J . Phys. Chem. 1987, 91, 5540-5543
5540
The first step is instantaneous ( 7 < 0.8 ps) on the time scale of the experiment. The second step involves either rearrangement of the coordinated ligand or exchange with another solvent molecule. Studies of the ligand displacement reactions of Cr(CO),L show that the mechanism follows a dissociative pathway.’ As a result, we would expect that the dissociation is rate-limiting. It is straightforward to show that the time-dependent concentrations are given by [Cr-alkyl(t)] . . =
Y1 - kz - k3elll
[Cr-alkyl(O)]
Y1
+
Y2
-72
- 71
[Cr-hydroxyl(t)] = klk3[Cr-alkyl(0)] X
.’[
YlYZ
Yl(Y1
- 72)
e-71:
+
] ]
- k2 - k3e-T2r Y2
1 YZ(Y2
- 71)
e-’t’2f
(4)
(5)
where y,and y2 are the negative roots to the following quadratic equation. (7) Geoffroy, G. L.; Wrighton, M. S. Organometallic Photochemistry; Academic: New York, 1979.
y2 + r ( k l
+ k2 + k,) + klk3 = 0
(6)
From the solvation dynamics in cyclohexane and methanol, it is clear that k2, k3 >> kl.’g In addition, these studies show that solvent coordination can occur as fast as < O S ps. If we assume that l / k 2 and l / k 3 are 0.5 ps, we obtain a half-life for the dissociation of 180 f 50 ps. The dotted lines in Figure 2 show this fit of the above equations to the experimental data. The value of i l k l is not affected by changing the association lifetimes (k2 = k,) from 0.5 to 2.5 ps (the solvation time in methanol). However, the value for k l is dependent on the ratio k2/k3. For example, assuming that l/ks = 1 ps, for the two cases, k2 = 5k3 and k2 = 0.2k3, the dissociation rate k l is 75 and 350 ps, respectively. As a result, a more detailed picture of the coordination dynamics is needed in order to be able to determine accurate time scales and activation parameters for this process. Acknowledgment. We are grateful for financial support from the National Science Foundation and the donors of the Petroleum Research Fund, administered by the America1 Chemical Society. We also thank Newport Corporation, Klinger Scientific, and Sun Computers for donating equipment which was used in these experiments.
Diode Laser Absorption Probe of Vibration-Vibration Energy Transfer in COP Thomas G. Kreutz, James A. O’Neill, and George W. Flynn* Department of Chemistry and Columbia Radiation Laboratory, Columbia University, New York, New York 10027 (Received: August 5, 1987)
Time domain absorption spectroscopy with a tunable diode laser has been used to measure the rate constant for vibration-to-vibration energy transfer in C 0 2 via the near-resonant “collisional up-pumping” process C02(OOo1) + C02(OOol) -+CO2(OO02)+ CO2(0Oo0). The diode laser, in combination with a C 0 2 discharge reference cell, is used to monitor the time-dependent population increase within the CO2(OO02)state in a 1O:l mixture of Ar and CO, following pulsed excitation of the C02(OOo1)level by a Q-switched C 0 2 laser. The intramode relaxation rate constant, k , for this process is found to be (5.6 h 0.7) X lo6 s-I Torr-’ or (1.7 f 0.2) X lo-’’ cm3 s-I molecule-’ at 298 K.
