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The collisionless IR absorption spectrum of C3F7I
Volume
CHEMICAL PHYSICS LETTERS
125, number 2
THE COLLISIONLESS
P. MUKHERJEE
IR ABSORPTION
SPECTRUM
28 March 1986
OF C,F,I
and H.S. KWOK
Department of Electrical and Compuier Engineertng, State University of New York at Buffalo, Amherst, NY 14260, USA Received 15 October 1985; in final form 21 January 1986
The collisionless infrared absorption spectrum of C,F,I was measured with an 80 ns CO* laser system. Comparison with the collisional absorption spectrum reveals that collisions induce a red-shift as well as significant broadening of the collisionless spectrum. The collisional broadening contribution was found to be much larger than anticipated. Possible physical explanations are given.
The infrared absorption spectra of polyatomic molecules provide important information on the structure and dynamics of these molecules. At very high resolution, it is possible to identify individual vibrationalrotational lines [ 11. However, that is possible only for molecules of moderate size. For large molecules such as C3F71, this resolution is difficult to obtain, especially at non-cryogenic temperatures. The spectrum is usually highly congested with multitudes of hot bands due to low-frequency modes. Interestingly, the IR absorption spectra of large molecules under these complicated situations become rather smooth and featureless. The study of the absorption spectrum of these large molecules can potentially elucidate the nature of the interaction between the large number of vibrational states in the molecule. Such investigations have been carried out on overtone absorption lines in a classic study on benzene and its derivatives [2]. Dubal et al. [3] also pointed out the potential benefits of studying the fundamental and first overtone absorptions of chromophores in large molecules in terms of the dynamics of IR photochemistry. In this Letter, we wish to present another aspect of the absorption by these highly congested vibrational structures, namely, the effect of collisions on the absorption spectra. The results are found to be quite interesting. The experiment was performed with a single longitudinal mode TEA (transverse electric atmospheric) 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
CO2 laser system. The laser pulse was 80 ns in duration and had a negligible tail. It was propagated for 10 m so that only the TEM,, mode remained to be used in the measurements. The sample was obtained in liquid form from Morton-Thiokol. It was stored in a glass vacuum system. The gas cell used in measuring the absorption spectrum was first evacuated and then filled with vapors of C,F,I. The pressure of the pure C,F,I vapor was carefully controlled with a capacitance manometer. Pressures of 0.1 to 30 Torr were used in the experiments. No trapping or purification of the sample was attempted. Two gas cells were used in the experiments. One has a length of 1.84 cm and the other was 125 cm long used in double pass. They were both fitted with NaCl windows. The laser pulse was not focused in order to reduce the laser intensity. To further attenuate the beam intensity and thus reducing the effects of any saturation that may be present, calibrated MgF2 and LiF flats were employed. In all the laser measurements, the maximum laser fluence was estimated to be 1.15 M/cm2. At such low intensities saturation and other intensity dependent effects on the transmission were found to be insignificant. The laser beam was split into two arms for normalization. Two calibrated liquid N2 cooled Ge : Au detectors were used to measure the absolute transmission of the gas sample. A digital storage oscilloscope was used to accurately record the signals with and without 101
28 March 1986
CHEMICAL PHYSICS LETTERS
Volume 125, number 2
0.3 0
0.1 Ton
A
2.0
0
Torr
30 Torr
0.0
-I
1020
1030
1050
1040 FREQUENCY
hi’
1060
)
Fig.1. Absorption spectra of C3F7I taken with weak 80 ns CO2 Iaser pulses at various pressures,
the gas in the sample cell. The accuracy of the transmission meas~ement was better than 5%. Fig. 1 shows the srn~~l-~~~l absorption spectra of C,F,I near the P(20) line of the 9.4 pm branch of the CO2 laser. Pressures from 0.1 to 30 Torr were used in the measurement. It can be seen that as the pressure increases, the absorption peak shifts to the red, and the spectral width increases. It was found that the results for 5,10, and 30 Torr overlap each other in fig. 1. Hence the shifting and broadening of the spectrum seems to “stabilize” beyond a certain pressure. At 0.2 Torr, the mean collision time was approximately 1.5 J.LS. Hence the 0.1 Torr data in fig. 1 can be regarded as the collisionless absorption spectrum. On the other hand, the measured absorption spectra at pressures higher than 5 Torr are dominated by col&ions. Therefore the results in fig. 1 seem to suggest that the spectrum does not change once collisions become dominant. As a comparison,
102
fig.
