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Deactivation of vibrationally excited CD3H using laser-induced fluorescence
Volume 47, number 2
CHEMICAL
PHYSICS
LETTERS
DEACTIVATION OF VIBRATIONALLY EXCITED CD+ Walter S. DROZDOSKI,
Asghar FAKHR
Department of Chemist.y. Georgetown Washington, D-C. 20057, USA Received 22 November
and Richard
15 April I977
USXNGLASER-INDUCED FLUORESCENCE
D. BATES Jr.
University,
1976
Infrared fluorescence observed after exciting to 0.5 (u = 1) of CD3H with a Q-switched CO2 laser yieIds the exponential Rate constants for deactivation of CD3H by rare gases vary from IA (for deactivation rate constant of 0.84 mf’ torr-‘. He) to 0.029 (for Xe) ms-’ torr-‘_
1. Introduction Laser-induced fluorescence is an important technique for studying the decay of selective vibrational excitation in small polyatomic molecules [ 11. A general sequence of important deactivation steps has been found for most polyatomic molecules studied by this method. Following an initial small perturbation of the vibrational populations in a specific mode by the laser pulse. the first step in the loss of vibrational selectivity involves the collisional excitation of some or all of the other vibrational degrees of freedom in the molecule, commonly known as V + V transfer. The second step involves the equilibration of these now-coupled vibrational degrees of freedom with the translational and rotational degrees of freedom, termed V + T, R transfer. Finally, in some cases, the subsequent cooling of the laser-heated gas by a transport process to the cell wall can be observed. The methyl halides have provided an interesting and accessible series for the study of vibrational energy transfer processes. Examination of the deactivation mechanisms in this series of molecules as well as between the hydrogen and deuterium analogs provide important comparisons. CHSF has been studied extensively [2--51, and investigations of CH,Cl [6-81, CH,Br [9],CH31 [lO],CD31 [ll],CDsBr [12],and CDsF [13] have been completed. A recent detailed study of CH4 extended earlier work on this molecule [14-161.
This paper describes a study of CD,H, a molecrde that complements the methyl halide series, and reports the self-deactivation rate constants (V + T, R) for several states of CD3H and the deactivation efficiencies for the inert gases as collision partners_
2. Experimental A detailed description of the Q-switched CO, Iaser fluorescence apparatus is available [17,18]. The laser is tuned by a diffraction grating to the P(30) !ine of the 9.6 p transition of CO2 and used to excite the Qbranch of the CD3 d-deformation fundamental of CD3H at 1037 cm-’ [19] _ Infrared fluorescence can be detected at right angles to the laser axis in the regions around 3.3 fl, 4.5 p, and 7.8 II. The v2 and u4 fundamentals at 4.7 lu and 4.4 ,u were not isolated and will be referred to jointly as 4.5 p fluorescence. The 3.3 or and 4.5 or fluorescence signals were observed by using an In :Sb detector (77 K)_ A Hg:Cd :Te detector (77 K) was used to observe 7.8 p fluorescence. Combined laser pulse, detector, and electronic risetimes for the two observation systems were approximately 5w and 2 ~.ls, respectively. Scattered laser light and very weak signals necessitated the use of a 7.2-8-O p germanium narrow bandpass filter in conjunction with LiF and MgF, filters to isolate the 7.8 p fluorescence. Fluorescence signals from the respective detectors were amplified, averaged on a waveform eductor, and re309
CHEMICAL PHYSICS LETTERS
Volume 47, number 2
corded for analysis. Fit of the data to an exponential decay produced standard deviations of 2% or less in the calculated rates. Research grade CD3H with an isotopic purity of greater than 94% (principal impurity cD2l-I~) and a chemical purity of greater than 99% was used. Rare gases had stated purities of 99.995% or greater. The deactivation rates for CD,H by the rare gases were obtained by placing a specific amount of the gas and a constant amount of CD3H into pre-calibrated sections of the vacuum system. Samples were mixed by opening a vaIve between the two gases and allowing them to diffuse together. A new sample was used for each data point. The rates for deactivation by rare gases were measured by using the combined 3.3 12and 4.5 p fluorescence from CD,H_ Sufficient time was allowed for the gases to mix before the final measurements were taken., Frequent checking of the deactivation rates as a function of time showed consistent results after an initial period. Qutgassing and/or leak rates for the entire mixing chamber and cell typically were between 5 mtorr/h and 10 mtorr/h, and were insignificant at pressures and times used.
