a significant amplitude clear fast recovery is not. Since the pumped state IO00 is rapidly coupled to 0200, and 02OOis filIed from 01’0 when it is depleted, we would expect 02OOto also be ftied from 01 10 when a state it is rapidly coupled to (lO”O) is depleted. The reason we do not see this clearly may be the following: when the l@O state is pumped, less ovation is removed from the lower laser Ievels then when 0200 is pumped since there is less ambient population in IO”Othen in 02OO.Additionally, when IO*0 is pumped 0200 may act like the middle level in a three-level system and it would not be depleted to as large an extent even for the same population transfer as when it is directly pumped. Both of these factors will lead to a reduced signal intensity for a 10.6 pm pump versus a 9.6 pm with the 10.6 pm pump signal being 4-i as intense as the 9.6 pm pump signal at the same CO2 pressure. This dissent in intensity is observed. The fast recovery is only a fraction of this already small signal. With only a 6 bit resolution digitizer, we feel that we
Voiume 83, number 1
APICAL
PHYSICS LRTTSRS
may well have reached the point where our digitizer c&nno longer accurately resofw features on a weak signal already heavily buried in noise,
5. cmlclusiona The rate of ~~~~~t~o~ of the Fermi mixed lower laser begs, the 10% and 02% states, is very rapid, >fxIOms -l Torr-le ~o~~~g betpveertthe ~e~d~g mode manifold and the lower laser levels is also rapid and occurs with a rate of 387 f 75 ms’1 Torr-1, which corresponds to the rate constant kb of eq_ (7). These results are in good agreement with the work of Rhodes et aL f 111.and we feel that these numbers will be of aid in modeling energy transfer in the CO2 system and in gain calculations for CO, lasers.
The financial support of the National Science Foundation via grant C!H&7610333 and CHE-7908501 is gratefully appreciated. We would like to thank V.A. Apkarian for a number of very useful discussions,
References f I J T.L. CottreR and IX!.. ~~~ubre~~ MoJccufar enetgy transfer in gases ~B~~e~o~~, London, 19611. f2 J R.L. Taylor and S, Bitterman, Rev. PAod. Phys. 41 fl969f
j3] FWcitz and G.W. FJyrm, Arm* Rev, Phys. Chcm. 25 (1974) 275. (41 L.O. Hodccr, MA. Kovsca, C.K. Rhodes, G.W. Fiynn and A. Javan, Phys. Rev. Letters 17 (1966) 233. [S] CR. Moore, RB. Wood, R-L. Wu and J.T. Yardley, J. Chcm. Fhys. 46 (1967) 4222. [6] WA. Rosscr Jr., A.D. Wood and E.T. Gerry, J. Chcm. Phys. 50 f1969) 4996.
1 October 19El
f7 j J.C. Stephenson, RR. Wood and CR. Moore. J. Chcm. Phys. 54 119713 3097. [S] J.T. Yart%cy and CR. Moore, J, Chcm. Phys. 46 (1967) 4491. [9] K.F. Jfcrgeki, J. #cm. Wys. 47 (1967) 743. [LO] RD. Sharma, J. C&m. Phys. 49 (1968) 5195. (111 UC. R3@cs, MJ. Kelly and A. Java& J, Chcm. Phys. 4S (1968) 5730. [12] R-R. Ja&bs, KJ. Pettipiece and SJ. Thomas, Pbys. Rev. I1A (1975154. [t3] EB. &ask Jr-.AppL Phys. Lcttcrs 23 (1973) 3%. [L4] T-A. DcTempLe, DR. Suhxc end PD. Cohmian, Altpt, P&s. Letters 22 (1973) 349. fls] W.A. Rosmr Jr., E. Haag and ET. Gerry, J.Chcm. Phys. 57 (1972) 4153. [X6] K. Rulthuis, J. C&cm. Phys 58 (X973) 5786. [ 171 MC. Cower and AJ. Carm&l, AppL Phys, Letters 22 (1973) 321. [ 181 T. Aoki and M. Katayama, Yapan. Y,Appl.whys. IO C1971) 1303. f 191 H. Auq and MI.Katayame, Japan. J, AppJ. Phys. 14 (1975) 82. [Ztl] F.R. Grabmer,Ph. D. Thcshr, Columbia ~~~r~y (1973). [Zl] M. H~e~-A~e~ and F. LcPo&rc, Phy&a 78 (1974) [22] ::.M. Simpson and T.R.D. Chandler, Proc. Roy. Sac. A317 (1970) 265. [23] DC. ARcn,T.J, Price and CJ.S.M. S~p~n,Chem. Pbys. Letters 45 (1977) 183. [24] RX. Hu~~e~o~ and E. We& Rulh Am. pfiys. Sot. 21 (1976) 609. [2s] DC. Allen, T. Sctagg and C.J.S.M. Simpson, Chem. Phys. Sl(1980) 279. f26] J. Ffnai and CR. Moore, J. Cbcm. Phys. 63 (1975) 2285, 1271 G.T. Fujimoto and E. Weitz, Chem. Phys. 27 f197R) 65. 