- Email: [email protected]
Measurement of the vibrational-virbrational exchange time (v = 2) for DF Gas
Volutie 23, number
4
CHEMICXL
MEASUREMENT
PHYSICS
15 December
LEI-TERS
OF THE WBRATIONAL-VIBRATIONAL
1973
EXCHANGE
TIME (u = 2) FOR DF GAS? K. ERNST*,
KM. OSGOOD
Deparrrncnr of Physics. Mmsac/r~~serrs Cambridge. Masxacl~usetrs
Jr.+,
A. JAVAN
lmtitrrtc of Tec/rr~o/o~~, 02139, U.S.4
P.B. SACKETT Air Force Cambridge Researcl! Lohoratorics, L.G. Hanscont Field, B&ford,Massacl~rrsetts 01730. Received
14 August
US.4
1973
A measurement oi the vibrational eschange process DF (u = 0) + DF (u = 2) - 2DF(u the technique of lascr.induccd fluorescence. The mcnsurcd rate is 6 X 10’ XC-’ torr-‘, corresponding rate for I-IF.
A measurement of the vibrational-vibrational transfer rate for the second vibrational level in DF gas has been made using the technique of laser-induced fluorescence. The specific method used in these measurements is an extension of that reported recently for HF [l ] , HBr [2] , and HCl [3] . A comparison of the V-V rate reported here along with that of the corresponding rate in HF can provide one useful test for evaluating the applicability of various theoretical models of vibrational energy exchange. The experiment consisted of exciting pure DF gas in a sample cell with the output from a DF laser operating on a single u = 1 --t u = 0 line, and observing the fluorescence signal of both the u = 1 + u =O and u = 2 + u = 1 bands. The u = 1 level was populated directly by the laser light,‘and the decay of the fluorescence from this level gave usdirect information about the depopulation’of the u = 1 level due to
= 1) has been mode using
o vduc within 20% of the
V-T, R energy transfer during collisions with ground state DF molecules. The second vibrational level is populated by collisions between two DF molecules in the u = 1 state. Such a collision produces one molecule in the u = 0 and the other in the u = 2 state 2DF(u = 1) + DF(u = 2) + DF(u = 0).
(1)
Thus the temporal behavior of the rising part of the fluorescence from the u = 2 level provides us with information about the above process. The experimental apparatus is similar to that described in ref. [l] . A DF helical pin laser of standard design was used to excite DF gas in a sample cell. By means of an intracavity grating the P, (5) lime [(u = 1 ,J = 4) + (u = 0, J = 5j] was chosen as a source of excitation. The emitted laser spectrum was ob-. served by a inonochromator to ensure that no other lines were present in the laser output. Thus only the u = 1 level was populated directly by the laser. The i Work supported by AFCRL zmd ONR. laser produced pulses of 0.8 Get width,qd several * On leave from Institute of Experimental Physics, Warsaw kilowatts peak p.ower at a repetition rate of about 1 Unjversity.Warsaw, Poland. per second. A Faraday tige was.,.used to minimi’ze : ?Present address: Lincoln Laboratory oi the M.I.T.. Lexinc.._ -. ton; Massachusetts, USK the.; eIectriea1 noise. ,. 1;: _. ., .. . . 553;‘: I:. .- ‘. ‘-‘, ‘..,., : : .. ., ‘..-,., L ,,I_.’ ,,1,.., .;. ::: ‘. ,_:.’ ‘, : -‘.‘,~. ., ,: ;_’ ., .-,. .y : . . .:. .‘_. .,. ,_ ;_.._.. _.. ,., ;.’ ,‘..,::_,:’ ‘: .:,‘::_._‘.._‘. 1 -. :. .,;, ,, .‘-.‘... :’ : ._’ -.,. ., . ._,_ ‘.-‘- .:‘. :,/ .,::,, ,-> 5,. : : 1’. . :_ :. . :.yl.;.‘_” _::,.: .,.. _:.:, ..,;.,:,.,: , _( ,.. . _, I. _-,.‘:::,_-,:;, :, :‘:’ ,; ,,. . . _..~?Z2 ‘. :., -.__.-: :.: .;; .:‘.’ .“,:,‘..,” x... ..’ ‘._.,_‘ .;. : : _; : : ‘, .:‘..; ::_ i .:_‘-,_.;. :_-,‘.-.) .;;:.--., -,I.. ,,_:,, ,.)*i’,.;,-:< .. :‘.’ . ,c.’ ) Y..,...~..:-.~~.:~;,.. _.‘.,....,_-_-,,:-: ” ..:. “..‘.:_:~...~-._. ..,_, . :-I /..,>..I. ,;;,._ 2;;
Volume 23, number J
CHEhlICAL PHYSICS LEl-l-ERS
15 December 1973