3. ResuIts The partial energy level diagram for CD,H is shown in fig. 1. Strong fhrorescence at 4.5 p was obtained
CD$l
from the ~2 and v4 levels. Preliminary data showed that the 3.3 p and 4.5 p fluorescences yielded the same deactivation rate, indicating that the fall of the fluorescence was characteristic of relaxation of the co.@ed vibrational modes. This was confirmed when fluorescence from the us level at 7.8 fi also yielded the same deactivation rate. The 3.3 p and 4.5 p signals were then observed simultaneously to maximize signal to noise ratios. These deactivation rates are shown as a function of CDsH pressure in fig. 2. Below one torr of pure CD3H, deviations from linearity in this plot become noticeable as diffusion contributions to the rate become increasingIy important. Signals at 7.8 II_were very weak and required longer signal averaging to obtain satisfactory curves. The decay portion of the ffuorescence curves showed slight translational heating of the CD3H following conversion of vibrational energy to translational and rotational energy. This tr~slation~y heated gas then decayed exponentially on the scale of milliseconds to tens ofmiihseconds, depending on the gas pressure. The heating tail of the ffuorescence curve was nearly removed with approximately a 15 : 1 ratio of Ar:CD$ [201The deactivation rates were also measured for He, Ne, Ar, Kr, and Xe as collision partners for CDsH and are presented in table I. For aU the piots of rare gas deactivation with a constant amount of CDSH, they intercept (~7~~ gas = 0) always agreed with the CDsH selfdeactivation value within expe~meRt~ error. A typical
ENERGY LEVELS
Fig_ 1. Par&I vibrational energy level d&ram for CD3H showing the mode pumped by the Iaser and the states from which fluorescence was observed. Infkred active states are IabeIled IR.
310
i5 April 1977
CDaH PRESSURE(TORR} Fig. 2. PIot of the self-deactivation of the combined 3.3 JZand 4.5 P fluorescence of C&H. The least squares determined slope at 25°C is 0.84 ms-1 ton-1 .
CHEMICAL
Volume 47, number 2 Table 1 Measured V--c T, R rate constants
PHYSICS
for CD3H
CD3H fluorescence
Collision partner
Rate constant (ms-’ torr-‘)
3.3 II + 4.5 Il
CD3H He Ne Ar Kr Xe
0.84 f 0.02 1.4 + 0.1 0.16 f 0.02 0.058 * 0.002 0.042 f 0.002 0.029 * 0.001
7.8 J.I
CD3H
0.86 t 0.04
-
2) Error limits are 20. b, Number of collisions needed for deactivation from formula: =) Experimental probability/collision, Pexp = l/Z.
5 torr CD,H
40
1
10
I
20
I
30
I
40
I
50
I
60
Ar PRESSURE
!
70
1
a0
I
90
I
loo
I( 110
120
(TORR)
Fig. 3. Plot of the deactivation of the combined 3.3 JI and 4.5 p fluorescence of CD3H 2s a function of Ar pressure, with 2 fixed CD3H pressure of 5.0 torr. The least squares determined slope at 25°C is 0.058
plot of deactivation in fig. 3.
i5 April L977
LETTERS
ms-’
torr-‘.
rate versus argon pressure
is shown
4. Discussion
The V + T, R rate obtained from both the 7.8 j.~and 3-4.5 p fluorescence bands is 0.84 ms-r torr-l. The V + V steps in the overall energy transfer process are efficient in coupling both these sets of states with the initially excited state on a time-scale short compared with the V + T, R process. Experiments currently underway indicate these V + V transfer rates are all on
a)
Number of
Probability
collisions b)
per collision Cl
14 000 10 000 56 000 160 000 210 000 330 000 14 000
2 = 2.56 X IO6 [(oa + ob)/2]*~~-‘~
7-L 9.8 1.8 6.3 4.8 _3.0
x x x x x x
10-s 10s 10” lo+ 1O-5 10-s
7.3 x 10-s
(10-3/rate).
