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V—V, V—R,T transfer in triatomic molecules. Results for ONF
Chemical Physics 60 (1981) 215-221 North-Holland Publishing Company
V-V AND RESULTS
V-R,T TRANSFER FCDR ONF
R. KADIBELBAN, Institut flir Physikaiische
IN TRIATQMIC
W. JANIESCH Chemie der UnivenitEt,
MQLECULES.
and P. HESS 69 Heidelberg I, FRG
Received 25 February 1981
The laser-induced fluorescence technique is applied to study vibrational energy transfer in pure ONF. Different vibrational modes are excited using a TEA CO2 laser and the rise and fall of Y1, Ye, and (IQ f vs) Ruorescence is detected. These measurements yield a detaiIed picture of V-V exchange in the re$on of the fundamentals and-V-R,T transfer to rotational and translational degrees of freedom. The relaxation behavior of ONF is mmpared with that of ONCI and other triatomic molecules.
1. Introduction Triatomic molecules are the simplest molecular systems where intramolecular energy transfer between different vibrational modes can be studied. In the region of the fundamentals the density of states is low and, therefore, it is possible to investigate experimentally the coupling between specific modes in favourable cases. For these reasons triatomic molecules are of special interest for both theoreticians and experimentalists; for the former to develop and test energy transfer models, for the latter to obtain state to state relaxation data. The simplest model for a polyatomic molecuie used by theoreticians is a system of three collinear atoms coupled by interaction potentials. This model is still not realistic because the bending motion is neglected, however, it allows, for example, model calculations of intramolecular energy transfer. It may also be used to study the normal mode and local mode description of vibrational motion in polyatomic molecules and this seems to be necessary for a better understanding of dynamic processes. A comparison of the experimental results obtained for CO* and Hz0 shows that the dynamic behavior concerning energy transfer may change completely going from one 0301-0104/81/0000-0000/S02.50
@ North-Holland
triatomic molecule to another. COz is a relatively harmonic molecule where a normal mode analysis seems to be reasonable. V-R,T transfer and the deactivation of the asymmetric stretch v3 in CO2 belong to the most inefficient exchange processes of vibwtional energy known at this time for polyatomic molecules [l, 21. On the other hand, Hz0 is a relatively anharmonic molecule and it has been argued that for this molecule the local-mode picture is simpler and converges faster than the normal-mode picture [3]. V-R,T transfer and V-V exchange are extremely efficient despite the large energy discrepancies involved [4]. One of the significant differences behveen CO2 and Hz0 is the quite different mass of the H and 0 atoms in HzO. Another interesting triatomic system is a molecule with atoms of similar mass as COz, but a large difference in the binding forces between the atoms. ONF may be considered as a prototype of this kind of molecule. The analysis of the vibrational spectra of four isotopic species of ONF performed in ref. [S] yields the following picture; z+ is an almost pure NO stretching vibration whereas vz and v3 are considerably mixed between NF stretching and ONF bending. In contrast to the normal situation, the lowest mode v3 in ONF is best described as N-F stretching and the second
R. Kadibelban et al. / V-V end V-R.-T transfer in rriatomic moiecuks
216
t
30301
I
ONF ---+3
2
f 9
ZOOD
-9
‘2 4 “5
----35 ----Lv3
detect fluorescence signals with a wavelength smaller than 5.5 urn, a SBRC photovoltaic InSb detector (cooled to 77 K) with a response time of 1.2 ps was employed. To observe fluorescence in the region of longer wavelengths a SBRC CuGe detector [cooled to 4.2 K) with a response time of 0.4 us was used.
Typically, several hundred laser shots were averaged. The signal processing system consists of a Biomation 8100 transient recorder and a Tracer 1710 digital signal analyser. All measurements reported were performed at 295 K. The pressure in the fluorescence cell
Fig. 1. Vibrational levels of ONF with possible laser excitation (+) and some fluorescence (-+) transitions indicated.
lowest mode ~2 is mostly ONF bending [S]. For the most abundant species r601’NF the corresponding wave numbers are: trl = 1843.5 cm-‘, u2 = 765.8 cm-‘, and ZJ:= 519.5 cm-’ (see fig. 1). In contrast to ONCI, which has already been studied with the laser-excited fluorescence method [6], ONF possesses relatively large !evel spacings in the region of the fundamentals. Therefore, an interesting question is whether inefiicient V-V transfer occurs in this molecule_ To get as much information as possible on selfre!axation of ONF, different vibrational levels were excited with the IR laser and the rise and decay of the fluorescence were detected from severa! infrared active levels. All modes are infrared active in ONF and, therefore, it should be possible to obtain a complete map of energy transfer rates for this molecule.
2. Experimental The laser-induced fluorescence experiments were performed using a Lumonics 102 TEA CO2 laser as excitation source. The repetition rate employed was 1 Hz. A typical pulse had a width of about 0.2 ps followed by a tail of 1.5 &isand an energy of about 100 mJ/pulse. To
was measured with a l\fKS Baratron capacitance manometer. The ONF was provided by Ozark-Mahoning company. According to the manufacturer the gas had a purity of 97-98%. The sample used for measurements was carefully purified before an experiment employing the following procedure: first the sample was cooled with liquid nitrogen to remove noncondensable impurities such as F2 and NZ; then the temperature of the sample was slowly raised by taking away the nitrogen trap. By pumping, impurities with a higher vapor pressure than ONF, such as NO, were removed.