The fluorescence cell was 2.5 cm in diameter and was provided with sapphire windows sealed with 1KEL-F wax. Because of the great reactivity of DF, the ceil and tubing were made of monel and the distiliation chambers of KEL-F. The DF sample from Union Carbide had an atom purity of 98%. Nevertheless, several steps of distillation were necessary to eliminate impurities such as CO,, DIO and D,. It ws quickly realized, however, that the most troublesome impurity was CO, (the DF-CO7 V-V rate is about 10 times faster than the DF-DF V-T rate) [a] ; even relativeiy smatl amounts of COz. can influence the DF decay rate+. Since the distillation technique of Airey and Fried [S] does not eliminate CO,, it was necessary to introduce an additional
pur:fication step of pumping on the sample while cooled to 195OK. This step elil~lixlated ah significant CO, inpurity. The pressure of DF was measured by means of a DF-resistant capacitance manometer calibrated with a M&cod mercury manometer. All pressure nleasurer~~ents were perforn~ed under static, nonflowing conditions and after e~uilibr3tio~l of wall absorption processes was cdmplete. DF fluorescence was observed in a direction perpendicular to the exciting bexn with un InSb liquid nitrogen cooled detector. In order ts measure the decay of only the u = 2 -+ u = I fluorescence, a 20 cm absorption ce!l containing about 20 torr of DF was placed between the fluorescence cell and the detector. Thus the u = 1 + u = 0 fluorescence was selectively absorbed. ~~e3surenlents of the decay time of the u = I * u = 0 fluorescence were made by recording the decay of the total fluorescence with the absorption cell evacuated. The decay rate was ev.aluated at times sufficiently long that the contribution of u = 2 + IJ = 1 fluorescence was negligible. It was found in ref. [ 1 ] fhat such a technique is a satisfactory method for separating u = I + u = 0 fluorescence from 0 = 2 + u = I fluorescence, as long as tha self-absorption within the sample cell is not strong (this condition holds as long as the DF‘sampIe pressure is less than about
Fig. 1. Pictures of typical scope tracts of the u = 1 -c u = 0 (upper) and u = 2 - u =.I flower) Huorescence at a DF pres&IO of 675~. The upper tract (time scale 50 psec/div)gives a decay rate of 1.1 X IO4 aec-‘_ The louver trace (time scale 20 pscc/div) gives a decay tale of1.4 X IO4 SW-’ _
I torr). The fluorescence signal was collimated using a BaF, lens and fecused on the element of the dctector by an ellipsoidal mirror placed after the absorption cell. The signal-to-noise ratio of each trace was very good and no avernging technique wxs necessary. Pictures of typical decay signals are presented in fig. 1. Measurements were repeated to check the reproducibility of the data. The variation among results was, in general, only statistical. To make sure that no significant heating effects were present, the decay times were measured
* A further complication is intxoduced by the large spontaneous emission rate of the CO2 4.3~ band. This rate m;iy cause the CO2 fluorescence to seriously interfere with that of DF.
.
.’ . .
..‘.:,
:‘_
:
‘. _:
_ ,,,..
,‘(
‘-,-.
.,
: .,;
._.,L
‘. _,
“
;.,
1
.:.
.’
.,
.,:. .:
laser intensities.
No
‘_..’
...,. ,‘. ,_
.
using different
change of decay time was observed after reducing the intensity of the exciting beam by a factor of three. All measurements were done in the pressure range between 0.1 and 1 torr. For higher pressure, because of self-absorption, the u = 2 --f u = 1 fluorescence became dominant in the total fluorescence signal. As the pressure was lowered, the ratio of the u = 2 -P u = 1 to u = 1 + u = 0 fluorescence decreased. This phenomenon may be understood on the basis of the
‘.