the order of 200 ms-l torr-I. This self-deactivation value of CD,H is an additional example of the very limited number of molecules with more than three atoms having V + T, R rates less than 1 ms-r torreL _ It is also in good agreement with the values of 0.59 ms-r torr-r for CH3F and 0.44 ms-t torref for CD3F. The lowest vibrational mode in both of these molecules is at about the same energy as the lowest modes in CD3H. The magnitude of the vibrational energy quantum is an important factor in determining the effectiveness of deactivation of that vibrational degree of freedom in the total V + T, R relaxation. Thus the lowest vibrational modes are generally regarded as prime contributors to the V * T, R process E 14I_ Fig_ indicates that v3, us, and v6 have their Iowest excited vibrational state in the 1000 to 1300 cm-r region, but that the other modes lie 850 cm-1 or more higher in energy. Thus these three lower lying modes probably all contribute, in varying percentages, to the overall V + T, R deactivation rate. The results for the V + T, R deactivation of’CD,H by collisions with rare gas atoms are displayed in fig. 4. The log of the probability of deactivation per cotlision is shown as a function of the square root of the reduced mass of the collision partners. This choice of coordinates Schwartz
is based on the theory first developed by
et ai. [2 11, and later modified
results for CD,H give-a good shown in fig. 4 are data from rare gas deactivation of CH4 Fig. 4 is predicted by SSH
[22-24I- The fit to a straight line. Ako previous studies of the [15] and CR,1 [EOI. theory to be tinear when
CHEMICAL PHYSICS LETIERS
Volume 47, number 2
iional velocity (r~-) f2.51. The ratio of the two velocities is related to the reduced mass of the colliding pair P, the radius of the rotor ri, and the molecular moment of inertia f, by the fo~o~g equation 1251.
t I
CD,@ i 10-aIc
R =lq&
=@dQp2.
Though this relation was derived for diatomic-rare
i
3
J
Fig. 4. Piot of experimental CD~H(O), CH4(*), and 031(A) deactivation probabilities versus tie square root of the reduced txss of the collision partners. The citcled symbols represent the self-deactivation points whereas the mtcircled symbols rep resent the deactivation by collisiun with rare gas atoms.
the f ransIationa1 velocity of the colliding molecules is the primary factor in determining the deactivation probab~iy. A straight Iine has not been obtained experimentahy for any of the methyl haiides or their deuterated analogs. For these curves, *he point representing the deactivation of CH,X/CD,X by He lies above the line determined by the other rare gas points. As shown in fig. 4, CD,H and CH, have the He deactivation point lying on the line determined by all the points. In the CH3X series, as X goes From F to 1, the straight line representing rare gas deactivation of the methyl halide becomes more horizontal, to the point that the line for CD31 is approximately horizontal. Moore has indicated that the V + R ~ont~bution becomes significantly important when the rotational velocity (2~~) of the molecule is greater than the transla312
15 April 1977
gas collisions, it is commoniy applied to polyatomics by considering only the most favorable rotational degree of freedom [IO]. Table 2 shows the calculated R values for CD,H compared with those For members of the CH3X series [IO]. The moments of inertia for CD3H areI, =I, = 8.537 X 10W40 gcm2, and&. = 10.634 X lOa g cm2, with Ic having been used in the calculations shown in table 2 [26]. Due to the approximate nature of the theories available for examining V -+ T, R energy transfer, application of these theories to pofyatomic molecules to produce quantitative comparisons is not successful. In examining the trends shown in table 2, the least variation in the values of R as one goes from He to Xe is observed for CD,H, whiIe the greatest variation is present for CH3 I. This indicates that the variation in the contribution of V + R relaxation to the totd V + T, R process is less for CD,H than for the methyl halides included for comparison, In fact, the experimental curve given in fig. 4 does not show the curvature observed for some methyl halides. This curvature was related to the increasing importance of V + R transfer. Moreover, the slope of the straight line in fig. 4 is much greater for CD,H than for CH31. This is consistent with the theoretical predictions of SSH type V --t T theory that a straight line predicting decreasing probability as the rare gas is varied from He to Xe should be obtained with the slope proportional
to the energy of the lowest
state. However, the results for CH4, for which the Iowest state is of greater energy than the three lowest funTable 2 Values of R calculated for C&H using R = &d2/r) In, and from ref. [ 101 for the other gases
CD3H CH3F CH3cI CH3Br CH3i
He
Ne
Ar
Kr
Xe
1.4 0.99 1.1 1.1 1.1
2.4 I.9 2.2 2.3 2.4
2.7 2.2 2.7 3.0 3.2
3.0 2.6 3.2 3.8 4.2
3.1 ;:; 4.3 4.7
Volume 47, number 2
CHEMICAL PHYSICS LETTERS
da~entals of CD3H, fit a straight line, but the slope is slightly less than for CD3H.