3. Results 3.1. vz jhorescence The ~a mode of ONF at 765.8 cm-’ is a strong infrared-active fundamental. Three interference filters were employed to observe the uz fluorescence free from scattered laser radiation. A narrow band pass filter with 75% maximum transmission, half-transmission points at 7.50 and 820 cm-‘, and less than 1% transmission outside 730-850 cm-’ was used. In addition, two long pass filters with 90% and 85% transmission and half-transmission at 905 cm-’ and 865 cm-*, respectively, were employed to block the laser wavelength. Excitation of ONF at 9.603 Pm (P 24) yields a fast rise time for the z+ fluorescence of 2.5+ 1 psTorr. The reciprocai lifetimes as a function
R. Kadibelban et al. / V-Vand
V-R,Ttransfer
in triatomic molecules
217
Fig. 3. ReciprocaI lifetime versus pressure for the fast fall of ~2 fluorescence and excitation at 9.603 pm. 1
2
3 plTorr1
Fig. 2. Reciprocal lifetime versus pressure for the rise of v1 Ruorescence and excitation at 9.603 pm_
of pressure are shown in fig. 2. The decay of the fluorescence signal is not a single exponentiai and it is possible to identify a relatively fast fall of 20 f 6 ps Torr and a much slower fall of 280 f 60 ys Torr. The corresponding values obtained from this analysis of the fluorescence decay at different pressures are presented in figs. 3 and 4 for illustration. Signai-to-noise was about 20: 1 for excitation at this wavelength. Weak v-, fluorescence could also be detected for excitation at 9.552 pm (P 20) and 9.305 pm (R 11). In these cases, however, the signal to noise was beIow 3: 1 after 500 laser shots and therefore, no accurate measurements were possible. 3.2.
lowest presstire investigated. This instantaneous rise is followed by a fast fall of about 6~~2 ps Torr and a much slower fall which could not be analysed accurately but may be in the region of 300 psTorr. The pattern of the vl fluorescence changes for excitation at 9.603 Km. A measurable rise time of 7 f 3 ps Torr is observed for the P 26 line. The decay again may consist of a relatively fast fall of about 17&8 ps Torr and a much slower part. The traces for this excitation wavelength show an additional decay to the base line in the ms time scale which is due to heating. This effect was studied in several experiments and the results will be discussed in more detail later. The signal to noise achieved for this laser line was only about 5 : 1.
I
VI fluorescence
The ZQmode at 1843.5 cm-’ is also a strong infrared-active fundamental. The interference filter employed to observe the fluorescence originating from the VI band had 85% maximum transmission, half-transmission at 1750 and 1950 cm-*, and less than 1% transmission outside 1700-2000 cm-‘. The strongest vl fluorescence was observed for excitation at 9.305 pm with S/N better than 20 : 1. The fast rise of the ffuorescence signals was determined by the response time of the detector (InSb: 1.2 ps) even at 0.3 Torr, the
1”
du
piToirl
Fig. 4. Reciprocal lifetime versus pressure Ear the slow fall of v1 Ruorescen~e and excitation at 9.603 m.
R. Kadibelbon
218
rmnsfer in m.afomic molecules
ef al. / V-V and V-R.T
3.3. (vl t vjJ fluorescence Strong laser-induced fluorescence could also be observed from the combination band (vI+yj) at 2365 cm-‘. The interference filter employed had 85% maximum transmission with halftransmission points at 2020 and 2490 cm-’ and less than 1% transmission outside 1940-2560 cm-‘. The best fluorescence signals were detected for excitatiqn at 9.552 pm_ With this line it was possible to perform measurements at pressures up to iO0 Torr. In the high pressure region S/N was better than 20 : 1. At 1.3 Torr, the lowest pressure studied, the rise of the (vr + 1~) fiuorescence was determined by the response time of the detector. The decay can be well characterized by a single relaxation time of 280; 6G psTorr as shown in fig. 5. No heating effect was observed. Similar fluorescence curves, however, with smaller S/N were obtained for excitation at 9.305 pm. The signal to noise decreased even more for excitation at 9.603 wrn and therefore, only a few traces were analysed for the latter laser line. A summary of fluorescence data obtained in this work is given in tabie 1. The collision numbers are estimated with a hard sphere diameter of 3.5 A. As mentioned above, the relatively high intensity of the laser radiation caused heating eEects which could be seen in the traces of or and Ye fluorescence. To study the temperature equilibration between the irradiated gas volume Table 1 Summary of fluorescence Excitation wavelength
*’ Hard sphere diaxxter Z,=
2Nc~~(2zRT/p)“‘;
1
10
20
30
Fig. 5. Rise and decay of (vI t ~3) fiuorescence at 9.552 grn and a pressure of 50Torr.
!!I
. tri.CA
for excitation
and the cell walls in more detail, the Buorescence curves were detected by operating the Biomation 8100 with dual time base. For illustration, fig. 6 shows results obtained from the analysis of vr fiuorescence induced by excitation with the P 26 laser line at 9.603 m. The accuracy of these measurements is not very high because only a few channels were used to analyse this very slow decay. Fig. 6 shows clearly, however, that the corresponding time for heat transfer possesses a value in the ms region and increases proportional to the pressure within experimental error.