128 j R.K. Hudd~~o~~ Ph, D. T&c& ~o~wc~c~ Uniivcrsity (1979); R.K, Hu~~~on and E. W&z, Opt. Commun. 30 ( 1973) 170; ?o bc pub&&d. [29 J RD. Bates Jr., J.T. K~dt~n, G.W. F&M and A.M. Ron& J. Chcm. Phys. 57 (1972) 4174. (JO] VA, Apkarian and E. W&z, J. Chcm. Phys, 71(19”9) 4349. (311 T.. Holstein, Phyr Rev. 72 (1947; 12X2.
I 79
Volttmr: 83, number 1
A LASER-iNDUCED
FLUO~~EN~E
1 October 1981
STUDY OF ENERGY TRANSFER
BETWEEN THE SYMMETRIC STRETCHING
AND BENDING MODES OF CO,
R.K. HUDDLESTON ’ and Eric WEITZ * Department of Chemistry, Northwestern University, Evanston, IIlinois 60201, USA Received 5 May 1981; in final form 16 June 1981
The equilibration of the lower laser levers in COz, loo0 and 02O0, has been studied via a laser-induced fluorescence technique. We conclude that the coupling between these leveis is rapid, >llOO ms-’ To& I and that these levels are also coupted though at a somewhat slower rate of 387 f 75 ms-* Torr-’ to the bending modes of C&.
or stepwise via
1. IntYoduction
energy transfer in gaseous CO, has been extensively studied [l-26]. While CO2 has come lo be regarded as a model compound for energy transfer studies, a number of vibration-vibration energy transfer rates in this system remain in dispute. The refaxation of the 001 state appears to be well established at a rate of 0.33 + 0.005 ms-l Torr-t [4-71 and a number of resonant vibration-vibration energy transVibrational
fer rates have recently been measured 1263. However, the rates for the process coupling 02OOand 1O"O, the
lower levels, CO,{ 1000) f C0,(0000) 2kb c02(0200) + C0,(0000), AE= 103 cm-l ,
(0
,hich due to Fermi mixing are a nearly equal mixture I &heunperturbed 02OOand I O”Ostates and the pro-
zss coupling the fund~ental of the bend to the fower I?‘:r levels and the 0220 state remain in question. Tf‘ %zrprocess may either proceed directljr via Cfizt_iO"O or 02OO)+ C02(OO”O)
* Presentaddress: Chemistry Division, Argonne National Laboratories Aqonne, Illinois 60439, USA. * Alfred. P. Sloan Fe&w.
174
CO~~Ol~O)+ ~02(01~0~ 2 CO2(0220) ~CO2{0~0) (3)
and CO,(O220) + co,@O*o) 2
CO(lOOOor 02OO)+ C02(OO”O).
(4)
Rates for process (1) range from a reported high value of IO3 ms” 1 Torr-l ffl] toaiowvalueof 140ms-t Torr-l [ 13J. In addition, the rate for the coupling of the fundamental of the bending mode to the lower laser levels is not well established. Rhodes et al. [ 1I ] report a value of 4 X 18 ms-1 Torr-1 while vdiues as low as 3.2 ms- t Torr-l 11’71or even l.Oms-t Torr-l [f 51 have been reported for this process. The apparent inconsistency of many of the above experimental results may, in part, be due to the variety of experimental conditions. Etectdcal discharges which were used in laser afterglow studies and gain measurements, may lead to unpredjctable effects of free electrons, ions, and dissociation products and uncertainties in temperature. Laser absorption and gain measurements are sensitive to popula~on d~eren~s between two states which are effected by changes in either state and to perturbations by the radiation tield. Discrepancies may also have resulted from the ambiguous assignment of specific kinetic steps to measured rates.