Introduction The dynamics of both pulsed and CW CO, lasers have been the subject of extensive research for many years.’-3 The behavior of these systems is now rather well understood, and kinetic models agree well with experimental results. Such models are based upon numerous rate constants for vibration-to-vibration (V-V) and vibration-to-translation (V-T) energy transfer between C 0 2 , N,, and rare gases, values for which have k e n measured by infrared fluorescence and CO, laser double-resonance techniques.,-’O (1) Patel. C. K . N. Phvs. Rev.Lett. 1964, 12, 588: 1964. 13. 617: ADDI. .. Phys. Lett. 1965, 7, 290.. (2) Gordictz, B. F.; Sobolev, N. N.; Sokovikov, V. V.; Shelepin, L. A. IEEE J . Quantum Electron 1968, 4, 796. Moore, C. B.: Wood. R. E.; Hu. B. E.; Ya;dley, J. T. J . Chem. Phys. 1967, 46, 4222. (3) Dang, C.; Reid, J.; Garside, B. K. Appl. Phys. 1983, B31, 163; IEEE J . Quantum Electron. 1983, 19, 755. Brimacombe, R. K.; Reid, J.; Znotins, T. A. Appl. Phys. 1985, B36, 115. (4) Stephenson, J. C.; Moore, C. B. J . Chem. Phys. 1972, 56, 1295. Stephenson, J. C.; Wood, R. E.; Moore, C. B. J . Chem. Phys. 1971,54,3097. Yardley, J . T.; Moore, C. B. J. Chem. Phys. 1967, 46, 4491. (5) Rosser, Jr., W. A.; Gerry, A. D.; Wood, E. T. J . Chem. Phys. 1969, 50, 4996. Rosser, Jr., W. A.; Sharma, R. D.; Wood, E. T. J . Chem. Phys. 1971, 54, 1196. Rosser, Jr., W. A.; Gerry, A. D. J . Chem. Phys. 1971, 54, 4131. (6) Huddleston, R. K.; Weitz, E. Chem. Phys. Lett. 1981, 83, 174. (7) Temple, T. A.; Suhre, D. R.; Coleman, P. D. Appl. Phys. Lett. 1973, 22, 349. Stark, Jr., E. E. Appl. Phys. Lett. 1973, 23, 335. Jacobs, R. R.; Pettipiece, K. J ; Thomas, S. J. Phys. Reu. A 1975, ZZ, 54.
0022-3654/87/2091-5540$01.50/0
Perhaps the most fundamental V-V energy-transfer process in CO, is the near-resonant “collisional up-pumping” process c02(0001)
+ c02(0001) _li c02(0002) + k-I CO2(0Oo0)
At = -25 cm-I (1)
which serves as a model for how vibrational energy is distributed within the asymmetric stretch (4mode of CO,. The intramode relaxation rate constant, k, for this process is expected to be approximately gas kinetic and has been calculated by Pack,” but an experimental value for the room-temperature rate constant has not been published to date.1° We have recently measured this rate using the powerful combination of a tunable diode laser (TDL) spectrometer and a C 0 2 discharge reference cell. The diode laser provides a high-resolution probe (-0.0003 cm-I) for time domain absorption spectroscopy and has been recently used to probe C 0 2 laser dynamic^.^ The C 0 2 discharge reference cell (8) Finzi, J.; Moore, C. B. J . Chem. Phys. 1975, 63, 2285. (9) Burak, I.; Noter, Y.; Szoke, A. IEEE J . Quantum Elecrron. 1973, 9, 541. (10) Thomason, M. D. Ph.D. Thesis, University of Virginia, Los Alamos National Laboratory, LA9420-T, 1982. (1 1) Pack, R. T. J . Chem. Phys. 1980, 72, 6140. Note that Pack‘s rate constant, k, written in terms of the disappearance of C02(OOo1),is twice as large as that defined in eq 1 and 2.
0 1987 American Chemical Society
’
The Journal of Physical Chemistry, Vo1.-91,No. 22, 1987 5541
Letters COLLISIONAL UP-PUMPING
co,
(00011
+ co,
(0O01 1
* co, (0002)+
CO;! DISCHARGE CELL ABSORPTION SPECTRUM --i~ 0 . 0 4 7 5 cm-’
c0,(00~0)
(0O02)L(0O03) R(141 ’%Oe 2310.035 cm-l
DIODE L A S E R ABSORPTION \
-
C0,(OO02;J= 20)t hv(4.3pm)-CO2(OO03; J = 21 Figure 1. Time domain absorption signal for the (00°2) (00°3)R(20) transition of C 0 2 following excitation of the (OOol) level by 9.6-pm radiation from a Q-switched C02laser. The sample is a 1:lO .mixture of C02:Ar at a total pressure of 1.0 Torr and a temperature of 298 K. The trace represents the average of 32000 signals and has a time base of 20 ps full scale.
creates steady-state populations of vibrationally hot C 0 2 and provides frequency references for thousands of high-lying rovibrational lines which are normally inaccessible at room temperature. The TDL/discharge cell combination allows virtually every important rovibrational level in the C 0 2 laser to be probed with extremely high temporal and spectral resolution.