2 shows a portion of the IR
‘li L S 0
IO00
I020
IO40
IO60
IO60
II00
WAVENUMBER
Fig. 2. IR absorption spectrum of CsF,I taken with a PerlcinElmer 1430 spectrometer with a resolution of 2 cm-t. This spectrum is very simiIar to the 30 Torr absorption spectrum in t&. 1 near the 1036 cm-’ absorption peak.
absorption spectrum of C,F,I at 30 Torr taken with a Perkin-Elmer model 1430 IR spectrometer. The IR spectrum in fig. 2 matches the collisional result in fig. 1 quite well near the 1036 cm-l absorption peak. Considering the 2 cm-l resolution of the IR spectrometer, it can safely be assumed that the collision dominated spectra in both figs. 1 and 2 are essentially the same. Because of the deliberate choice of very low laser intensities, energy absorption and saturation cannot be used to explain the experimental data. The peak absorption cross section u was 0.3 Mbarn (IO-l8 cmm2). Hence at the laser fluence used in the experiment, the average number of photons deposited, (n> = a@0
28 March 1986
CHEMICAL PHYSICS LETTERS
Volume 125, number 2
)
(1)
was less than 10T5. In eq. (l), J is the laser fluence. We have also performed a measurement on the change of the’cross section u as a function of the OFID pulse intensity. The results indicated that u was independent of J at the low fluence used in the present experiment. Both the peak and width of the absorption spectrum were independent of J.
The only physical difference that can account for the change in the absorption spectrum between the two cases is the presence of collisions for the high pressure data. The 0.1 Torr data shows the spectrum of an isolated molecule initidy in thermal equilibrium with its surrounding while the 30 Torr data shows the spectrum of a molecule in constant thermal equilibrium with its surrounding. Actually, the collisional spectrum can be empirically derived from the collisionless spectrum if we assume that each state in the collisionless spectrum is (i) redshifted by AU and (ii) broadened homogeneously by I’. If the collisionless spectrum is given by cui(o), then the collisional spectrum will be given by c%(w) 00 = J {o,&‘)AF/lr[(o
- w’+Au)~
++]}do
,
_m
(2)
where A is a renormalization constant. In fig. 3, the collisionless spectrum (0.1 Torr) and
0.3
0.2
1020
1030
1040
1050
1060
FREQUENCY (cm” ) Fig.3. Theoretical fit to the collisionless (0.1 Tom) and collisional (30 Torr) spectra using a Gaussian and a shifted Voigt integral. 103
Volume 125, number 2
CHEMICAL PHYSICS LETTERS
the collisional spectrum (30 Torr) are plotted. The dotted line represents a Gaussian fit to the collisionless data. The Gaussian function was chosen only to facilitate the computation of (2) and beared no real physical meaning. With a Gaussian assumed for or.(o), eq. (2) becomes a shifted Voigt integral. The line passing through the collisional data in fig. 3 is the best fit to oc(o) using a value of Aw = 3.0 cm-l, I’ = 3.0 cm-l and A = 1.25. It can be seen that the fits are quite good. Empirically, it is concluded that collisions tend to red-shift and broaden individual absorption lines in the collisionless spectrum. The total absorption strength is also stronger by 1.25, as indicated by the renormalization constant A. Physically, the additional absorption arises from collision-assisted excitation. The broadening and shifting of spectral lines due to collisions have been a subject of much study [4]. However in the present case, the broadening appears to be much too large to be consistent with simple collisional broadening. No data exists for the collisional broadening coefficient of CsF,I. In a similarly large and polar molecule C,F,H, pressure broadening was estimated to be 0.1 cm-l at a pressure of lo5 Pa (~1 atm). Certainly at 30 Torr, the pressure linewidth of C,F,I should be much smaller than the F = 3.0 cm-l value observed. To further ascertain that normal pressure broadening is unimportant, we performed a study of the IR transmission spectra of C3F71 as a function of pressure. Fig. 4 is a plot of the IR transmission spectrum of C,F,I at various pressures ranging from 10 to 120 Torr. It can be seen that indeed the fwhm of the absorption line as well as the peak position are independent