Volume83, number 1
CHEMICAL PHYSICSLETTERS
The present experiments employ the laser-induced fluorescence technique to directly observe the time evolution of population in CO, vibrationat states followhrg creation of a non~~~m d~t~ution of population via a pulsed infrared laser [24 1. This expcr. imental technique avoids many of the abovementioned diificulties,
1 October1981
averaged, and then plotted on an X-Y recorder and stored in digiti form for computer analysis. The response time of the &Ge detector loaded to 5 kf2 and the associated electronics was carefully measured to be 1.OPS [27].
3. Results 2. Experimental A detailed description of the experimental procedure used in this study has been previously presented [27]. Briefly the experiment consisted of monitoring the ffuorescence emission from the bending and symmetric stretching modes of CO, following excitation of CO, with a Q-switched CO2 laser. The CO, infrared laser consisted of a 2.5 m water-cooled tube with Brewster angle NaCl windows mounted at each end. A longitudinal discharge at approximately 20 kV and 15 mA was maintained throu8h a flowing mixture of CO2, N2, and He. The laser was Q-switched with a 10 m radius of curvature gold mirror rotating at I00 HZ. The output of the laser could be tuned over the 9.6 and 10.6 lun vibrational bands of CO2 by a diffraction grating blazed for 10.0 WII,yielding 2 mJ in 2 MS pulses (full width at base) on a single rotational line. The laser beam was directed through an aluminum cell closed with NaCl windows. Fluorescence in the 15 m region was detected perpendicular to the beam with a liquid He cooled GeCu detector looking through a 5 mm thick KBr window. Interference filters were used to isolate certain wavelength regions. Available were 13.48, 13.97, and 15.475 E.cmlong-pass filters (5% points) with average tr~~itt~~s of 6070% and a 14.00-16.53 lun bandpass falter (50% points), The bandpass falter could be cooled inside the detector dewar to limit room-temperature blackbody radiation and increase the s~n~-t~no~e ratio. Typically, a combination of the cooled bandpass filter and long-passWters was used. For most long-wavelength measurements, both the 13.48 and the 15.475 pm long-passWters were used in conjunction with the cooled fdter. These filters produced an effective bandpass filter with a bandpass of 15.48-16.92 pm (5% pts). The three filters were able to almost completely eliminate laser scatter. The si8nalswere ~pl~ed, d&itized with a model 610B Biomation transient recorder,
Following absorption of the CO2 &switched laser pulse on either the 9.6 or 10.6 elm branch, the fhrorescence intensity of the signal observed through the combination of 14.00-16.53 pm bandpass and 13.97 @n long-pass filters is seen to decrease. Fig. 1 shows a typical signal taken on a long-time base. While the details of the energy transfer processes governing the time evolution of the entire fluorescence signal will not be discussed here, the overall interpretation of this signal is straightforward [28]. As will be discussed, on the time scale of the recovery and subsequent fall of the signalin fig. 1, the lower laser levels in CO,, the Fermi mixed states 1000 and 0200, are rapidly collisionally coupled. These levefs are also rap idly coupled on this timescale to the fundamental of the bending mode. The CO2 laser pulse depletes these levels causing a decrease in intensity of fluorescence emission from this system at the wavelengths corresponding to transitions of the type
I
0.0
0.2
0.4
0.6 Time
0.6
II0
I
12
(msec)
Fig. 1. Averagedfluorescence@ml from CO2 observed through a 14.00- 16.53 gm optical window followi?@sxcitntion of 25 Ton of C02. Tbe prep&c bamline is IndicHedby the zero position on the ordinate,The fastdropinsignathitens& which occursat time t = 0 is not expltdUYvisible.