4. Discussion The results discussed in section 3 show clearly that the different CO2 laser lines excite different
data for ONF
z =’
Fast decay
coil.
pr b-s To4
16 45 Cl3 C3 Cl3
2056 17ss 6*2 -
(w-n) 9.603 9.603 9.552 9.305 9.305
I
z =I coI1.
Slow decay
130 110
280~60 (-300) 28Oi60 (=300) 280-60
;S -
pr (v-s To4
of ONF was taken as c-3.5 A (estimated!). The gas kinetic collision and the number of collisions Z from: Z = 72,
2 =! call.
1800 1800 1800 rate
has been calculatedfrom:
R. Kadibelban et al. / V-V and V-R,T transfer in t-homic
4
I
:
c M-
75
/ I /
-
/‘;
I
Fig. 6. Decay time of the heating
cence cures
effect in the zq fluoresfor excitationat 9.603 pm.
vibrational modes in ONF. Considering the rise times and the signal to noise observed for the laser-induced fluorescence of the ONF bands investigated, we may assign the excitation wavelengths to specific transitions in ONF. However, we cannot exclude that more than one level is excited with a laser line. The finding of a rise of 2.5 l.~sTorr and 7 us Torr of y2 and vr fluorescence for excitation at 9.603 p.m suggests that the overtone 2vs is excited with this laser line. In this case the short relaxation time wottld describe the equilibration between v2 and v3 and the relaxation time of 7 ps Torr would be due to V-V transfer to the vr mode. With this assignment it is hard to understand the fast decay of 20 l~s Torr observed in the v2 iluorescence curves. Another explanation is that preferably the v2 mode is excited with the P 26 line perhaps through ~3 + 2~2. If only this transition is important, the rise of 2.5 psTorr would be due to the transition 2v2 + v2. The relaxation time of 7 psTorr would describe the equilibration of va with v: and the fast decay of 20 I.LSTorr could be explained by energy transfer to the v3 mode. This would be a surprising result because a pathway with a small energy gap exists for the slower process of equilibration between u2 and v; (2~2 -, 34, whereas only channels with large energy gaps are available
molecules
219
for the faster transfer process to the vr mode. The pulse energy employed is relatively high and therefore, non-linear relaxation processes cannot be excluded. It may be possible that both levels 2~s and 2~ are excited. Unfortunately, we did not succeed to observe v3 fluorescence. These results are necessary for a final interpretation of the ~2 fluorescence data. The laser line at 9.305 pm produces the strongest v1 fluorescence. The rise is faster than 0.5 us Torr and could not be resolved in the present experiments. This immediate rise and the high S/N suggest that the transition v2 + v1 may be excited with this laser wavelength. In agreement with this assumption of a direct excitation of the v1 mode is the fact that the corresponding fluorescence traces show a fast fall of 6 t.~sTorr, which should be attributed to V-V exchange with the v2 and u3 mode, and a much slower fall, which may be due to V-R,T transfer. We wish to point out, however, that other possibilities exist for an excitation of ONF at 9.303 urn. For example, the transition (v2+v3) + (v1+v3) between two combination bands, which is centered at 9.24 pm, is a possible candidate_ The relatively strong (vr + v3) fluorescence observed for the R 11 line would support such an assignment. Within experimental error, excitation at 9.552 urn leads to an identical pattern of v1 and (vr + v3) fluorescence as excitation at 9.305 ym. The main difference is a stronger u1 fluorescence for excitation at 9.305 pm, whereas the P 20 line produces stronger (vI + vj) signals. A simple expianation of this finding would be that the R 11 line preferably excites the v2 --, vr transition and the P 20 line (~2 + v3) + (vr + v3)_ The unmeasurable fast rise times of vl and (v: + v3) fiuorescence for both excitation wavelengths imply extremely fast V-V exchange between vI and (+ + v3) or excitation of both levels. The most interesting feature of the (vt i- ~3) fluorescence curves is the slow single exponential decay time of 2801k 60 TVTorr. This relaxation time is practically identical to the slow decay part of the ~1 and IQ fluorescence and may be identified as due to the V-R,T process. At this point the question arises why the fluorescence
220
R. Kadibelban et al. / V-Vnnd
traces of the vi and ZJ~band first show a fast decay pointing at an equilibration between al1 vibrational levels in the time scale of 6-20 us Torr, whereas the fast rise and the decay of the (ZQ+ UJ fluorescence with the V-R,T rate imply an equilibration of the vibrational modes faster than 2 us Torr. It is interesting to compare the results obtained for ONF with the data reported in ref. [6] for ONCl. Following excitation of the (~a+ ran)level in ONCI the rise time of the vI level was found to be 0.72 ps Torr. This corresponds to about 4 gas kinetic collisions compared to about 45 collisions needed for activation of vl following excitation at 9.603 Frn in ONF. We may conclude from this example that V-V transfer in ONCI is much faster than in ONF as expected from the higher density of states. The same is true for V-R,T transfer. In ONCl the vibrational energy degrades from the lowest level yg at 332 cm-i in about 32 collisions [6]. In comparison with this result, 1800 collisions were determined for V-R,T transfer in ONF with the lowest level at v3 = 519.9 cm-‘. For both molecules V-R,T transfer is somewhat more effective than expected from the LambertSalrer plot [7). These deviations may be due to the polarity of 0-F (ILL=1.81 D) and ONCI (p. = 1.83 D), because other polar molecules show a similar e!Iect. For intermode vibration to vibration transfer, larger deviations from simple correlations and energy transfer rules are observed than for V-R,T exchange of ONF. A more or less complete analysis of V-V and V-R,T transfer processes is available for the triatomic molecules COa, N20, COS. and SOz. Even for these triatomic molecules a comparison is not straightforward because ONF possesses a different level structure_ Nevertheless it is useful to compare collision numbers of similar processes to gain insight into the efficiency of dynamic processes in ONF. 3ne of the goals of the present experiments w.as to determine the collisional iifetime of the VI level which is isolated by relatively large energy gaps from the other levels. From simple
V-R,T
transferin niatomic molecules V-V transfer rules we expect that the two processes: ONF(ZQ)+ONF+ ONF(V~)+ONF
0NF(2vr)+ONF+321 --, ONF(3&
+ONF+
cm 2290
--:
,
cm -1
are the main deactivation channels. For the endothermic process ZQ+ 4va the energy gap is somewhat smaller; however, the quantum exchange is larger. For the endothermic channel u1 + 3~2, both energy deficit and quantum exchange are unfavourable. The channel ZQ-+ 2~2 in ONF should be compared with the symmetric stretch-to-bend relaxation in SOZ, OCS, N20, and C02. In SO*, 3300 collisions are needed for this equilibration process which possesses an energy gap of only 120 cm-‘. In the other three molecules this exchange process becomes more and more effective for comparable energy deficits going from OCS to CO1 due to Fermi rescmance couphng (see tabIe 4 in ref_ [8]). For ONF, V-V exchange is not enhanced by Fermi mixing with other modes. Therefore, energy transfer between v1 and 2~2 should be considerably less efiective in ONF than in SO1 because a much. larger energy gap is involved. The same is true for the other deactivation channel vi + 3~3. This again is a channel with a large energy difference and a formal quantum exchange of even four. This is a process similar to u3 deactivation in CO2 and N20, where also only channels with large energy gaps and unEavourable quantum exchange are available (see table 5 in ref. [S])_ In COa and NzO these facts cause a very ineffective V-V exchange with the ZQmode, whereas in ONF, only about 38 collisions are needed for the deactivation of the z+ mode. The fact that the collisional lifetime of this Ievel is orders of magnitudes too small can also be seen from a correlation of slow V-V processes presented for several polyatomic molecules in ref. [9]. The reason why the v1 deactivation in ONF is several orders of magnitude faster than e,_pected is not known. We can only speculate about possible explanations. As mentioned in the
R. Kadibelban et al. / V-V and V-R.T transfer in friatomic molecules
introduction, or is an almcst pure NO stretching vibration. The frequency of ZQis nearly the same as in the diatomic NO molecule [lo]. Such highly localized vibrational states have also been studied recently in polyatomic molecules containing X-H bonds. The frequencies for the excitation of high overtones in benzene for example, can be described with a one-dimensional anharmonic C-H local mode oscillator model. These highly excited IocaI mode states decay in ultrafast intramolcular relaxation and dephasing processes [ll]. Similar to these findings, the ONF result indicates a short collisional life time for localized vibrational motion in the region of the fundamentals.
5. Conclusions In this paper, data on energy transfer in ONF are reported for the first time. ONF belongs to the group of molecules where equilibration of the vibrational modes occurs considerably faster than V-R,T transfer. Less than 130 gas kinetic collisions are needed to equilibrate the vibrational modes by V-V transfer. The most surprising result is the short collisional lifetime of the ~1 level, which corresponds to about 38 gas kinetic collisions. This is orders of magnitudes shorter than expected from the collisional life times of comparable levels in SOz, COZ, and N20_ The slowest process investigated is the exchange of vibrational energy with the rota-
tional result to the polar
221
and translational degrees of freedom. The of 1800 gas kinetic coilisions corresponds value expected from V-R,T data of other molecules.
Acknowledgement We are grateful to the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Endustrie for research support.
References [1] J.D. Lambert, Vibrational and rotational relaxation in gases (Clarendon Press, Oxford, 1977). [2] R.T. Bailey and F.R. Cruickshank, in: Gas kinetics and energy transfer, Vol. 3. Chem. Sot. Specialist Periodiocal Reports (Chem. Sot., London, 1978). [3] H.S. Mailer and 0-S. Mortmsen, Chem. Phys. Letters 66 (1979) 539. Cd] 3. Fin& F.E. Ho&, V.N. Panfilov, P. Hess and C.B. Moore, J. Chem. Phys. 67 (1977) 4053. [5] L-H. Jones, L.B. Asprey. and R.R. Ryan, J. Chem. Phys. 47 (1967) 3371. [6] A. Hartford Jr., Chem. Phys. Letters 50 (1977) 85. [7] J.D. Lamben, J. Chem. Sot. Faraday Trans. II 68 (1972) 364. [8] M.L. Mandich and G.W. Flynn, J. Chem. Phys. 73 (1980) 1265. [9] W. Janiesch, M. Mashni, R. Kadibelban and P. Hess, J. Mol. Struct. 61 (1980) 43. [IO] LJ. Lawlor, K. Vasudevan and F. Grein, J. Am. Chem. Sot. iO0 (1978) 8062. [ll] R.G. Bray and MJ. Berry, I. Chem. Phys. 7: (1979) 4909.