of the gas cell pressure. Hence the difference in the collisional and collisionless absorption spectra shown in figs. 1 and 3 cannot be accounted for by simple pressure broadening. A plausible explanation can be given in terms of the multi-tier classification scheme of energy levels in a large molecule [5,6]. For large molecules at room temperature, or for smaller molecules in highly vibrationally excited states in the quasi-continuum (QC), the density of states is very large. Various conibination bands and low frequency hot bands exist. In the multi-tier classification scheme, states that interact with the laser field are placed in the first tier (fig. 5). Each first tier state is connected to a homogeneous 104
28 March 1986
Ol-
WAVENUMBER
Fig. 4. IR transmission spectrum of CaF,I at various gas cell pressures. The pressures from the top curve are 45,60,80, 90 and 120 Torr respectively. Transmission of the gas cell at vacuum is 73%. The peak absorption and the spectral width remain constant independent of pressure. Note the reverse frequency scale.
ensemble of second-tier states. This is similar to the “homogeneous vibrational contribution” concept discussed by Dubal and Quack [3]. The second tier states are then linked to the third tier and so on until all the states are classified. The interaction between each first
Al Fig. 5. The multi-tier energy level scheme. Each state that interacts with the photon field is coupled to an ensemble of second-tier states. The ensemble of states is homogeneous in the sense that they can be saturated together.
Volume 125, number
2
CHEMICALPHYSICSLETTERS
tier state and its own homogeneous ensemble can be due to anharmonic or Coriolis coupling. Homogeneity here means that the entire ensemble of states can be saturated together. Different second tier ensembles may or may not be coupled to each other. The collisionless absorption spectrum reflects the quiescent state of this interaction picture among all the energy levels in the molecule. However, in the presence of collisions, different second tier ensembles that normally are not coupled are now forced to interact with each other, The classification of states is therefore completely different. Hence the absorption spectrum will be different. In particular, the homogeneous vibrational ensembles are now larger because of this forced mixing. From the experimental results, it can be concluded that each second tier ensemble is broadened by F = 3.0 cm-l. Moreover, because the interaction is predominantly due to anharmonicity, the broadening tends to be red-shifted. The main difference between the above picture and normal pressure broadening of an absorption line is that the collisional mixing scheme discussed here should be relatively insensitive to pressure once collisional effect takes place. The collisional spectrum depends on whether there is any collision and not on the frequency of the collisions. Hence the colhsional spectrum should be independent of the gas cell pressure, in agreement with the result in fig. 4.
28 March1986
In summary, we have observed a signikant difference between the collisional and collisionless IR absorption spectrum of C, F, I. This difference cannot be explained by the usual pressure or laser intensity saturation effects. The similarity of the fundamental absorption band of a large molecule such as C,F, I and the QC of vibrationally hot polyatomic molecule was noted. It is believed that the dynamics and structure of the ensemble of the high number of states in both cases can be described by a multi-tier classifkation picture. This research was supported by the US Department of Energy, Division of Chemical Sciences. The technical assistance of Robert Barone and Todd Rossi is acknowledged.
References [ 11 G.W.Halsey, O.E. Jenningsand W.E.Blass,J. Opt. Sot. Am. B2 (1985) 837.
[ 21 K.V. Reddy, D.F. Heller and M.J. Berry, J. Chem. Phys. 76 (1982) 2814. [3] H. DubaJ and M. Quack, Chem. Phys. Letters 72 (1980) 342. [4] S.Y. Chen and M. Takeo, Rev. Mod. Phys. 29 (1957) 20. [ 5] P. Mukhejee and H.S. Kwok, J. Chem. Phys. (February 1986), to be published. [6] E.L. Sibert, J.T. Hynes end W.R. Reinhardt, I. Chem. Phys. 81(1984) 1115.
