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Vibration-vibration energy transfer iln CH3F
Volume 17, number 3
1 December
CHEMICAL PHYSICS LElTERS
VIBRATION-VIBRATION
ENERGY TRANSFER
IN dI-QF*
1972
,,
Z. KARNY, A.M. RONNS,4 Departments
of
Chemistry
and Physics,
Tel-Aviv
University,
Tel-Aviv.
Israel
1
and Eric WEITZ* and G.W. FLYNN# Department
of Chemistry,
Columbia
University.
New
York, New York
10027.
US.4
Received 4 September 1972
Previous works have reported vibration-vibration and vibration-translation transfer rates in CHJF and CHg F-X mixtures. fn this letter we report the study of the fast V-V transfer rate populating the 3~3, u1 and ~4 states of CHJF. GaseousCHsF was initially exited to the ~3 state by a TEA CO2 laser operating on the P(20) 9.6 g line and collisional pumping to the 3~3, ur and v4 states was measured by monitoring the rise time of the fluorescence at 3000 cm-‘. The rate constant was found to be 2.2 X 10s set-r tom-‘.
Laser induced infrared fluorescence has been used recently to measure energy transfer processes in a number of hydrogen and methyl halide systems [l-7] . Studies of the comparatively slow transfer of energy from vibration to translation and rotation (V-T/R), or to the vibrations of another molecule (V-V) have received most attention. In contrast, the exchange of vibrational energy among molecules of ‘he same kind has only been reported for the hydrogen halides [S-7]. These processes are very fast since in a typical collision only the small amount of energ;r
corresponding to the vibrational anharmonicity is transferred to the rotational and translational degrees of freedom of the colliding molecules. In this experiment we have measured the V-V energy exchange in CH3F by monitoring the fluorescence of the v4 state (C-H stretch at 3000 cm-‘) subsequent to excitation of the v3 state (C-F stretch at 1050 cm-l). The rise time of the fluorescence measures the thermalization of the CH3F ~3 overtone manifold with the v4 (and vl) nearby states whiie the fall tunes measure the V-T/R rate of equilibration with the ground state. A typical Iaser induced fluorescence apparatus was used. The TEA C02-N2-He laser was operated on the F(20) transition of the 9.6 /L band. A photovoltaic InSb detectcr was used in conjunction with a feedback transistor amplifier which also kept a zero bias across the element. The fall time of the detector-amplifier combination was less then 1 psec. The detector was shielded from electrical noise by enclosing the laser and the fluorescence cell in separate copper boxes. Measurements of the u4 fall time were first made and the V-T/R times measured agreed well with those reported by Weitz et al. [4]. Quantitative rise time measurements were made subsequently with a PAR Waveform * This work was supported by tion and the Army Research $ On leave from the Chemistry #Alfred P. Sloan Fel!ow. * National Science Foundation
the Petroleum Research Fund of the American Chemical,Society, the National Science FoundaOffice (Durham). Department, Polytechnic Institute of Brooklyn, BrookIyn, New York 11201, USA. Predoctoral
Trainee. 347
Volume 17, number 3
CHEMICAL
PHYSICS LETTERS
1 December
t972
l
t .
l :
. .
.*
0.1 t
:
.
0.06
*
l
‘
0.02
/ ’
0.2
0.4
0.6
a8
1.0
1.2
1.4 ’
I:6 ’
I.8
1
c P:0rr.
II
Urersy Level D&qmm
SimfM%d
uf CH3F Fig. f. Deactivation rate for faser excited CH3F fiuorescence versus pressure. Slope = 7.2 X 10s secWxtorr-l.
Fig. 2. Energy level diagram of CHsF showing relevant ievels for V-V exchange between the v3 manifold and Y.+,~1 states.