175
Volume 83, number 1
CHEMICAL PHYSICS LL-!XERS
co~(1ooo)
+ CO~(O1’0)
+ hv,
@a)
co2(0200)
+ CO,(O110)
+ tzv’,
(5b)
CO,(O110)
+ co,(ooOo)
+ Izv”,
(SC)
C07(0220)
+ CO,(O110)
+ hv”‘.
(5d)
These states are gradually refried from neighbormg states and the asymmetnc stretch. The mtensrty of emission from the transitrons m eqs. (5) gradually mcreases, as does the populatron. to somewhat above the pre-laser pulse level. This mrght be expected smce the laser mtroduces addrtional vrbrational energy mto the system whrch at vrbrational equrhbnum results m an elevated vibratronal temperature and therefore more exerted-state molecules and a larger fluorescence srgnal than at the ambient prepulse vibratronal temperature_ The populatron then decays back to the imtral pre-pulse equihbnum value due to V + T/R and heat and mass transport processes [3_9] _ The observed V + T/R rate agrees weU wrth ultrasoruc results for co, [28]. Additronal mformatron IS available d thus signal is observed on a much faster timescale. Usmg the three filters m combinatron, when pumpmg the 10.6 pm transrtron, the imtral drop m fluorescence mtensrty was observed to be very fast. Due to the finite detector response time and laser pulse wrdth the fastest rate that could be accurately measured in these expenments was 900 ms-I. At a pressure of 0.8 Torr of CO, the initral drop m fluorescence intenstty was
clearly rate limited by the comomatron of these factors. Thus a mirumum rate for this fast fall could be estabhshed as being in excess of 1100 ms-1 Torr-I_ When pumping the 10.6 E.cmtransttion, rf the pressure IS decreased to 0.5 Torr, the mitral decrease in fluorescence intensrty appears to sIow up. However, at this pressure the signal-to-noise ratio has degraded sufficrentiy so that an actual measurement of the rate of the decrease in fluorescence intennty versus pressure was not possrble. Followmg the rapid fall, the signal etibits a slow recovery for the reasons drscussed above. A fast recovery is observable on some signals but due to the poor signal-to-noise ratro of the unaveraged srgnal the rate cannot be measured even after extensive averaging. When pumping the 9.6 pm transition, rmmediately 176
1 October
198 1
a
Frg 2 Averaged fluorescence signal from CO2 observed through a 15.48-16 92 pm ophcal wmdow following 9.6 pm pumping of 0.75 Torr of COz. The prepuke basehne is indrcated by the zero posrtion on the ordmate. (a), (b) and (c) indmate the important features in the sgnaL The peak mdicared by (a) rs due to laser scatter and thus mdicates the position of the laser pulse relative to the start of the pretriggered trace which occurs at t=O. @) mdicates the response of the observed state to remoral of populatron via laser pumpmg, (c) mdrcates the refii of the observed state from other states m the system. Process (c) has a rate, as discussed m the telt, of 387 ms-r Torr-‘. Followmg process (c) 1sa much slower flow of populatron mto the observed state. Thrs ts shown, on a much longer tunescale, m fg. 1.
after the uutial ialI of the signal a raped increase in
fluorescence mtensity IS seen. Thrs is shown in fig. 2. After thrs process is complete, the level of fluorescence mtensity is still below the baseline, and the rest of the recovery process appears on this timescale as a very slow rise. Thrs is the slow rise that is shown on an even longer tune scale in fig. l_ The fact that the pressure range over which the signals corresponding to the aforementioned fast recovery can be observed is small, being limited on the high srde by the response time of the apparatus and on the low side by the pressure at which reasonable signal-to-noise ratros can be obtained, leads to somewhat larger than desrrable error brackets on the measured pressure dependent rate of this process. However, as shown in fig. 3, the rate has been measured over the pressure range from 0.4 to 1.5 Torr and IS reported
as 387 f 75 ms-1
Torr-1.
With a 9.6 Drn pump and observation of the signal through the three-filter combination, on addition of up to 9.00 Torr of argon, the fast recovery rate of
Volume 83. number 1
CHEhIICAL
700
. ?-:,A WO-
.
500-
2
l
5
.