V-V AND RESULTS
V-R,T TRANSFER FCDR ONF
R. KADIBELBAN, Institut flir Physikaiische
IN TRIATQMIC
W. JANIESCH Chemie der UnivenitEt,
MQLECULES.
and P. HESS 69 Heidelberg I, FRG
Received 25 February 1981
The laser-induced fluorescence technique is applied to study vibrational energy transfer in pure ONF. Different vibrational modes are excited using a TEA CO2 laser and the rise and fall of Y1, Ye, and (IQ f vs) Ruorescence is detected. These measurements yield a detaiIed picture of V-V exchange in the re$on of the fundamentals and-V-R,T transfer to rotational and translational degrees of freedom. The relaxation behavior of ONF is mmpared with that of ONCI and other triatomic molecules.
1. Introduction Triatomic molecules are the simplest molecular systems where intramolecular energy transfer between different vibrational modes can be studied. In the region of the fundamentals the density of states is low and, therefore, it is possible to investigate experimentally the coupling between specific modes in favourable cases. For these reasons triatomic molecules are of special interest for both theoreticians and experimentalists; for the former to develop and test energy transfer models, for the latter to obtain state to state relaxation data. The simplest model for a polyatomic molecuie used by theoreticians is a system of three collinear atoms coupled by interaction potentials. This model is still not realistic because the bending motion is neglected, however, it allows, for example, model calculations of intramolecular energy transfer. It may also be used to study the normal mode and local mode description of vibrational motion in polyatomic molecules and this seems to be necessary for a better understanding of dynamic processes. A comparison of the experimental results obtained for CO* and Hz0 shows that the dynamic behavior concerning energy transfer may change completely going from one 0301-0104/81/0000-0000/S02.50
@ North-Holland
triatomic molecule to another. COz is a relatively harmonic molecule where a normal mode analysis seems to be reasonable. V-R,T transfer and the deactivation of the asymmetric stretch v3 in CO2 belong to the most inefficient exchange processes of vibwtional energy known at this time for polyatomic molecules [l, 21. On the other hand, Hz0 is a relatively anharmonic molecule and it has been argued that for this molecule the local-mode picture is simpler and converges faster than the normal-mode picture [3]. V-R,T transfer and V-V exchange are extremely efficient despite the large energy discrepancies involved [4]. One of the significant differences behveen CO2 and Hz0 is the quite different mass of the H and 0 atoms in HzO. Another interesting triatomic system is a molecule with atoms of similar mass as COz, but a large difference in the binding forces between the atoms. ONF may be considered as a prototype of this kind of molecule. The analysis of the vibrational spectra of four isotopic species of ONF performed in ref. [S] yields the following picture; z+ is an almost pure NO stretching vibration whereas vz and v3 are considerably mixed between NF stretching and ONF bending. In contrast to the normal situation, the lowest mode v3 in ONF is best described as N-F stretching and the second
R. Kadibelban et al. / V-V end V-R.-T transfer in rriatomic moiecuks
216
t
30301
I
ONF ---+3
2
f 9
ZOOD
-9
‘2 4 “5
----35 ----Lv3
detect fluorescence signals with a wavelength smaller than 5.5 urn, a SBRC photovoltaic InSb detector (cooled to 77 K) with a response time of 1.2 ps was employed. To observe fluorescence in the region of longer wavelengths a SBRC CuGe detector [cooled to 4.2 K) with a response time of 0.4 us was used.
Typically, several hundred laser shots were averaged. The signal processing system consists of a Biomation 8100 transient recorder and a Tracer 1710 digital signal analyser. All measurements reported were performed at 295 K. The pressure in the fluorescence cell
Fig. 1. Vibrational levels of ONF with possible laser excitation (+) and some fluorescence (-+) transitions indicated.
lowest mode ~2 is mostly ONF bending [S]. For the most abundant species r601’NF the corresponding wave numbers are: trl = 1843.5 cm-‘, u2 = 765.8 cm-‘, and ZJ:= 519.5 cm-’ (see fig. 1). In contrast to ONCI, which has already been studied with the laser-excited fluorescence method [6], ONF possesses relatively large !evel spacings in the region of the fundamentals. Therefore, an interesting question is whether inefiicient V-V transfer occurs in this molecule_ To get as much information as possible on selfre!axation of ONF, different vibrational levels were excited with the IR laser and the rise and decay of the fluorescence were detected from severa! infrared active levels. All modes are infrared active in ONF and, therefore, it should be possible to obtain a complete map of energy transfer rates for this molecule.
2. Experimental The laser-induced fluorescence experiments were performed using a Lumonics 102 TEA CO2 laser as excitation source. The repetition rate employed was 1 Hz. A typical pulse had a width of about 0.2 ps followed by a tail of 1.5 &isand an energy of about 100 mJ/pulse. To
was measured with a l\fKS Baratron capacitance manometer. The ONF was provided by Ozark-Mahoning company. According to the manufacturer the gas had a purity of 97-98%. The sample used for measurements was carefully purified before an experiment employing the following procedure: first the sample was cooled with liquid nitrogen to remove noncondensable impurities such as F2 and NZ; then the temperature of the sample was slowly raised by taking away the nitrogen trap. By pumping, impurities with a higher vapor pressure than ONF, such as NO, were removed.