Eductor. For each point shown in fig. I both rise and fall times were taken to ensure Sase fine integrity. The time evolution of the V-V exchange reactions can be described in terms of the following V-V processes
and the s~~fi~ed
energy level diagram shown In fig. 2:
Slv CX-$F(V~= 1) + ~X$F(V~ = 1) * CH3F(v3 = 0) t CH,F(V, = 2) + AL!‘, (= 2C cm-‘)
,
co
(= 40 cm- I > ,
Q>
z--lv “2v CH,W,
=
2) t CH,F(u,
= 1) =*,
CH,F(v,
= 3) + CH,F(Y, = 0) + AE,
-..V
CH,F(v,
= 3) + C!H,F(V, = 0)
x3v
*
CH$
= 0) +- AZ?3 (= 100 cm-‘)
t
(3)
=-3&p and by the slower V-T/R reIz:ration of all the vibrationa levels. All X:, are related to Ci,, through I;1, = Z._, exp(--AEilkT), where AEi is either the energy defect due to anharmonicity or the energy difference between
the 31.9 and u4 states. Jf Iawr excitation of v3 is low, i.e., a small change in the vibrational temperature is achieved, then one may Linearize the rate equations for the [S-71 processes above and obtain the following solution for the population of the 39 level: N3(ti=i(NIo?2~~F/(ivo~2~3,)
exp(-~roT:Iv~C1
- exp(--NoZ3vfll
,
where@ is rhe initial population of the v3 Ievei, No the total number of C!H,F mofecufes, X,,, V-V rates of foiurard and backward reactions (1) through (3).
(4) L’2v,Zfy
are the
This solution does not allow complete separation of ihe.two rates LX:,,and C,,. Since the vibrational tiarmoticity of reaction (2) is considerably smaller than the energy defect of reaction (3) and a four-quantum transi348
1 December 1972
CHEMICALPHYSICS LETTERS
Volume 17, number 3
tion is involved in (3) it can be assumed that C2v Z+ Csv and that the rate measured should then be the slower of the two processes. The rise times of the fluorescence measurements were analyzed in terms of (4) and an effective rate constant K was plotted against CH,F pressure yielding a slope of (2.2 k 0.4) X IO5 set-1 torr-’ as shown in fig. 1. With this measured value of the rate constant one can calculate the cross section for collisions for process (3). For 1 torr of pressure: 1/7=K=nvu,
0 =
1.7 A2 ,
which is l/25 of the known gas kinetic cross section for CH,F, 44.1 A2 [S] . For process (2) one has to consider the number of molecules excited to v3 and to 2~3 by the laser pulse. For the present experimental conditions about 3-5% of the ground state molecules are excited to v3 by the laser pulse. If process (2) has a cross section near gas kinetic as expected [lo], the rate of filling of 3~3 will be about 10 times faster than the measured
V-V
rate, and process (3) will be rate limiting
as assumed
in the analysis
leading
to
eq. (4). This is in excellent agreement with previous calculations [3], with work currently in progress [4] on the fluorescence from other vibrational states in CH3F and with the simple Af? argument presented above. Moreover, since the rapid relaxation rate found in CH3F is in very good agreement with V-V exchange rates found in CH4 [9] and SF6 [ 133 it is tempting to sugest that a single mechanism is involved in near resonant energy transfer in polyatomic molecujes. It should be pointed out however that processes such as: CH3F&
= 2) + CH3F(v3 = 1) = CH3F(~1 = 1) f CH3F(0) + AE (= 100 cm-‘)
,
(5)
cannot be ruled out on the basis of this work. From simple SSH [ 1 I] breathing sphere arguments, this process should have the same cross section as process (3) but should also be dependent upon the amount of excitation at ~3. Measurements of the intensity of the fluorescence rise time versus laser power were not feasible due to S/N limitations. Further experiments are underway to measure the rise time of the 2v3 overtone band, and rate and power versus pressure data wilI be reported on elsewhere. In conclusion we would like to point out that a growing body of data is now available for theoretical interpretation. It has been shown that BCl3 [ 121, SF6 [ 13, 141, CH3F [l-4], CH3Cl [ 151, C2H4 [ 161, HF [7], HCI [6], HBr [5], CH4 [S], to name a few, exhibit rapid V-V transfer up the vibrational ladder. It is very likely that this is the mechanism largely responsible for decomposition of samples irradiated at 10 p with high power CO2 lasers [12, 17, 181 since, if the V-V rate is very rapid compared to the V-T/R relaxation, gas molecules can retain excitation at high lying vibrational states. Subsequently, still on a time scale shorter than V-T/R r&xation times, sufficiently high states may be populated leading to bond rupture.
References [11 E. Weitz, G.W. Flynn and A.M. Ronn, Bull. Am. Phyn Sot_ 16 (1971) 42.