‘. .-
,’ ‘.
‘._ .:
.I l.‘.’
.~ .,
.,
‘, -_ -.
.-‘,
Volume 23, number 4
CHEMICAL PHYSICS LETTERS
vibrational
15 December 1973
temperature
of the DF gas is lowg. This
assumption allows us to neglect the u2dependent terms which would otherwise appear in eq. (2) for
“1 _ The solutions
of the above equations
are as fol-
lows: (4)
ny is the initial population of the u = 1 level introduced by laser excitation and where the rates expressed by the gammas are simply related to the r’ and 7: defined above by multiplication of the latter by no _
where
Fti.2. Plot or measured dewy rates of the u = I (solid points) and u = 2 (open points) levcis versus DF pressure. twoquantum process populating u = 2, as well as the saturated nature of the Doppler broadened line at low DF pressures.
Experimentally measured values of decay rates for different pressures are plotted in fig. 2. As expected the decay rate for u = 2 -+ IJ = 1 is twice as fast as the rate for u = 1 + IJ = 0. This is reasonable in Ii&t of the rate equations for the first two vibrationally excited levels dn, /dt = - n1 nay; ) drrz/dt =II~IZ&~--
(2) fz,r+,r;
- n,n,~;,
(3)
where, I+ is the population density of the ith vibrational level; 7; is the rate constant for (V-T, R) process excited
leading to de-excitation molecules
of the vibrationaUy
DF(u = i) + DF(u = 0) -+ DF(u = i-l
) + DF(u = 0);
K’:is the rate constant
process
for the V-V
DF(u = i) + DF(u = 0) + DF(u = i-l)
+ DF(u = 1);
the factor expressing the ratio of the forward to backward rate in (1). This factor arises becaux of the anharmonicity of the vibrational levels, which causes the energy of the right side to be less than the energy of the left side. An implicit assumption in the above equations is that IIJ~~_~
fis
The temporal behavior of fz2 is a product of two cxponentials. The rising part iS determined mainly by vibrational exchange (lTz) and the decaying part
is twice as fast as for 11~de-excitation. That the decay rate of u = 2 should be equal to 2yl arises from the fact that 12~is proportional to ,I: (PI2 a$ Q:e-2rlr). The measured value for 7; at room temperature is (1.62 0.3) X IO4 set-l torr-l .This is abput 40% lower than the rate given in the second series of DF experiments by Cool and coworkers [4]. This difference is greater than the combined error Limits of the two measurements. At this point it seems appropriate to emphasize that in our work pressure measurements were made under static, non-flowing conditions with undiluted DF. This was not true in the measurements of ref. [4] The measured decay rate constant of the second vibrational level is 3.1 X lo4 see-1 torr-1 which as expected from (5) is almost exactly twice as large as r;. That the plots of experimental decay rates versus pressure do not pass through the origin indicates the important role of diffusion of excited DF molecules to the wall of the cell. As seen from fig. 2 the diffusion dependent
curmture
is more pronounced
in the
?+However, we also assume that the thermal population of u = 1 is such that it is much smaller than the laser-induced population of the same level. This implies that the induced vibrztionzJ tcmpersture is much greater than room temperature. See ref. [6] for a more complete discussion of this point. 555,
:
,. ,’ :,,
Volume 23, number 4
CtlBhllCAL PtlYSICS LETTERS
I.5 December 1973
c&e of the u = 2 --t u = 1 fluorescence. This effect can be explained by the existence of the phenomenon of vibrational temperature diffusion. Ref. [7] gives a detailed discussion of this effect for the case of HF.