D
cs30
.
Slope
rcec
.
: 387
: 7i
’ 1c.r. ’
.
200
loo
OO
05
IO
15
3. Rate of rise of the fast recorery signalin CO2 versus pressure.The data were obtamed from fluorescence signals observedthror@r a 15.48-16.92 pm optical windowfollowing9.6 pm pumpmg of COa. Fg.
the signal shown m fig. 2 did not change for a constant CO, pressure. The imphcations of this will be discussed m the next section. 4. Discussion The fact that more than one CO2 vibrational state contributes to the fluorescence signal complicates the mterpretation of the results of this study. The wide band-pass filter used in these expernnents passes the emission from 02O0,0220,and 01 1 0 and a small part of the lOoO-01 l0 band (~3% of the total 1s loo0 + 01 IO emission). This and other estimates are based on room-temperature bandpasses whrch change slightly on cooling of filters *_ Even with the three-filter combination there is some emission from transitions SC and 5d, but the majority of the fluorescence comes from Sb (02OO). With this filter combination a very fast initial fall of the signal is observed pumping either the 10.6 or 9.6 pm CO2 laser transition. ‘lks drop in amplitude has a rate of > 1100 ms-1 Torr-l .The most significant observation is that pumping the IO00 state casues a
* Optical Coating Laboratory, Inc, Santa Rosa, California Stock Film Catalog.
PHYSICS LETTERS
1 October 198 L
response m the 02OO state with the rate cited above. This defimtely shows that these states are coupled on this times&e. With the three-filter combination and a 9.6 can pump, a significant amplitude fast recovery of population is observed. The rate of this recovery is inertgas pressure independent. Thus, the population must be coming from a state with significant ambient population and vra a pathway for which the rate hmiting step would be expected to be inert-gas pressure independent [30].Thiswould fingerprint this process as being the transfer of population from the 0110 state to 02OO erther drrectly or through an intermediate state such as 02’0 or even 10°O. The population of the bending mode fundamental is expected to decrease as it comes into equilibrium with the depleted lower laser levels. The rate of this population decrease would be the same as the rate of the increase in the lower laser IeveIs if ret%ng the lower laser levels involves a single rate limiting step within the bending mode manifold. Thus, if ail states were observed sunultaneously and with the same emission intensity, the signal corresponding to the fall of population in 01 l0 would cancel the population rise in the upper states, and under these hypothetical circumstances no fast depletion or fast recovery signal would be observed. In the actual case, observed emisraon intensities are tiected by the filter bandpass, the ernissron band strengths, and by the degree of self-trapping of a given state. Self-trapping can be significant m these circumstances. When radiation is emitted and absorbed over the same Doppler line shape, the degree of self-trapping can be evaluated from the integral given by Holstein 1311 which for this case can be expressed as the infiite series. T(kol) =
m$o (-ko’y”lm!(m
f
1)1’2,
where 1 is the pathlength, and kg istheabsorption coefficient at line center. Ihe r2sult of a cakulation using eq. (6) and the individual rotational linestrengths is that for the 01’0 + OO”Oemission band in CO, at a pressure of 1 Torr and a path length of 1.5 cm (our cell radius), 89% of the fluorescence emission will be self-trapped! Hot bands terminating in the 01 IO state will be absorbed only about one-fourth as much with 02*0 + 0110 emission expected to be absorbed more strongly than 02OO + 0 1 l0 emission since the former 177
Volume 83. number 1
CHEMICALPHSYICSLEITERS
transition ahnost exactly overlaps the fundamental 0110 + 0000 transition. The assumption of an average path length will lead to an overestimate of the amount of fluorescence reabsorbed but will not change the conclusion that reabsorption can be s~~c~t. As would be predicted from the above discussion, the relative contribution of the fast recovery to the total signal amplitude decreases when the signal corresponding to a 9.6 pm pump is viewed with the wide bandpass falter versus the three-falter combination. This is due to the observation of relatively more 0 1i 0 + 0000 emission in the former case which will cancel some of the amplitude of the recovery signal from the upper states (principally, 02OOand 10°O, though 0220 may also be involved if it is an intermediate state in the transfer of energy from 01 l0 to the lower laser levels). This cancellation of amplitude is