[ai
E. Weitz, G.W. Flynn and A.M. Ronn, J. Appl. Phys. 42 (1971) 5 187.
E. Weitz, G.W. Flynn and A.M. Ronn, J. Chem. Phys. 56 (1972) 6060. E. Weitz and G.W. Flynn, J. Chem. Phys., to be published.
151I. Burak, Y. Noter, A.M. Ronn and A. Szijke, Chem. Phys. Letters 16 (1972) 306. 161I. Burak, Y. Noter. A.M. Ronn and A. SzGke, J. Chem. Phys.. to be published; Chem. Phys Letters 17 (1072) 345. [71 R.M. Osgood Jr., A. Javan and P.B. Sackett, AppL Phys. Letters 20 (lY72) 469. [81 GA. Mitterand R.D. Bernstein, J. Phys. Chem. 63 (1959) 710.
191 J.T. Yardley and C.B. Moore, J. Chem. Phys. 49 (1968) 1111. [lOI J.C. Stephenson; R.E. Wood and C.B. Moore, J. Chem. Phys. 48 (1968) 4790. [Ill F.R. Tanczos, J. Chem. Phys. 25 (1956) 439. [I21 N.V. Karlov, Yu.N. Petrox, A.Am. Prokhorov and 0-M. Stel’makh. ZhETF Pis. Red. 11 (1970) 220 [ JETP Letters 11 (1970) 1351. 349
Volume I’l,,num&x f 13j ,[14j [IS] j16]
3’
CHEhfICAL PHYSfCS LETTERS
1 December 1972
RD. B&s, G-W. Fly&
J.T. ~nudt~~ and,A.M. Roan, J. C&-m. Phys. 53 (1970) 3621. J-T. Knudtsan and A.M. Ronn, J. &hem. Phyr, to be published. J.T. Knudtsox and G.W. Flynn, J. Chem. Phys., lo be published. R.I& Bates, C.W:FIynn,
R.C.t Yuan and G.W. Flynn, 3. Chem. Phys., to be published. 1171 C, Bwde, A; Henry and L. Henry, Cdmpt. Rend. Acad. Sci (Paris) 262B (f966) 1389. [ 181 C. Borde, A. Henry and L. Henq, Compt Rend. Acad. Sci (Pkis) 263B (19&I) 619.
:
‘..
.3&l:.,.
”
1 December
CHEMICAL PHYSICS LElTERS
VIBRATION-VIBRATION
ENERGY TRANSFER
IN dI-QF*
1972
,,
Z. KARNY, A.M. RONNS,4 Departments
of
Chemistry
and Physics,
Tel-Aviv
University,
Tel-Aviv.
Israel
1
and Eric WEITZ* and G.W. FLYNN# Department
of Chemistry,
Columbia
University.
New
York, New York
10027.
US.4
Received 4 September 1972
Previous works have reported vibration-vibration and vibration-translation transfer rates in CHJF and CHg F-X mixtures. fn this letter we report the study of the fast V-V transfer rate populating the 3~3, u1 and ~4 states of CHJF. GaseousCHsF was initially exited to the ~3 state by a TEA CO2 laser operating on the P(20) 9.6 g line and collisional pumping to the 3~3, ur and v4 states was measured by monitoring the rise time of the fluorescence at 3000 cm-‘. The rate constant was found to be 2.2 X 10s set-r tom-‘.
Laser induced infrared fluorescence has been used recently to measure energy transfer processes in a number of hydrogen and methyl halide systems [l-7] . Studies of the comparatively slow transfer of energy from vibration to translation and rotation (V-T/R), or to the vibrations of another molecule (V-V) have received most attention. In contrast, the exchange of vibrational energy among molecules of ‘he same kind has only been reported for the hydrogen halides [S-7]. These processes are very fast since in a typical collision only the small amount of energ;r
corresponding to the vibrational anharmonicity is transferred to the rotational and translational degrees of freedom of the colliding molecules. In this experiment we have measured the V-V energy exchange in CH3F by monitoring the fluorescence of the v4 state (C-H stretch at 3000 cm-‘) subsequent to excitation of the v3 state (C-F stretch at 1050 cm-l). The rise time of the fluorescence measures the thermalization of the CH3F ~3 overtone manifold with the v4 (and vl) nearby states whiie the fall tunes measure the V-T/R rate of equilibration with the ground state. A typical Iaser induced fluorescence apparatus was used. The TEA C02-N2-He laser was operated on the F(20) transition of the 9.6 /L band. A photovoltaic InSb detectcr was used in conjunction with a feedback transistor amplifier which also kept a zero bias across the element. The fall time of the detector-amplifier combination was less then 1 psec. The detector was shielded from electrical noise by enclosing the laser and the fluorescence cell in separate copper boxes. Measurements of the u4 fall time were first made and the V-T/R times measured agreed well with those reported by Weitz et al. [4]. Quantitative rise time measurements were made subsequently with a PAR Waveform * This work was supported by tion and the Army Research $ On leave from the Chemistry #Alfred P. Sloan Fel!ow. * National Science Foundation
the Petroleum Research Fund of the American Chemical,Society, the National Science FoundaOffice (Durham). Department, Polytechnic Institute of Brooklyn, BrookIyn, New York 11201, USA. Predoctoral
Trainee. 347
Volume 17, number 3
CHEMICAL
PHYSICS LETTERS
1 December
t972
l
t .