The value of IY, for vibrational-tibrational energy transfer cm be obtained from the rising part of the u = 2 -+ u = 1 Huorescence traces. However, a much simpler way consists of measuring the time at which the maximum population of the u =2 level is obtained (I,). Using eq. (5), one can easily firId the relation between fm and the decay rates:
t
=-- 1 m r,+Y2-2YI
In
_r2-Q2 t.7-Y, >-
As long as the rise time is much shorter than decay time one can calculate the value of I’, + -Q _App!ica-
tion of this equation at different pressures (fig. 3) gives a rate constant J?, + r; of 6.2 X 105 set-l torr-I*. Since this rate is a factor of 40 greater than ri, it is reasonable to assume 7; 4 I$. Thus the vibrational-vibrational exchange rater; for DF is about 6 X lo5 SCC-~ torr-l . This value is about 20%
smaller than the reported value for HF. Sharma has recently applied his theory
of resonant vibrational-vibrational energy exchange to processes involving HF and DF. The specifics of this
calculation will appear in a later paper by that author; however, a description of the general approach may be found in ref. [9]. In conclusion, we would like to acknowledge ful discussions on the tlleory of resonant energy
helptrans-
* After this work was completed we learned of the recent experiment of Bolt and Cohen 181. Our values for 7’, and ri+y; are 25% and lo%, respectively, smaller than their values for these quantities.
Fig. 3. Plot of r2 + 72 values versus pressure. fer with Professor R.D. Sharma, and to thank Dr. J. Both For kiridly providing us with a preprint of his work prior to publication.
References [l] R.M. Osgood Jr.. A. Javan and P.B. Snckett, Appl. Phys. Letters 20 (1972) 469. [2] B. Hopkins ond H.L. Chen. J. Chem. Phys. 57 (1973,) 38I 6. 13) 1. Burnk, Y. Noter, A.M. Ronn and A. SzEke,Chem. Phys. Letters 17 (1972) 345. (41 R.R. Stephens and T.A. Cool, J. Chem. Phys. 56 (1972) 5863; J.L. All and T.A. Cool, J. Chem. Phys. 58 (1973) 5540. [S] J.R. Airey and S. Fried, Chem. Phys. Let!ers 8 (1971) 23. (61 W.D. Breshears, Chem. Phys, Letters 20 (1973) 429. (71 RM Osgood Jr., P.B. Sackett nnd A. J&van, J. Chem. Phys., IO be published. [al JF. Bott and N. Cohen, J. Chem. Phys. 59 (1973) 447. [9] R.D. Sharma and H. Schlossberg, Chem. Phys. Letters 20 (1973) 5.
556
.’
,-.
.’
I , ‘.
.:
:, .I
. ,‘._...__
_’ ./. ._;.
.-,.
-..z
.
.
..
,.
,.”
,, _.:
‘.
:,, .,
,.
..,:
_, ‘;.
,. -.y
;
,.
‘_
4
CHEMICXL
MEASUREMENT
PHYSICS
15 December
LEI-TERS
OF THE WBRATIONAL-VIBRATIONAL
1973
EXCHANGE
TIME (u = 2) FOR DF GAS? K. ERNST*,
KM. OSGOOD
Deparrrncnr of Physics. Mmsac/r~~serrs Cambridge. Masxacl~usetrs
Jr.+,
A. JAVAN
lmtitrrtc of Tec/rr~o/o~~, 02139, U.S.4
P.B. SACKETT Air Force Cambridge Researcl! Lohoratorics, L.G. Hanscont Field, B&ford,Massacl~rrsetts 01730. Received
14 August
US.4
1973
A measurement oi the vibrational eschange process DF (u = 0) + DF (u = 2) - 2DF(u the technique of lascr.induccd fluorescence. The mcnsurcd rate is 6 X 10’ XC-’ torr-‘, corresponding rate for I-IF.
A measurement of the vibrational-vibrational transfer rate for the second vibrational level in DF gas has been made using the technique of laser-induced fluorescence. The specific method used in these measurements is an extension of that reported recently for HF [l ] , HBr [2] , and HCl [3] . A comparison of the V-V rate reported here along with that of the corresponding rate in HF can provide one useful test for evaluating the applicability of various theoretical models of vibrational energy exchange. The experiment consisted of exciting pure DF gas in a sample cell with the output from a DF laser operating on a single u = 1 --t u = 0 line, and observing the fluorescence signal of both the u = 1 + u =O and u = 2 + u = 1 bands. The u = 1 level was populated directly by the laser light,‘and the decay of the fluorescence from this level gave usdirect information about the depopulation’of the u = 1 level due to
= 1) has been mode using
o vduc within 20% of the
V-T, R energy transfer during collisions with ground state DF molecules. The second vibrational level is populated by collisions between two DF molecules in the u = 1 state. Such a collision produces one molecule in the u = 0 and the other in the u = 2 state 2DF(u = 1) + DF(u = 2) + DF(u = 0).