ES ApriI I.977
References E. Weitz and G-W. Flynn, Ann. Rev. Phyn Chem. 25 (1974) 27s. f21 E. Web, G-W. FIynn and A.M. Rann, 1F.Cf&tt_ P&S, 56 (1972) 6060. r31 E. We& and G.W. Flynn, I. Cbem Phys. 58 (X933) 2679. t41 E. Weitz and G.W Ftynn, J. Chem. I?hys. 58 (t973)
iit
5. Condusions Coll~ion~ deactIvatiou of four coupled vibrational modes in the CD3H molecule have been examined experiqentally. For the several infrared fluorescences observed, a V + T, R rate constant of 0.84 ms-l torr was established. The pattern of energy transfer is similar to the CH3XfCD,H series, involving a rapid collisiondependent coupling of the vibrational degrees of freedom followed by a considerably slower V + T, R deactivation. However, in comparing the deactivation probability of collisions with rare gas atoms, the CD3H results are more similar to those obtained for CH, than to those observed for the analogous CH3X molecules. Most probably, the V -+ T, R deactivation of CD3H involves significant contributions from the Iowest three vibrational fundamentals. Comparison with existing V -+ T, R theories provides good qualitative trends in the CDS&rare
gas results, and indicates
the impor-
tance of V + T mechanisms in these coliisions, A future paper wiI1 examine the activation kinetics for the ~bration~ degrees of freedom in CD3H other than those initially excited, and will analyze in depth the theoretical correlation of ail the rate constants studied.
Acknowledgement The authors gratefully acknowledge the partial support of this research by the Petroleum Research Fund, administered by the American Chemical Society2 the Research Corporation, and the National Science Foundation, the Naval Research Laboratories for the loan of the Hg :Cd I Te detector used in the experiments, and Ruthann Bates for critically reading the mauusscript.
2781.
1st F.R. Grabiner, G-W. E31nn and AM_ Ronn, 3. c&m. Phys. 59 (i973)
2330.