105
CHEMICAL PHYSICS LETTERS
125, number 2
THE COLLISIONLESS
P. MUKHERJEE
IR ABSORPTION
SPECTRUM
28 March 1986
OF C,F,I
and H.S. KWOK
Department of Electrical and Compuier Engineertng, State University of New York at Buffalo, Amherst, NY 14260, USA Received 15 October 1985; in final form 21 January 1986
The collisionless infrared absorption spectrum of C,F,I was measured with an 80 ns CO* laser system. Comparison with the collisional absorption spectrum reveals that collisions induce a red-shift as well as significant broadening of the collisionless spectrum. The collisional broadening contribution was found to be much larger than anticipated. Possible physical explanations are given.
The infrared absorption spectra of polyatomic molecules provide important information on the structure and dynamics of these molecules. At very high resolution, it is possible to identify individual vibrationalrotational lines [ 11. However, that is possible only for molecules of moderate size. For large molecules such as C3F71, this resolution is difficult to obtain, especially at non-cryogenic temperatures. The spectrum is usually highly congested with multitudes of hot bands due to low-frequency modes. Interestingly, the IR absorption spectra of large molecules under these complicated situations become rather smooth and featureless. The study of the absorption spectrum of these large molecules can potentially elucidate the nature of the interaction between the large number of vibrational states in the molecule. Such investigations have been carried out on overtone absorption lines in a classic study on benzene and its derivatives [2]. Dubal et al. [3] also pointed out the potential benefits of studying the fundamental and first overtone absorptions of chromophores in large molecules in terms of the dynamics of IR photochemistry. In this Letter, we wish to present another aspect of the absorption by these highly congested vibrational structures, namely, the effect of collisions on the absorption spectra. The results are found to be quite interesting. The experiment was performed with a single longitudinal mode TEA (transverse electric atmospheric) 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
CO2 laser system. The laser pulse was 80 ns in duration and had a negligible tail. It was propagated for 10 m so that only the TEM,, mode remained to be used in the measurements. The sample was obtained in liquid form from Morton-Thiokol. It was stored in a glass vacuum system. The gas cell used in measuring the absorption spectrum was first evacuated and then filled with vapors of C,F,I. The pressure of the pure C,F,I vapor was carefully controlled with a capacitance manometer. Pressures of 0.1 to 30 Torr were used in the experiments. No trapping or purification of the sample was attempted. Two gas cells were used in the experiments. One has a length of 1.84 cm and the other was 125 cm long used in double pass. They were both fitted with NaCl windows. The laser pulse was not focused in order to reduce the laser intensity. To further attenuate the beam intensity and thus reducing the effects of any saturation that may be present, calibrated MgF2 and LiF flats were employed. In all the laser measurements, the maximum laser fluence was estimated to be 1.15 M/cm2. At such low intensities saturation and other intensity dependent effects on the transmission were found to be insignificant. The laser beam was split into two arms for normalization. Two calibrated liquid N2 cooled Ge : Au detectors were used to measure the absolute transmission of the gas sample. A digital storage oscilloscope was used to accurately record the signals with and without 101
28 March 1986
CHEMICAL PHYSICS LETTERS
Volume 125, number 2
0.3 0
0.1 Ton
A
2.0
0
Torr
30 Torr
0.0
-I
1020
1030
1050
1040 FREQUENCY
hi’
1060
)
Fig.1. Absorption spectra of C3F7I taken with weak 80 ns CO2 Iaser pulses at various pressures,
the gas in the sample cell. The accuracy of the transmission meas~ement was better than 5%. Fig. 1 shows the srn~~l-~~~l absorption spectra of C,F,I near the P(20) line of the 9.4 pm branch of the CO2 laser. Pressures from 0.1 to 30 Torr were used in the measurement. It can be seen that as the pressure increases, the absorption peak shifts to the red, and the spectral width increases. It was found that the results for 5,10, and 30 Torr overlap each other in fig. 1. Hence the shifting and broadening of the spectrum seems to “stabilize” beyond a certain pressure. At 0.2 Torr, the mean collision time was approximately 1.5 J.LS. Hence the 0.1 Torr data in fig. 1 can be regarded as the collisionless absorption spectrum. On the other hand, the measured absorption spectra at pressures higher than 5 Torr are dominated by col&ions. Therefore the results in fig. 1 seem to suggest that the spectrum does not change once collisions become dominant. As a comparison,
102
fig.