(1)
Thus the temporal behavior of the rising part of the fluorescence from the u = 2 level provides us with information about the above process. The experimental apparatus is similar to that described in ref. [l] . A DF helical pin laser of standard design was used to excite DF gas in a sample cell. By means of an intracavity grating the P, (5) lime [(u = 1 ,J = 4) + (u = 0, J = 5j] was chosen as a source of excitation. The emitted laser spectrum was ob-. served by a inonochromator to ensure that no other lines were present in the laser output. Thus only the u = 1 level was populated directly by the laser. The i Work supported by AFCRL zmd ONR. laser produced pulses of 0.8 Get width,qd several * On leave from Institute of Experimental Physics, Warsaw kilowatts peak p.ower at a repetition rate of about 1 Unjversity.Warsaw, Poland. per second. A Faraday tige was.,.used to minimi’ze : ?Present address: Lincoln Laboratory oi the M.I.T.. Lexinc.._ -. ton; Massachusetts, USK the.; eIectriea1 noise. ,. 1;: _. ., .. . . 553;‘: I:. .- ‘. ‘-‘, ‘..,., : : .. ., ‘..-,., L ,,I_.’ ,,1,.., .;. ::: ‘. ,_:.’ ‘, : -‘.‘,~. ., ,: ;_’ ., .-,. .y : . . .:. .‘_. .,. ,_ ;_.._.. _.. ,., ;.’ ,‘..,::_,:’ ‘: .:,‘::_._‘.._‘. 1 -. :. .,;, ,, .‘-.‘... :’ : ._’ -.,. ., . ._,_ ‘.-‘- .:‘. :,/ .,::,, ,-> 5,. : : 1’. . :_ :. . :.yl.;.‘_” _::,.: .,.. _:.:, ..,;.,:,.,: , _( ,.. . _, I. _-,.‘:::,_-,:;, :, :‘:’ ,; ,,. . . _..~?Z2 ‘. :., -.__.-: :.: .;; .:‘.’ .“,:,‘..,” x... ..’ ‘._.,_‘ .;. : : _; : : ‘, .:‘..; ::_ i .:_‘-,_.;. :_-,‘.-.) .;;:.--., -,I.. ,,_:,, ,.)*i’,.;,-:< .. :‘.’ . ,c.’ ) Y..,...~..:-.~~.:~;,.. _.‘.,....,_-_-,,:-: ” ..:. “..‘.:_:~...~-._. ..,_, . :-I /..,>..I. ,;;,._ 2;;
Volume 23, number J
CHEhlICAL PHYSICS LEl-l-ERS
15 December 1973
The fluorescence cell was 2.5 cm in diameter and was provided with sapphire windows sealed with 1KEL-F wax. Because of the great reactivity of DF, the ceil and tubing were made of monel and the distiliation chambers of KEL-F. The DF sample from Union Carbide had an atom purity of 98%. Nevertheless, several steps of distillation were necessary to eliminate impurities such as CO,, DIO and D,. It ws quickly realized, however, that the most troublesome impurity was CO, (the DF-CO7 V-V rate is about 10 times faster than the DF-DF V-T rate) [a] ; even relativeiy smatl amounts of COz. can influence the DF decay rate+. Since the distillation technique of Airey and Fried [S] does not eliminate CO,, it was necessary to introduce an additional
pur:fication step of pumping on the sample while cooled to 195OK. This step elil~lixlated ah significant CO, inpurity. The pressure of DF was measured by means of a DF-resistant capacitance manometer calibrated with a M&cod mercury manometer. All pressure nleasurer~~ents were perforn~ed under static, nonflowing conditions and after e~uilibr3tio~l of wall absorption processes was cdmplete. DF fluorescence was observed in a direction perpendicular to the exciting bexn with un InSb liquid nitrogen cooled detector. In order ts measure the decay of only the u = 2 -+ u = I fluorescence, a 20 cm absorption ce!l containing about 20 torr of