161 J-T. Knudtson and G.W. Flynn, J. Cbem. Phys, 5% (L973)
2684. I71 F-R. Grabiner and G.W. Flynn, 3, Chem Phys. 60 (l.474) 398. IS1 S.hl. Lee and AX Ronn, C&m. Phyn Letters 22 f1973) 279. [91 B-L. Earl and A.&i, Ronn, Chem. PIxys. Letters41 (1976) 29. flOl Y. Langsam, S.?+i~Lee and A.&¶.ROM, Chem. P’ftys. L4 (1976) 3?5.lllf Y. Langsam, SM. Lee and A.M. Rona, Cheat. Pkys_ i5 (1976) 43. fl21 S.T. Lia, B-L. Earl and A.M. Ronn, &hem. Pltys. 16 (1976) 117. ll3l LA. Gamss, B-H. Kohn, A.M. Ronn and G-IV. Etynn, Chem. Phys. Letters41 (L976) 4X3. t141 J.T. Yardley and C.B. Moore, 3. Chem. Pkys- 49 (V368) 11x1. I151 3-T. YardIey, M.N. Fe&g and C-B. &ifoore,$. Chem. Phys. 52 (1970) 1450. U61 P. Hess and C.B. Moore, J. Chem. @tys. 65 fI976) 2339. [X71 R-D. Bates Jr_ G-W_ Flynn. J-T. Kttudtson and AX Ronn, J. Chem. Phys. 53 (I970) 3621. USI G.W. Flynn, in: Chemical and biockernic;rf ~p~I~~~ian~ of lasers, ed. C-B. Moore (Academic Press, New York, 1974). u91 J.K. Wilmsburst and H.J. Bernstein, Can. J. Chem. 35 (1957) 226. I201 R.D. Bates Jr., J.T. Knudtson, G-W. FIynn and AX. Ronn, Citem- Phys. Letters 8 (1972) 104. 1211 R.N. Schwartz, 2.X SIawsky and K-T. Wenfeld, I.. Ckem Pbys. 20 (1952) 1.591. I221 R.N. Schwartz and K-T. Herzfeld, J. Cbem Phys.‘kZ (1954) 767. [231 F.R. Tanczos, I. Cbem. Phys. 25 ZI956) 439. J.L. Stretton, Trans. Faraday Sot- 6L 4L96SI 10% fz; C.B. Moore, J_ Cbem. Phyr; 43 (i96S) 2979. f261 W.N.J. Cbitds and HA. J&n, Proc. Roy. SOC A I69 (1939) 428.
CHEMICAL
PHYSICS
LETTERS
DEACTIVATION OF VIBRATIONALLY EXCITED CD+ Walter S. DROZDOSKI,
Asghar FAKHR
Department of Chemist.y. Georgetown Washington, D-C. 20057, USA Received 22 November
and Richard
15 April I977
USXNGLASER-INDUCED FLUORESCENCE
D. BATES Jr.
University,
1976
Infrared fluorescence observed after exciting to 0.5 (u = 1) of CD3H with a Q-switched CO2 laser yieIds the exponential Rate constants for deactivation of CD3H by rare gases vary from IA (for deactivation rate constant of 0.84 mf’ torr-‘. He) to 0.029 (for Xe) ms-’ torr-‘_
1. Introduction Laser-induced fluorescence is an important technique for studying the decay of selective vibrational excitation in small polyatomic molecules [ 11. A general sequence of important deactivation steps has been found for most polyatomic molecules studied by this method. Following an initial small perturbation of the vibrational populations in a specific mode by the laser pulse. the first step in the loss of vibrational selectivity involves the collisional excitation of some or all of the other vibrational degrees of freedom in the molecule, commonly known as V + V transfer. The second step involves the equilibration of these now-coupled vibrational degrees of freedom with the translational and rotational degrees of freedom, termed V + T, R transfer. Finally, in some cases, the subsequent cooling of the laser-heated gas by a transport process to the cell wall can be observed. The methyl halides have provided an interesting and accessible series for the study of vibrational energy transfer processes. Examination of the deactivation mechanisms in this series of molecules as well as between the hydrogen and deuterium analogs provide important comparisons. CHSF has been studied extensively [2--51, and investigations of CH,Cl [6-81, CH,Br [9],CH31 [lO],CD31 [ll],CDsBr [12],and CDsF [13] have been completed. A recent detailed study of CH4 extended earlier work on this molecule [14-161.