2 shows a portion of the IR
‘li L S 0
IO00
I020
IO40
IO60
IO60
II00
WAVENUMBER
Fig. 2. IR absorption spectrum of CsF,I taken with a PerlcinElmer 1430 spectrometer with a resolution of 2 cm-t. This spectrum is very simiIar to the 30 Torr absorption spectrum in t&. 1 near the 1036 cm-’ absorption peak.
absorption spectrum of C,F,I at 30 Torr taken with a Perkin-Elmer model 1430 IR spectrometer. The IR spectrum in fig. 2 matches the collisional result in fig. 1 quite well near the 1036 cm-l absorption peak. Considering the 2 cm-l resolution of the IR spectrometer, it can safely be assumed that the collision dominated spectra in both figs. 1 and 2 are essentially the same. Because of the deliberate choice of very low laser intensities, energy absorption and saturation cannot be used to explain the experimental data. The peak absorption cross section u was 0.3 Mbarn (IO-l8 cmm2). Hence at the laser fluence used in the experiment, the average number of photons deposited, (n> = a@0
28 March 1986
CHEMICAL PHYSICS LETTERS
Volume 125, number 2
)
(1)
was less than 10T5. In eq. (l), J is the laser fluence. We have also performed a measurement on the change of the’cross section u as a function of the OFID pulse intensity. The results indicated that u was independent of J at the low fluence used in the present experiment. Both the peak and width of the absorption spectrum were independent of J.
The only physical difference that can account for the change in the absorption spectrum between the two cases is the presence of collisions for the high pressure data. The 0.1 Torr data shows the spectrum of an isolated molecule initidy in thermal equilibrium with its surrounding while the 30 Torr data shows the spectrum of a molecule in constant thermal equilibrium with its surrounding. Actually, the collisional spectrum can be empirically derived from the collisionless spectrum if we assume that each state in the collisionless spectrum is (i) redshifted by AU and (ii) broadened homogeneously by I’. If the collisionless spectrum is given by cui(o), then the collisional spectrum will be given by c%(w) 00 = J {o,&‘)AF/lr[(o
- w’+Au)~
++]}do
,
_m
(2)
where A is a renormalization constant. In fig. 3, the collisionless spectrum (0.1 Torr) and
0.3
0.2
1020
1030
1040
1050
1060
FREQUENCY (cm” ) Fig.3. Theoretical fit to the collisionless (0.1 Tom) and collisional (30 Torr) spectra using a Gaussian and a shifted Voigt integral. 103
Volume 125, number 2
CHEMICAL PHYSICS LETTERS
the collisional spectrum (30 Torr) are plotted. The dotted line represents a Gaussian fit to the collisionless data. The Gaussian function was chosen only to facilitate the computation of (2) and beared no real physical meaning. With a Gaussian assumed for or.(o), eq. (2) becomes a shifted Voigt integral. The line passing through the collisional data in fig. 3 is the best fit to oc(o) using a value of Aw = 3.0 cm-l, I’ = 3.0 cm-l and A = 1.25. It can be seen that the fits are quite good. Empirically, it is concluded that collisions tend to red-shift and broaden individual absorption lines in the collisionless spectrum. The total absorption strength is also stronger by 1.25, as indicated by the renormalization constant A. Physically, the additional absorption arises from collision-assisted excitation. The broadening and shifting of spectral lines due to collisions have been a subject of much study [4]. However in the present case, the broadening appears to be much too large to be consistent with simple collisional broadening. No data exists for the collisional broadening coefficient of CsF,I. In a similarly large and polar molecule C,F,H, pressure broadening was estimated to be 0.1 cm-l at a pressure of lo5 Pa (~1 atm). Certainly at 30 Torr, the pressure linewidth of C,F,I should be much smaller than the F = 3.0 cm-l value observed. To further ascertain that normal pressure broadening is unimportant, we performed a study of the IR transmission spectra of C3F71 as a function of pressure. Fig. 4 is a plot of the IR transmission spectrum of C,F,I at various pressures ranging from 10 to 120 Torr. It can be seen that indeed the fwhm of the absorption line as well as the peak position are independent