DF was placed between the fluorescence cell and the detector. Thus the u = 1 + u = 0 fluorescence was selectively absorbed. ~~e3surenlents of the decay time of the u = I * u = 0 fluorescence were made by recording the decay of the total fluorescence with the absorption cell evacuated. The decay rate was ev.aluated at times sufficiently long that the contribution of u = 2 + IJ = 1 fluorescence was negligible. It was found in ref. [ 1 ] fhat such a technique is a satisfactory method for separating u = I + u = 0 fluorescence from 0 = 2 + u = I fluorescence, as long as tha self-absorption within the sample cell is not strong (this condition holds as long as the DF‘sampIe pressure is less than about
Fig. 1. Pictures of typical scope tracts of the u = 1 -c u = 0 (upper) and u = 2 - u =.I flower) Huorescence at a DF pres&IO of 675~. The upper tract (time scale 50 psec/div)gives a decay rate of 1.1 X IO4 aec-‘_ The louver trace (time scale 20 pscc/div) gives a decay tale of1.4 X IO4 SW-’ _
I torr). The fluorescence signal was collimated using a BaF, lens and fecused on the element of the dctector by an ellipsoidal mirror placed after the absorption cell. The signal-to-noise ratio of each trace was very good and no avernging technique wxs necessary. Pictures of typical decay signals are presented in fig. 1. Measurements were repeated to check the reproducibility of the data. The variation among results was, in general, only statistical. To make sure that no significant heating effects were present, the decay times were measured
* A further complication is intxoduced by the large spontaneous emission rate of the CO2 4.3~ band. This rate m;iy cause the CO2 fluorescence to seriously interfere with that of DF.
.
.’ . .
..‘.:,
:‘_
:
‘. _:
_ ,,,..
,‘(
‘-,-.
.,
: .,;
._.,L
‘. _,
“
;.,
1
.:.
.’
.,
.,:. .:
laser intensities.
No
‘_..’
...,. ,‘. ,_
.
using different
change of decay time was observed after reducing the intensity of the exciting beam by a factor of three. All measurements were done in the pressure range between 0.1 and 1 torr. For higher pressure, because of self-absorption, the u = 2 --f u = 1 fluorescence became dominant in the total fluorescence signal. As the pressure was lowered, the ratio of the u = 2 -P u = 1 to u = 1 + u = 0 fluorescence decreased. This phenomenon may be understood on the basis of the
‘.
‘. .-
,’ ‘.
‘._ .:
.I l.‘.’
.~ .,
.,
‘, -_ -.
.-‘,
Volume 23, number 4
CHEMICAL PHYSICS LETTERS
vibrational
15 December 1973
temperature
of the DF gas is lowg. This
assumption allows us to neglect the u2dependent terms which would otherwise appear in eq. (2) for
“1 _ The solutions
of the above equations
are as fol-
lows: (4)
ny is the initial population of the u = 1 level introduced by laser excitation and where the rates expressed by the gammas are simply related to the r’ and 7: defined above by multiplication of the latter by no _
where
Fti.2. Plot or measured dewy rates of the u = I (solid points) and u = 2 (open points) levcis versus DF pressure. twoquantum process populating u = 2, as well as the saturated nature of the Doppler broadened line at low DF pressures.