This paper describes a study of CD,H, a molecrde that complements the methyl halide series, and reports the self-deactivation rate constants (V + T, R) for several states of CD3H and the deactivation efficiencies for the inert gases as collision partners_
2. Experimental A detailed description of the Q-switched CO, Iaser fluorescence apparatus is available [17,18]. The laser is tuned by a diffraction grating to the P(30) !ine of the 9.6 p transition of CO2 and used to excite the Qbranch of the CD3 d-deformation fundamental of CD3H at 1037 cm-’ [19] _ Infrared fluorescence can be detected at right angles to the laser axis in the regions around 3.3 fl, 4.5 p, and 7.8 II. The v2 and u4 fundamentals at 4.7 lu and 4.4 ,u were not isolated and will be referred to jointly as 4.5 p fluorescence. The 3.3 or and 4.5 or fluorescence signals were observed by using an In :Sb detector (77 K)_ A Hg:Cd :Te detector (77 K) was used to observe 7.8 p fluorescence. Combined laser pulse, detector, and electronic risetimes for the two observation systems were approximately 5w and 2 ~.ls, respectively. Scattered laser light and very weak signals necessitated the use of a 7.2-8-O p germanium narrow bandpass filter in conjunction with LiF and MgF, filters to isolate the 7.8 p fluorescence. Fluorescence signals from the respective detectors were amplified, averaged on a waveform eductor, and re309
CHEMICAL PHYSICS LETTERS
Volume 47, number 2
corded for analysis. Fit of the data to an exponential decay produced standard deviations of 2% or less in the calculated rates. Research grade CD3H with an isotopic purity of greater than 94% (principal impurity cD2l-I~) and a chemical purity of greater than 99% was used. Rare gases had stated purities of 99.995% or greater. The deactivation rates for CD,H by the rare gases were obtained by placing a specific amount of the gas and a constant amount of CD3H into pre-calibrated sections of the vacuum system. Samples were mixed by opening a vaIve between the two gases and allowing them to diffuse together. A new sample was used for each data point. The rates for deactivation by rare gases were measured by using the combined 3.3 12and 4.5 p fluorescence from CD,H_ Sufficient time was allowed for the gases to mix before the final measurements were taken., Frequent checking of the deactivation rates as a function of time showed consistent results after an initial period. Qutgassing and/or leak rates for the entire mixing chamber and cell typically were between 5 mtorr/h and 10 mtorr/h, and were insignificant at pressures and times used.
3. ResuIts The partial energy level diagram for CD,H is shown in fig. 1. Strong fhrorescence at 4.5 p was obtained
CD$l
from the ~2 and v4 levels. Preliminary data showed that the 3.3 p and 4.5 p fluorescences yielded the same deactivation rate, indicating that the fall of the fluorescence was characteristic of relaxation of the co.@ed vibrational modes. This was confirmed when fluorescence from the us level at 7.8 fi also yielded the same deactivation rate. The 3.3 p and 4.5 p signals were then observed simultaneously to maximize signal to noise ratios. These deactivation rates are shown as a function of CDsH pressure in fig. 2. Below one torr of pure CD3H, deviations from linearity in this plot become noticeable as diffusion contributions to the rate become increasingIy important. Signals at 7.8 II_were very weak and required longer signal averaging to obtain satisfactory curves. The decay portion of the ffuorescence curves showed slight translational heating of the CD3H following conversion of vibrational energy to translational and rotational energy. This tr~slation~y heated gas then decayed exponentially on the scale of milliseconds to tens ofmiihseconds, depending on the gas pressure. The heating tail of the ffuorescence curve was nearly removed with approximately a 15 : 1 ratio of Ar:CD$ [201The deactivation rates were also measured for He, Ne, Ar, Kr, and Xe as collision partners for CDsH and are presented in table I. For aU the piots of rare gas deactivation with a constant amount of CDSH, they intercept (~7~~ gas = 0) always agreed with the CDsH selfdeactivation value within expe~meRt~ error. A typical
ENERGY LEVELS
Fig_ 1. Par&I vibrational energy level d&ram for CD3H showing the mode pumped by the Iaser and the states from which fluorescence was observed. Infkred active states are IabeIled IR.
310
i5 April 1977
CDaH PRESSURE(TORR} Fig. 2. PIot of the self-deactivation of the combined 3.3 JZand 4.5 P fluorescence of C&H. The least squares determined slope at 25°C is 0.84 ms-1 ton-1 .
CHEMICAL
Volume 47, number 2 Table 1 Measured V--c T, R rate constants
PHYSICS
for CD3H
CD3H fluorescence
Collision partner
Rate constant (ms-’ torr-‘)
3.3 II + 4.5 Il
CD3H He Ne Ar Kr Xe
0.84 f 0.02 1.4 + 0.1 0.16 f 0.02 0.058 * 0.002 0.042 f 0.002 0.029 * 0.001
7.8 J.I
CD3H
0.86 t 0.04
-
2) Error limits are 20. b, Number of collisions needed for deactivation from formula: =) Experimental probability/collision, Pexp = l/Z.