l :
. .
.*
0.1 t
:
.
0.06
*
l
‘
0.02
/ ’
0.2
0.4
0.6
a8
1.0
1.2
1.4 ’
I:6 ’
I.8
1
c P:0rr.
II
Urersy Level D&qmm
SimfM%d
uf CH3F Fig. f. Deactivation rate for faser excited CH3F fiuorescence versus pressure. Slope = 7.2 X 10s secWxtorr-l.
Fig. 2. Energy level diagram of CHsF showing relevant ievels for V-V exchange between the v3 manifold and Y.+,~1 states.
Eductor. For each point shown in fig. I both rise and fall times were taken to ensure Sase fine integrity. The time evolution of the V-V exchange reactions can be described in terms of the following V-V processes
and the s~~fi~ed
energy level diagram shown In fig. 2:
Slv CX-$F(V~= 1) + ~X$F(V~ = 1) * CH3F(v3 = 0) t CH,F(V, = 2) + AL!‘, (= 2C cm-‘)
,
co
(= 40 cm- I > ,
Q>
z--lv “2v CH,W,
=
2) t CH,F(u,
= 1) =*,
CH,F(v,
= 3) + CH,F(Y, = 0) + AE,
-..V
CH,F(v,
= 3) + C!H,F(V, = 0)
x3v
*
CH$
= 0) +- AZ?3 (= 100 cm-‘)
t
(3)
=-3&p and by the slower V-T/R reIz:ration of all the vibrationa levels. All X:, are related to Ci,, through I;1, = Z._, exp(--AEilkT), where AEi is either the energy defect due to anharmonicity or the energy difference between
the 31.9 and u4 states. Jf Iawr excitation of v3 is low, i.e., a small change in the vibrational temperature is achieved, then one may Linearize the rate equations for the [S-71 processes above and obtain the following solution for the population of the 39 level: N3(ti=i(NIo?2~~F/(ivo~2~3,)
exp(-~roT:Iv~C1
- exp(--NoZ3vfll
,
where@ is rhe initial population of the v3 Ievei, No the total number of C!H,F mofecufes, X,,, V-V rates of foiurard and backward reactions (1) through (3).