.
Experimental Section In the present doubleresonance experiment, the 9.6-pm output of a Q-switched C 0 2 laser is propagated through a 2-m-long sample cell containing a 1:10 mixture of C 0 2 and argon, populating the CO2(OO01)vibrational state. The argon promotes rotational relaxation within each C 0 2 vibrational level without significantly affecting vibrational relaxation, so that the rotational levels are described by a Boltzmann distribution throughout the experiment. In addition, the rare gas limits radial diffusion of excited C 0 2 molecules out of the probe beam. The diode laser, which is used to monitor (via absorption at 4.3 pm) the timedependent populations in the (00°2) level, is copropagated along the cell axis, passed through a monochromator (to discriminate against competing spatial and longitudinal modes), and detected with a cooled (77 K) InSb detector. Time-resolved changes in the transmitted intensity of the diode radiation are acquired with a Biomation 8100 transient digitizer and averaged on a Nicolet 1170 signal averager. A trigger is provided by detecting a portion of the C 0 2 laser pulse (-0.4-ps width) with a cooled (77 K) HgCdTe detector having a response time of -0.1 ps. A typical time domain absorption signal for the (00°2) level is shown in Figure 1, where the diode laser is tuned to the (00°2) (00°3) R(20) transition at 2313.959 cm-’. In order to locate this absorption line and lock the diode laser to this frequency, a portion of the beam is split off before the sample cell and directed through a C 0 2 discharge reference cell and into a monochromator/IR detector. The reference cell absorption signal is sent to a lock-in amplifier whose output is fed back into the diode laser current controller for frequency stabilization. This configuration fixes the frequency of the diode laser at the peak of a single absorption line throughout the duration of the experiment. The discharge reference cell consists of a high-voltage dc discharge (16 kV; 25 mA) applied to a low-pressure mixture of C02, N2, and He. It provides a steady-state, non-Boltzmann
-
l?igure 2. Typical COzdischarge cell absorption spectra in the 2300-cm-’ region with the discharge (a) turned off and (b) ignited (25 mA). Note that the intensity of the (00°2) (00°3) R(14) line at 2310.035 cm-’ is increased by 8 orders of magnitude when the discharge is turned on.
-
population of highly vibrationally excited C 0 2 ,with “effective” (Treanor-type12)vibrational mode temperatures as high as 2900 K.13 In this experiment, the discharge enhances the (00°2) to population by more than 8 orders of magnitude (from 0.05 of the ground-state population), providing a precise frequency (00°3) absorption line. Accurate reference for each (00°2) assignments of the additional lines present in the discharge are made possible by high-resolution FTIR spectroscopy of discharge excited Typical reference cell absorption spectra are shown in Figure 2. Note the dramatic increase of available absorption lines when the discharge is employed.
-
-
Data Analysis The kinetics of the collisional up-pumping process given in eq 1 may be modeled simply by fi2(t) = k [ N l ( t ) l 2- k-lNdVz(0 (2) where N,(t) is the population in (OOOn) and k and k-’ are the forward and backward rate constants. Since No and N l ( t ) are not significantly perturbed by the up-pumping process, eq 2 is uncoupled from the analogous equations for No and N l ( t ) . As a result, the general solution to eq 2 may be written N2(t) = k ~ z [ N l ( 7 ) ] 2 e - ~ ~ &d7 -l(r-T)
(3)
As a first approximation, we assume that the (OOol) population has no significant time dependence on the time scale of interest, 1 / N 0 k l , and so N l ( t ) may be approximated by using a step function with amplitude, Nl. Assuming N2(t