mitigated by the more efficient self-trapping of the 01 IO + 0000 transition versus transitions terminating in 01 10 and, of course, by our selection of falters which transmit mostly emission from 02OO. It is now of interest to relate the observed rates to elemental rate constants for ~dividu~ steps. In the case of V-V equilibration of the two lower laser leveIs, the observed rate will be the sum of the forward and reverse rates of process (I), under the assumption that these levels can be considered isolated from other states in the system on the timescale of equilibration between them. Thus, a lower limit of 700 ms-l Torr-1 can be placed on the forward rate (exothermic direction) of process (1). The remaining question is assignment of the recovery rate of 387 ms- ’ Torr-l to a specific process. If coupling between 1000 and 02OOis rapid and if these states are also rapidly coupled to 0220, for purposes of assignment of a rate process to the 387 ms-1 ‘I’orr-t rate, the system can be considered as a threerevel system with the levels being the ground state, 01’0 and the combined 02O0, @O and 1000 states. I- this case, the measured rate of 387 ms-1 Torr-1 :ire lower laser level * bend equ~ibration process L I responds to a good approximate to the backward rate of ~.12(0110j + COz(oi~oj 2
~0~(02~0/02~0/~0~0)+ ~O~(OO~Oj.
(7)
Though our data are consistent with this mechanism,
178
1 October 1981
0220 does not have to be rapidly coupled to 02OO and 1000 if 02OOand/or 10”O are directly filled from 01 10 by a near resonant process. In this case, the rate of 387 ms- 1 Torr-lwill stlll be assigned to the back rate of process (7) with the fast species on the right being indicated as C~~(~~O/I~O). The assignment of the observed rates of 387 ms-1 Torr-i to kb @Ieq. (7) can be most easily understood by considering a hypothetical situation in which the lower laser levels had initial excess population. As is generally true, a change in the initially perturbed state wifi not change the rates in a kinetic system, only the ampiitude of the rates. Thus the observed rates for the hypothetical situation corresponding to excess population in the lower laser levels would be identical to the actual experiment described here since only the initial conditions for the kinetic equation are different. In this hypo~etic~ case, energy rransferred from the lower laser levels to 0220 is rapidly equilibrated with 0110 so that on the average the lifetime of a molecule in 0220 is short and the reverse process, tE20 + (lOuO/ 02OO)is unlikely. Thus in the present experiments the rapid filing of the lower laser levels is also contro~ed by the backward rate constant kb in eq. (7). The only experimental feature that poses a question about our analysis is that with a 10.6 pm pump and observation with the three-filter combination, though a fast drop in intensity is observed, a significant amplitude clear fast recovery is not. Since the pumped state IO00 is rapidly coupled to 0200, and 02OOis filIed from 01’0 when it is depleted, we would expect 02OOto also be ftied from 01 10 when a state it is rapidly coupled to (lO”O) is depleted. The reason we do not see this clearly may be the following: when the l@O state is pumped, less ovation is removed from the lower laser Ievels then when 0200 is pumped since there is less ambient population in IO”Othen in 02OO.Additionally, when IO*0 is pumped 0200 may act like the middle level in a three-level system and it would not be depleted to as large an extent even for the same population transfer as when it is directly pumped. Both of these factors will lead to a reduced signal intensity for a 10.6 pm pump versus a 9.6 pm with the 10.6 pm pump signal being 4-i as intense as the 9.6 pm pump signal at the same CO2 pressure. This dissent in intensity is observed. The fast recovery is only a fraction of this already small signal. With only a 6 bit resolution digitizer, we feel that we
Voiume 83, number 1
APICAL
PHYSICS LRTTSRS
may well have reached the point where our digitizer c&nno longer accurately resofw features on a weak signal already heavily buried in noise,
5. cmlclusiona The rate of ~~~~~t~o~ of the Fermi mixed lower laser begs, the 10% and 02% states, is very rapid, >fxIOms -l Torr-le ~o~~~g betpveertthe ~e~d~g mode manifold and the lower laser levels is also rapid and occurs with a rate of 387 f 75 ms’1 Torr-1, which corresponds to the rate constant kb of eq_ (7). These results are in good agreement with the work of Rhodes et aL f 111.and we feel that these numbers will be of aid in modeling energy transfer in the CO2 system and in gain calculations for CO, lasers.