Experimentally measured values of decay rates for different pressures are plotted in fig. 2. As expected the decay rate for u = 2 -+ IJ = 1 is twice as fast as the rate for u = 1 + IJ = 0. This is reasonable in Ii&t of the rate equations for the first two vibrationally excited levels dn, /dt = - n1 nay; ) drrz/dt =II~IZ&~--
(2) fz,r+,r;
- n,n,~;,
(3)
where, I+ is the population density of the ith vibrational level; 7; is the rate constant for (V-T, R) process excited
leading to de-excitation molecules
of the vibrationaUy
DF(u = i) + DF(u = 0) -+ DF(u = i-l
) + DF(u = 0);
K’:is the rate constant
process
for the V-V
DF(u = i) + DF(u = 0) + DF(u = i-l)
+ DF(u = 1);
the factor expressing the ratio of the forward to backward rate in (1). This factor arises becaux of the anharmonicity of the vibrational levels, which causes the energy of the right side to be less than the energy of the left side. An implicit assumption in the above equations is that IIJ~~_~
fis
The temporal behavior of fz2 is a product of two cxponentials. The rising part iS determined mainly by vibrational exchange (lTz) and the decaying part
is twice as fast as for 11~de-excitation. That the decay rate of u = 2 should be equal to 2yl arises from the fact that 12~is proportional to ,I: (PI2 a$ Q:e-2rlr). The measured value for 7; at room temperature is (1.62 0.3) X IO4 set-l torr-l .This is abput 40% lower than the rate given in the second series of DF experiments by Cool and coworkers [4]. This difference is greater than the combined error Limits of the two measurements. At this point it seems appropriate to emphasize that in our work pressure measurements were made under static, non-flowing conditions with undiluted DF. This was not true in the measurements of ref. [4] The measured decay rate constant of the second vibrational level is 3.1 X lo4 see-1 torr-1 which as expected from (5) is almost exactly twice as large as r;. That the plots of experimental decay rates versus pressure do not pass through the origin indicates the important role of diffusion of excited DF molecules to the wall of the cell. As seen from fig. 2 the diffusion dependent
curmture
is more pronounced
in the
?+However, we also assume that the thermal population of u = 1 is such that it is much smaller than the laser-induced population of the same level. This implies that the induced vibrztionzJ tcmpersture is much greater than room temperature. See ref. [6] for a more complete discussion of this point. 555,
:
,. ,’ :,,
Volume 23, number 4
CtlBhllCAL PtlYSICS LETTERS
I.5 December 1973
c&e of the u = 2 --t u = 1 fluorescence. This effect can be explained by the existence of the phenomenon of vibrational temperature diffusion. Ref. [7] gives a detailed discussion of this effect for the case of HF.
The value of IY, for vibrational-tibrational energy transfer cm be obtained from the rising part of the u = 2 -+ u = 1 Huorescence traces. However, a much simpler way consists of measuring the time at which the maximum population of the u =2 level is obtained (I,). Using eq. (5), one can easily firId the relation between fm and the decay rates:
t
=-- 1 m r,+Y2-2YI
In
_r2-Q2 t.7-Y, >-
As long as the rise time is much shorter than decay time one can calculate the value of I’, + -Q _App!ica-
tion of this equation at different pressures (fig. 3) gives a rate constant J?, + r; of 6.2 X 105 set-l torr-I*. Since this rate is a factor of 40 greater than ri, it is reasonable to assume 7; 4 I$. Thus the vibrational-vibrational exchange rater; for DF is about 6 X lo5 SCC-~ torr-l . This value is about 20%
smaller than the reported value for HF. Sharma has recently applied his theory
of resonant vibrational-vibrational energy exchange to processes involving HF and DF. The specifics of this
calculation will appear in a later paper by that author; however, a description of the general approach may be found in ref. [9]. In conclusion, we would like to acknowledge ful discussions on the tlleory of resonant energy
helptrans-
* After this work was completed we learned of the recent experiment of Bolt and Cohen 181. Our values for 7’, and ri+y; are 25% and lo%, respectively, smaller than their values for these quantities.
Fig. 3. Plot of r2 + 72 values versus pressure. fer with Professor R.D. Sharma, and to thank Dr. J. Both For kiridly providing us with a preprint of his work prior to publication.
References [l] R.M. Osgood Jr.. A. Javan and P.B. Snckett, Appl. Phys. Letters 20 (1972) 469. [2] B. Hopkins ond H.L. Chen. J. Chem. Phys. 57 (1973,) 38I 6. 13) 1. Burnk, Y. Noter, A.M. Ronn and A. SzEke,Chem. Phys. Letters 17 (1972) 345. (41 R.R. Stephens and T.A. Cool, J. Chem. Phys. 56 (1972) 5863; J.L. All and T.A. Cool, J. Chem. Phys. 58 (1973) 5540. [S] J.R. Airey and S. Fried, Chem. Phys. Let!ers 8 (1971) 23. (61 W.D. Breshears, Chem. Phys, Letters 20 (1973) 429. (71 RM Osgood Jr., P.B. Sackett nnd A. J&van, J. Chem. Phys., IO be published. [al JF. Bott and N. Cohen, J. Chem. Phys. 59 (1973) 447. [9] R.D. Sharma and H. Schlossberg, Chem. Phys. Letters 20 (1973) 5.
556
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