5 torr CD,H
40
1
10
I
20
I
30
I
40
I
50
I
60
Ar PRESSURE
!
70
1
a0
I
90
I
loo
I( 110
120
(TORR)
Fig. 3. Plot of the deactivation of the combined 3.3 JI and 4.5 p fluorescence of CD3H 2s a function of Ar pressure, with 2 fixed CD3H pressure of 5.0 torr. The least squares determined slope at 25°C is 0.058
plot of deactivation in fig. 3.
i5 April L977
LETTERS
ms-’
torr-‘.
rate versus argon pressure
is shown
4. Discussion
The V + T, R rate obtained from both the 7.8 j.~and 3-4.5 p fluorescence bands is 0.84 ms-r torr-l. The V + V steps in the overall energy transfer process are efficient in coupling both these sets of states with the initially excited state on a time-scale short compared with the V + T, R process. Experiments currently underway indicate these V + V transfer rates are all on
a)
Number of
Probability
collisions b)
per collision Cl
14 000 10 000 56 000 160 000 210 000 330 000 14 000
2 = 2.56 X IO6 [(oa + ob)/2]*~~-‘~
7-L 9.8 1.8 6.3 4.8 _3.0
x x x x x x
10-s 10s 10” lo+ 1O-5 10-s
7.3 x 10-s
(10-3/rate).
the order of 200 ms-l torr-I. This self-deactivation value of CD,H is an additional example of the very limited number of molecules with more than three atoms having V + T, R rates less than 1 ms-r torreL _ It is also in good agreement with the values of 0.59 ms-r torr-r for CH3F and 0.44 ms-t torref for CD3F. The lowest vibrational mode in both of these molecules is at about the same energy as the lowest modes in CD3H. The magnitude of the vibrational energy quantum is an important factor in determining the effectiveness of deactivation of that vibrational degree of freedom in the total V + T, R relaxation. Thus the lowest vibrational modes are generally regarded as prime contributors to the V * T, R process E 14I_ Fig_ indicates that v3, us, and v6 have their Iowest excited vibrational state in the 1000 to 1300 cm-r region, but that the other modes lie 850 cm-1 or more higher in energy. Thus these three lower lying modes probably all contribute, in varying percentages, to the overall V + T, R deactivation rate. The results for the V + T, R deactivation of’CD,H by collisions with rare gas atoms are displayed in fig. 4. The log of the probability of deactivation per cotlision is shown as a function of the square root of the reduced mass of the collision partners. This choice of coordinates Schwartz
is based on the theory first developed by
et ai. [2 11, and later modified
results for CD,H give-a good shown in fig. 4 are data from rare gas deactivation of CH4 Fig. 4 is predicted by SSH
[22-24I- The fit to a straight line. Ako previous studies of the [15] and CR,1 [EOI. theory to be tinear when
CHEMICAL PHYSICS LETIERS
Volume 47, number 2
iional velocity (r~-) f2.51. The ratio of the two velocities is related to the reduced mass of the colliding pair P, the radius of the rotor ri, and the molecular moment of inertia f, by the fo~o~g equation 1251.
t I
CD,@ i 10-aIc
R =lq&
=@dQp2.
Though this relation was derived for diatomic-rare
i
3
J
Fig. 4. Piot of experimental CD~H(O), CH4(*), and 031(A) deactivation probabilities versus tie square root of the reduced txss of the collision partners. The citcled symbols represent the self-deactivation points whereas the mtcircled symbols rep resent the deactivation by collisiun with rare gas atoms.