(4) L’2v,Zfy
are the
This solution does not allow complete separation of ihe.two rates LX:,,and C,,. Since the vibrational tiarmoticity of reaction (2) is considerably smaller than the energy defect of reaction (3) and a four-quantum transi348
1 December 1972
CHEMICALPHYSICS LETTERS
Volume 17, number 3
tion is involved in (3) it can be assumed that C2v Z+ Csv and that the rate measured should then be the slower of the two processes. The rise times of the fluorescence measurements were analyzed in terms of (4) and an effective rate constant K was plotted against CH,F pressure yielding a slope of (2.2 k 0.4) X IO5 set-1 torr-’ as shown in fig. 1. With this measured value of the rate constant one can calculate the cross section for collisions for process (3). For 1 torr of pressure: 1/7=K=nvu,
0 =
1.7 A2 ,
which is l/25 of the known gas kinetic cross section for CH,F, 44.1 A2 [S] . For process (2) one has to consider the number of molecules excited to v3 and to 2~3 by the laser pulse. For the present experimental conditions about 3-5% of the ground state molecules are excited to v3 by the laser pulse. If process (2) has a cross section near gas kinetic as expected [lo], the rate of filling of 3~3 will be about 10 times faster than the measured
V-V
rate, and process (3) will be rate limiting
as assumed
in the analysis
leading
to
eq. (4). This is in excellent agreement with previous calculations [3], with work currently in progress [4] on the fluorescence from other vibrational states in CH3F and with the simple Af? argument presented above. Moreover, since the rapid relaxation rate found in CH3F is in very good agreement with V-V exchange rates found in CH4 [9] and SF6 [ 133 it is tempting to sugest that a single mechanism is involved in near resonant energy transfer in polyatomic molecujes. It should be pointed out however that processes such as: CH3F&
= 2) + CH3F(v3 = 1) = CH3F(~1 = 1) f CH3F(0) + AE (= 100 cm-‘)
,
(5)
cannot be ruled out on the basis of this work. From simple SSH [ 1 I] breathing sphere arguments, this process should have the same cross section as process (3) but should also be dependent upon the amount of excitation at ~3. Measurements of the intensity of the fluorescence rise time versus laser power were not feasible due to S/N limitations. Further experiments are underway to measure the rise time of the 2v3 overtone band, and rate and power versus pressure data wilI be reported on elsewhere. In conclusion we would like to point out that a growing body of data is now available for theoretical interpretation. It has been shown that BCl3 [ 121, SF6 [ 13, 141, CH3F [l-4], CH3Cl [ 151, C2H4 [ 161, HF [7], HCI [6], HBr [5], CH4 [S], to name a few, exhibit rapid V-V transfer up the vibrational ladder. It is very likely that this is the mechanism largely responsible for decomposition of samples irradiated at 10 p with high power CO2 lasers [12, 17, 181 since, if the V-V rate is very rapid compared to the V-T/R relaxation, gas molecules can retain excitation at high lying vibrational states. Subsequently, still on a time scale shorter than V-T/R r&xation times, sufficiently high states may be populated leading to bond rupture.
References [11 E. Weitz, G.W. Flynn and A.M. Ronn, Bull. Am. Phyn Sot_ 16 (1971) 42.
[ai
E. Weitz, G.W. Flynn and A.M. Ronn, J. Appl. Phys. 42 (1971) 5 187.
E. Weitz, G.W. Flynn and A.M. Ronn, J. Chem. Phys. 56 (1972) 6060. E. Weitz and G.W. Flynn, J. Chem. Phys., to be published.
151I. Burak, Y. Noter, A.M. Ronn and A. Szijke, Chem. Phys. Letters 16 (1972) 306. 161I. Burak, Y. Noter. A.M. Ronn and A. SzGke, J. Chem. Phys.. to be published; Chem. Phys Letters 17 (1072) 345. [71 R.M. Osgood Jr., A. Javan and P.B. Sackett, AppL Phys. Letters 20 (lY72) 469. [81 GA. Mitterand R.D. Bernstein, J. Phys. Chem. 63 (1959) 710.
191 J.T. Yardley and C.B. Moore, J. Chem. Phys. 49 (1968) 1111. [lOI J.C. Stephenson; R.E. Wood and C.B. Moore, J. Chem. Phys. 48 (1968) 4790. [Ill F.R. Tanczos, J. Chem. Phys. 25 (1956) 439. [I21 N.V. Karlov, Yu.N. Petrox, A.Am. Prokhorov and 0-M. Stel’makh. ZhETF Pis. Red. 11 (1970) 220 [ JETP Letters 11 (1970) 1351. 349
Volume I’l,,num&x f 13j ,[14j [IS] j16]
3’
CHEhfICAL PHYSfCS LETTERS
1 December 1972
RD. B&s, G-W. Fly&
J.T. ~nudt~~ and,A.M. Roan, J. C&-m. Phys. 53 (1970) 3621. J-T. Knudtsan and A.M. Ronn, J. &hem. Phyr, to be published. J.T. Knudtsox and G.W. Flynn, J. Chem. Phys., lo be published. R.I& Bates, C.W:FIynn,
R.C.t Yuan and G.W. Flynn, 3. Chem. Phys., to be published. 1171 C, Bwde, A; Henry and L. Henry, Cdmpt. Rend. Acad. Sci (Paris) 262B (f966) 1389. [ 181 C. Borde, A. Henry and L. Henq, Compt Rend. Acad. Sci (Pkis) 263B (19&I) 619.
:
‘..
.3&l:.,.
”