The financial support of the National Science Foundation via grant C!H&7610333 and CHE-7908501 is gratefully appreciated. We would like to thank V.A. Apkarian for a number of very useful discussions,
References f I J T.L. CottreR and IX!.. ~~~ubre~~ MoJccufar enetgy transfer in gases ~B~~e~o~~, London, 19611. f2 J R.L. Taylor and S, Bitterman, Rev. PAod. Phys. 41 fl969f
j3] FWcitz and G.W. FJyrm, Arm* Rev, Phys. Chcm. 25 (1974) 275. (41 L.O. Hodccr, MA. Kovsca, C.K. Rhodes, G.W. Fiynn and A. Javan, Phys. Rev. Letters 17 (1966) 233. [S] CR. Moore, RB. Wood, R-L. Wu and J.T. Yardley, J. Chcm. Fhys. 46 (1967) 4222. [6] WA. Rosscr Jr., A.D. Wood and E.T. Gerry, J. Chcm. Phys. 50 f1969) 4996.
1 October 19El
f7 j J.C. Stephenson, RR. Wood and CR. Moore. J. Chcm. Phys. 54 119713 3097. [S] J.T. Yart%cy and CR. Moore, J, Chcm. Phys. 46 (1967) 4491. [9] K.F. Jfcrgeki, J. #cm. Wys. 47 (1967) 743. [LO] RD. Sharma, J. C&m. Phys. 49 (1968) 5195. (111 UC. R3@cs, MJ. Kelly and A. Java& J, Chcm. Phys. 4S (1968) 5730. [12] R-R. Ja&bs, KJ. Pettipiece and SJ. Thomas, Pbys. Rev. I1A (1975154. [t3] EB. &ask Jr-.AppL Phys. Lcttcrs 23 (1973) 3%. [L4] T-A. DcTempLe, DR. Suhxc end PD. Cohmian, Altpt, P&s. Letters 22 (1973) 349. fls] W.A. Rosmr Jr., E. Haag and ET. Gerry, J.Chcm. Phys. 57 (1972) 4153. [X6] K. Rulthuis, J. C&cm. Phys 58 (X973) 5786. [ 171 MC. Cower and AJ. Carm&l, AppL Phys, Letters 22 (1973) 321. [ 181 T. Aoki and M. Katayama, Yapan. Y,Appl.whys. IO C1971) 1303. f 191 H. Auq and MI.Katayame, Japan. J, AppJ. Phys. 14 (1975) 82. [Ztl] F.R. Grabmer,Ph. D. Thcshr, Columbia ~~~r~y (1973). [Zl] M. H~e~-A~e~ and F. LcPo&rc, Phy&a 78 (1974) [22] ::.M. Simpson and T.R.D. Chandler, Proc. Roy. Sac. A317 (1970) 265. [23] DC. ARcn,T.J, Price and CJ.S.M. S~p~n,Chem. Pbys. Letters 45 (1977) 183. [24] RX. Hu~~e~o~ and E. We& Rulh Am. pfiys. Sot. 21 (1976) 609. [2s] DC. Allen, T. Sctagg and C.J.S.M. Simpson, Chem. Phys. Sl(1980) 279. f26] J. Ffnai and CR. Moore, J. Cbcm. Phys. 63 (1975) 2285, 1271 G.T. Fujimoto and E. Weitz, Chem. Phys. 27 f197R) 65. 128 j R.K. Hudd~~o~~ Ph, D. T&c& ~o~wc~c~ Uniivcrsity (1979); R.K, Hu~~~on and E. W&z, Opt. Commun. 30 ( 1973) 170; ?o bc pub&&d. [29 J RD. Bates Jr., J.T. K~dt~n, G.W. F&M and A.M. Ron& J. Chcm. Phys. 57 (1972) 4174. (JO] VA, Apkarian and E. W&z, J. Chcm. Phys, 71(19”9) 4349. (311 T.. Holstein, Phyr Rev. 72 (1947; 12X2.
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