the f ransIationa1 velocity of the colliding molecules is the primary factor in determining the deactivation probab~iy. A straight Iine has not been obtained experimentahy for any of the methyl haiides or their deuterated analogs. For these curves, *he point representing the deactivation of CH,X/CD,X by He lies above the line determined by the other rare gas points. As shown in fig. 4, CD,H and CH, have the He deactivation point lying on the line determined by all the points. In the CH3X series, as X goes From F to 1, the straight line representing rare gas deactivation of the methyl halide becomes more horizontal, to the point that the line for CD31 is approximately horizontal. Moore has indicated that the V + R ~ont~bution becomes significantly important when the rotational velocity (2~~) of the molecule is greater than the transla312
15 April 1977
gas collisions, it is commoniy applied to polyatomics by considering only the most favorable rotational degree of freedom [IO]. Table 2 shows the calculated R values for CD,H compared with those For members of the CH3X series [IO]. The moments of inertia for CD3H areI, =I, = 8.537 X 10W40 gcm2, and&. = 10.634 X lOa g cm2, with Ic having been used in the calculations shown in table 2 [26]. Due to the approximate nature of the theories available for examining V -+ T, R energy transfer, application of these theories to pofyatomic molecules to produce quantitative comparisons is not successful. In examining the trends shown in table 2, the least variation in the values of R as one goes from He to Xe is observed for CD,H, whiIe the greatest variation is present for CH3 I. This indicates that the variation in the contribution of V + R relaxation to the totd V + T, R process is less for CD,H than for the methyl halides included for comparison, In fact, the experimental curve given in fig. 4 does not show the curvature observed for some methyl halides. This curvature was related to the increasing importance of V + R transfer. Moreover, the slope of the straight line in fig. 4 is much greater for CD,H than for CH31. This is consistent with the theoretical predictions of SSH type V --t T theory that a straight line predicting decreasing probability as the rare gas is varied from He to Xe should be obtained with the slope proportional
to the energy of the lowest
state. However, the results for CH4, for which the Iowest state is of greater energy than the three lowest funTable 2 Values of R calculated for C&H using R = &d2/r) In, and from ref. [ 101 for the other gases
CD3H CH3F CH3cI CH3Br CH3i
He
Ne
Ar
Kr
Xe
1.4 0.99 1.1 1.1 1.1
2.4 I.9 2.2 2.3 2.4
2.7 2.2 2.7 3.0 3.2
3.0 2.6 3.2 3.8 4.2
3.1 ;:; 4.3 4.7
Volume 47, number 2
CHEMICAL PHYSICS LETTERS
da~entals of CD3H, fit a straight line, but the slope is slightly less than for CD3H.
ES ApriI I.977
References E. Weitz and G-W. Flynn, Ann. Rev. Phyn Chem. 25 (1974) 27s. f21 E. Web, G-W. FIynn and A.M. Rann, 1F.Cf&tt_ P&S, 56 (1972) 6060. r31 E. We& and G.W. Flynn, I. Cbem Phys. 58 (X933) 2679. t41 E. Weitz and G.W Ftynn, J. Chem. I?hys. 58 (t973)
iit
5. Condusions Coll~ion~ deactIvatiou of four coupled vibrational modes in the CD3H molecule have been examined experiqentally. For the several infrared fluorescences observed, a V + T, R rate constant of 0.84 ms-l torr was established. The pattern of energy transfer is similar to the CH3XfCD,H series, involving a rapid collisiondependent coupling of the vibrational degrees of freedom followed by a considerably slower V + T, R deactivation. However, in comparing the deactivation probability of collisions with rare gas atoms, the CD3H results are more similar to those obtained for CH, than to those observed for the analogous CH3X molecules. Most probably, the V -+ T, R deactivation of CD3H involves significant contributions from the Iowest three vibrational fundamentals. Comparison with existing V -+ T, R theories provides good qualitative trends in the CDS&rare
gas results, and indicates
the impor-
tance of V + T mechanisms in these coliisions, A future paper wiI1 examine the activation kinetics for the ~bration~ degrees of freedom in CD3H other than those initially excited, and will analyze in depth the theoretical correlation of ail the rate constants studied.
Acknowledgement The authors gratefully acknowledge the partial support of this research by the Petroleum Research Fund, administered by the American Chemical Society2 the Research Corporation, and the National Science Foundation, the Naval Research Laboratories for the loan of the Hg :Cd I Te detector used in the experiments, and Ruthann Bates for critically reading the mauusscript.
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