3. Results 3.1. vz jhorescence The ~a mode of ONF at 765.8 cm-’ is a strong infrared-active fundamental. Three interference filters were employed to observe the uz fluorescence free from scattered laser radiation. A narrow band pass filter with 75% maximum transmission, half-transmission points at 7.50 and 820 cm-‘, and less than 1% transmission outside 730-850 cm-’ was used. In addition, two long pass filters with 90% and 85% transmission and half-transmission at 905 cm-’ and 865 cm-*, respectively, were employed to block the laser wavelength. Excitation of ONF at 9.603 Pm (P 24) yields a fast rise time for the z+ fluorescence of 2.5+ 1 psTorr. The reciprocai lifetimes as a function
R. Kadibelban et al. / V-Vand
V-R,Ttransfer
in triatomic molecules
217
Fig. 3. ReciprocaI lifetime versus pressure for the fast fall of ~2 fluorescence and excitation at 9.603 pm. 1
2
3 plTorr1
Fig. 2. Reciprocal lifetime versus pressure for the rise of v1 Ruorescence and excitation at 9.603 pm_
of pressure are shown in fig. 2. The decay of the fluorescence signal is not a single exponentiai and it is possible to identify a relatively fast fall of 20 f 6 ps Torr and a much slower fall of 280 f 60 ys Torr. The corresponding values obtained from this analysis of the fluorescence decay at different pressures are presented in figs. 3 and 4 for illustration. Signai-to-noise was about 20: 1 for excitation at this wavelength. Weak v-, fluorescence could also be detected for excitation at 9.552 pm (P 20) and 9.305 pm (R 11). In these cases, however, the signal to noise was beIow 3: 1 after 500 laser shots and therefore, no accurate measurements were possible. 3.2.
lowest presstire investigated. This instantaneous rise is followed by a fast fall of about 6~~2 ps Torr and a much slower fall which could not be analysed accurately but may be in the region of 300 psTorr. The pattern of the vl fluorescence changes for excitation at 9.603 Km. A measurable rise time of 7 f 3 ps Torr is observed for the P 26 line. The decay again may consist of a relatively fast fall of about 17&8 ps Torr and a much slower part. The traces for this excitation wavelength show an additional decay to the base line in the ms time scale which is due to heating. This effect was studied in several experiments and the results will be discussed in more detail later. The signal to noise achieved for this laser line was only about 5 : 1.
I
VI fluorescence
The ZQmode at 1843.5 cm-’ is also a strong infrared-active fundamental. The interference filter employed to observe the fluorescence originating from the VI band had 85% maximum transmission, half-transmission at 1750 and 1950 cm-*, and less than 1% transmission outside 1700-2000 cm-‘. The strongest vl fluorescence was observed for excitation at 9.305 pm with S/N better than 20 : 1. The fast rise of the ffuorescence signals was determined by the response time of the detector (InSb: 1.2 ps) even at 0.3 Torr, the
1”
du
piToirl
Fig. 4. Reciprocal lifetime versus pressure Ear the slow fall of v1 Ruorescen~e and excitation at 9.603 m.
R. Kadibelbon
218
rmnsfer in m.afomic molecules
ef al. / V-V and V-R.T
3.3. (vl t vjJ fluorescence Strong laser-induced fluorescence could also be observed from the combination band (vI+yj) at 2365 cm-‘. The interference filter employed had 85% maximum transmission with halftransmission points at 2020 and 2490 cm-’ and less than 1% transmission outside 1940-2560 cm-‘. The best fluorescence signals were detected for excitatiqn at 9.552 pm_ With this line it was possible to perform measurements at pressures up to iO0 Torr. In the high pressure region S/N was better than 20 : 1. At 1.3 Torr, the lowest pressure studied, the rise of the (vr + 1~) fiuorescence was determined by the response time of the detector. The decay can be well characterized by a single relaxation time of 280; 6G psTorr as shown in fig. 5. No heating effect was observed. Similar fluorescence curves, however, with smaller S/N were obtained for excitation at 9.305 pm. The signal to noise decreased even more for excitation at 9.603 wrn and therefore, only a few traces were analysed for the latter laser line. A summary of fluorescence data obtained in this work is given in tabie 1. The collision numbers are estimated with a hard sphere diameter of 3.5 A. As mentioned above, the relatively high intensity of the laser radiation caused heating eEects which could be seen in the traces of or and Ye fluorescence. To study the temperature equilibration between the irradiated gas volume Table 1 Summary of fluorescence Excitation wavelength
*’ Hard sphere diaxxter Z,=
2Nc~~(2zRT/p)“‘;
1
10
20
30
Fig. 5. Rise and decay of (vI t ~3) fiuorescence at 9.552 grn and a pressure of 50Torr.
!!I
. tri.CA
for excitation
and the cell walls in more detail, the Buorescence curves were detected by operating the Biomation 8100 with dual time base. For illustration, fig. 6 shows results obtained from the analysis of vr fiuorescence induced by excitation with the P 26 laser line at 9.603 m. The accuracy of these measurements is not very high because only a few channels were used to analyse this very slow decay. Fig. 6 shows clearly, however, that the corresponding time for heat transfer possesses a value in the ms region and increases proportional to the pressure within experimental error.