of the gas cell pressure. Hence the difference in the collisional and collisionless absorption spectra shown in figs. 1 and 3 cannot be accounted for by simple pressure broadening. A plausible explanation can be given in terms of the multi-tier classification scheme of energy levels in a large molecule [5,6]. For large molecules at room temperature, or for smaller molecules in highly vibrationally excited states in the quasi-continuum (QC), the density of states is very large. Various conibination bands and low frequency hot bands exist. In the multi-tier classification scheme, states that interact with the laser field are placed in the first tier (fig. 5). Each first tier state is connected to a homogeneous 104
28 March 1986
Ol-
WAVENUMBER
Fig. 4. IR transmission spectrum of CaF,I at various gas cell pressures. The pressures from the top curve are 45,60,80, 90 and 120 Torr respectively. Transmission of the gas cell at vacuum is 73%. The peak absorption and the spectral width remain constant independent of pressure. Note the reverse frequency scale.
ensemble of second-tier states. This is similar to the “homogeneous vibrational contribution” concept discussed by Dubal and Quack [3]. The second tier states are then linked to the third tier and so on until all the states are classified. The interaction between each first
Al Fig. 5. The multi-tier energy level scheme. Each state that interacts with the photon field is coupled to an ensemble of second-tier states. The ensemble of states is homogeneous in the sense that they can be saturated together.
Volume 125, number
2
CHEMICALPHYSICSLETTERS
tier state and its own homogeneous ensemble can be due to anharmonic or Coriolis coupling. Homogeneity here means that the entire ensemble of states can be saturated together. Different second tier ensembles may or may not be coupled to each other. The collisionless absorption spectrum reflects the quiescent state of this interaction picture among all the energy levels in the molecule. However, in the presence of collisions, different second tier ensembles that normally are not coupled are now forced to interact with each other, The classification of states is therefore completely different. Hence the absorption spectrum will be different. In particular, the homogeneous vibrational ensembles are now larger because of this forced mixing. From the experimental results, it can be concluded that each second tier ensemble is broadened by F = 3.0 cm-l. Moreover, because the interaction is predominantly due to anharmonicity, the broadening tends to be red-shifted. The main difference between the above picture and normal pressure broadening of an absorption line is that the collisional mixing scheme discussed here should be relatively insensitive to pressure once collisional effect takes place. The collisional spectrum depends on whether there is any collision and not on the frequency of the collisions. Hence the colhsional spectrum should be independent of the gas cell pressure, in agreement with the result in fig. 4.
28 March1986
In summary, we have observed a signikant difference between the collisional and collisionless IR absorption spectrum of C, F, I. This difference cannot be explained by the usual pressure or laser intensity saturation effects. The similarity of the fundamental absorption band of a large molecule such as C,F, I and the QC of vibrationally hot polyatomic molecule was noted. It is believed that the dynamics and structure of the ensemble of the high number of states in both cases can be described by a multi-tier classifkation picture. This research was supported by the US Department of Energy, Division of Chemical Sciences. The technical assistance of Robert Barone and Todd Rossi is acknowledged.
References [ 11 G.W.Halsey, O.E. Jenningsand W.E.Blass,J. Opt. Sot. Am. B2 (1985) 837.
[ 21 K.V. Reddy, D.F. Heller and M.J. Berry, J. Chem. Phys. 76 (1982) 2814. [3] H. DubaJ and M. Quack, Chem. Phys. Letters 72 (1980) 342. [4] S.Y. Chen and M. Takeo, Rev. Mod. Phys. 29 (1957) 20. [ 5] P. Mukhejee and H.S. Kwok, J. Chem. Phys. (February 1986), to be published. [6] E.L. Sibert, J.T. Hynes end W.R. Reinhardt, I. Chem. Phys. 81(1984) 1115.
105