4. Discussion The results discussed in section 3 show clearly that the different CO2 laser lines excite different
data for ONF
z =’
Fast decay
coil.
pr b-s To4
16 45 Cl3 C3 Cl3
2056 17ss 6*2 -
(w-n) 9.603 9.603 9.552 9.305 9.305
I
z =I coI1.
Slow decay
130 110
280~60 (-300) 28Oi60 (=300) 280-60
;S -
pr (v-s To4
of ONF was taken as c-3.5 A (estimated!). The gas kinetic collision and the number of collisions Z from: Z = 72,
2 =! call.
1800 1800 1800 rate
has been calculatedfrom:
R. Kadibelban et al. / V-V and V-R,T transfer in t-homic
4
I
:
c M-
75
/ I /
-
/‘;
I
Fig. 6. Decay time of the heating
cence cures
effect in the zq fluoresfor excitationat 9.603 pm.
vibrational modes in ONF. Considering the rise times and the signal to noise observed for the laser-induced fluorescence of the ONF bands investigated, we may assign the excitation wavelengths to specific transitions in ONF. However, we cannot exclude that more than one level is excited with a laser line. The finding of a rise of 2.5 l.~sTorr and 7 us Torr of y2 and vr fluorescence for excitation at 9.603 p.m suggests that the overtone 2vs is excited with this laser line. In this case the short relaxation time wottld describe the equilibration between v2 and v3 and the relaxation time of 7 ps Torr would be due to V-V transfer to the vr mode. With this assignment it is hard to understand the fast decay of 20 l~s Torr observed in the v2 iluorescence curves. Another explanation is that preferably the v2 mode is excited with the P 26 line perhaps through ~3 + 2~2. If only this transition is important, the rise of 2.5 psTorr would be due to the transition 2v2 + v2. The relaxation time of 7 psTorr would describe the equilibration of va with v: and the fast decay of 20 I.LSTorr could be explained by energy transfer to the v3 mode. This would be a surprising result because a pathway with a small energy gap exists for the slower process of equilibration between u2 and v; (2~2 -, 34, whereas only channels with large energy gaps are available
molecules
219
for the faster transfer process to the vr mode. The pulse energy employed is relatively high and therefore, non-linear relaxation processes cannot be excluded. It may be possible that both levels 2~s and 2~ are excited. Unfortunately, we did not succeed to observe v3 fluorescence. These results are necessary for a final interpretation of the ~2 fluorescence data. The laser line at 9.305 pm produces the strongest v1 fluorescence. The rise is faster than 0.5 us Torr and could not be resolved in the present experiments. This immediate rise and the high S/N suggest that the transition v2 + v1 may be excited with this laser wavelength. In agreement with this assumption of a direct excitation of the v1 mode is the fact that the corresponding fluorescence traces show a fast fall of 6 t.~sTorr, which should be attributed to V-V exchange with the v2 and u3 mode, and a much slower fall, which may be due to V-R,T transfer. We wish to point out, however, that other possibilities exist for an excitation of ONF at 9.303 urn. For example, the transition (v2+v3) + (v1+v3) between two combination bands, which is centered at 9.24 pm, is a possible candidate_ The relatively strong (vr + v3) fluorescence observed for the R 11 line would support such an assignment. Within experimental error, excitation at 9.552 urn leads to an identical pattern of v1 and (vr + v3) fluorescence as excitation at 9.305 ym. The main difference is a stronger u1 fluorescence for excitation at 9.305 pm, whereas the P 20 line produces stronger (vI + vj) signals. A simple expianation of this finding would be that the R 11 line preferably excites the v2 --, vr transition and the P 20 line (~2 + v3) + (vr + v3)_ The unmeasurable fast rise times of vl and (v: + v3) fiuorescence for both excitation wavelengths imply extremely fast V-V exchange between vI and (+ + v3) or excitation of both levels. The most interesting feature of the (vt i- ~3) fluorescence curves is the slow single exponential decay time of 2801k 60 TVTorr. This relaxation time is practically identical to the slow decay part of the ~1 and IQ fluorescence and may be identified as due to the V-R,T process. At this point the question arises why the fluorescence
220
R. Kadibelban et al. / V-Vnnd
traces of the vi and ZJ~band first show a fast decay pointing at an equilibration between al1 vibrational levels in the time scale of 6-20 us Torr, whereas the fast rise and the decay of the (ZQ+ UJ fluorescence with the V-R,T rate imply an equilibration of the vibrational modes faster than 2 us Torr. It is interesting to compare the results obtained for ONF with the data reported in ref. [6] for ONCl. Following excitation of the (~a+ ran)level in ONCI the rise time of the vI level was found to be 0.72 ps Torr. This corresponds to about 4 gas kinetic collisions compared to about 45 collisions needed for activation of vl following excitation at 9.603 Frn in ONF. We may conclude from this example that V-V transfer in ONCI is much faster than in ONF as expected from the higher density of states. The same is true for V-R,T transfer. In ONCl the vibrational energy degrades from the lowest level yg at 332 cm-i in about 32 collisions [6]. In comparison with this result, 1800 collisions were determined for V-R,T transfer in ONF with the lowest level at v3 = 519.9 cm-‘. For both molecules V-R,T transfer is somewhat more effective than expected from the LambertSalrer plot [7). These deviations may be due to the polarity of 0-F (ILL=1.81 D) and ONCI (p. = 1.83 D), because other polar molecules show a similar e!Iect. For intermode vibration to vibration transfer, larger deviations from simple correlations and energy transfer rules are observed than for V-R,T exchange of ONF. A more or less complete analysis of V-V and V-R,T transfer processes is available for the triatomic molecules COa, N20, COS. and SOz. Even for these triatomic molecules a comparison is not straightforward because ONF possesses a different level structure_ Nevertheless it is useful to compare collision numbers of similar processes to gain insight into the efficiency of dynamic processes in ONF. 3ne of the goals of the present experiments w.as to determine the collisional iifetime of the VI level which is isolated by relatively large energy gaps from the other levels. From simple
V-R,T
transferin niatomic molecules V-V transfer rules we expect that the two processes: ONF(ZQ)+ONF+ ONF(V~)+ONF
0NF(2vr)+ONF+321 --, ONF(3&
+ONF+
cm 2290
--:
,
cm -1
are the main deactivation channels. For the endothermic process ZQ+ 4va the energy gap is somewhat smaller; however, the quantum exchange is larger. For the endothermic channel u1 + 3~2, both energy deficit and quantum exchange are unfavourable. The channel ZQ-+ 2~2 in ONF should be compared with the symmetric stretch-to-bend relaxation in SOZ, OCS, N20, and C02. In SO*, 3300 collisions are needed for this equilibration process which possesses an energy gap of only 120 cm-‘. In the other three molecules this exchange process becomes more and more effective for comparable energy deficits going from OCS to CO1 due to Fermi rescmance couphng (see tabIe 4 in ref_ [8]). For ONF, V-V exchange is not enhanced by Fermi mixing with other modes. Therefore, energy transfer between v1 and 2~2 should be considerably less efiective in ONF than in SO1 because a much. larger energy gap is involved. The same is true for the other deactivation channel vi + 3~3. This again is a channel with a large energy difference and a formal quantum exchange of even four. This is a process similar to u3 deactivation in CO2 and N20, where also only channels with large energy gaps and unEavourable quantum exchange are available (see table 5 in ref. [S])_ In COa and NzO these facts cause a very ineffective V-V exchange with the ZQmode, whereas in ONF, only about 38 collisions are needed for the deactivation of the z+ mode. The fact that the collisional lifetime of this Ievel is orders of magnitudes too small can also be seen from a correlation of slow V-V processes presented for several polyatomic molecules in ref. [9]. The reason why the v1 deactivation in ONF is several orders of magnitude faster than e,_pected is not known. We can only speculate about possible explanations. As mentioned in the
R. Kadibelban et al. / V-V and V-R.T transfer in friatomic molecules
introduction, or is an almcst pure NO stretching vibration. The frequency of ZQis nearly the same as in the diatomic NO molecule [lo]. Such highly localized vibrational states have also been studied recently in polyatomic molecules containing X-H bonds. The frequencies for the excitation of high overtones in benzene for example, can be described with a one-dimensional anharmonic C-H local mode oscillator model. These highly excited IocaI mode states decay in ultrafast intramolcular relaxation and dephasing processes [ll]. Similar to these findings, the ONF result indicates a short collisional life time for localized vibrational motion in the region of the fundamentals.
5. Conclusions In this paper, data on energy transfer in ONF are reported for the first time. ONF belongs to the group of molecules where equilibration of the vibrational modes occurs considerably faster than V-R,T transfer. Less than 130 gas kinetic collisions are needed to equilibrate the vibrational modes by V-V transfer. The most surprising result is the short collisional lifetime of the ~1 level, which corresponds to about 38 gas kinetic collisions. This is orders of magnitudes shorter than expected from the collisional life times of comparable levels in SOz, COZ, and N20_ The slowest process investigated is the exchange of vibrational energy with the rota-
tional result to the polar
221
and translational degrees of freedom. The of 1800 gas kinetic coilisions corresponds value expected from V-R,T data of other molecules.
Acknowledgement We are grateful to the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Endustrie for research support.
References [1] J.D. Lambert, Vibrational and rotational relaxation in gases (Clarendon Press, Oxford, 1977). [2] R.T. Bailey and F.R. Cruickshank, in: Gas kinetics and energy transfer, Vol. 3. Chem. Sot. Specialist Periodiocal Reports (Chem. Sot., London, 1978). [3] H.S. Mailer and 0-S. Mortmsen, Chem. Phys. Letters 66 (1979) 539. Cd] 3. Fin& F.E. Ho&, V.N. Panfilov, P. Hess and C.B. Moore, J. Chem. Phys. 67 (1977) 4053. [5] L-H. Jones, L.B. Asprey. and R.R. Ryan, J. Chem. Phys. 47 (1967) 3371. [6] A. Hartford Jr., Chem. Phys. Letters 50 (1977) 85. [7] J.D. Lamben, J. Chem. Sot. Faraday Trans. II 68 (1972) 364. [8] M.L. Mandich and G.W. Flynn, J. Chem. Phys. 73 (1980) 1265. [9] W. Janiesch, M. Mashni, R. Kadibelban and P. Hess, J. Mol. Struct. 61 (1980) 43. [IO] LJ. Lawlor, K. Vasudevan and F. Grein, J. Am. Chem. Sot. iO0 (1978) 8062. [ll] R.G. Bray and MJ. Berry, I. Chem. Phys. 7: (1979) 4909.