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J. Phys. Chem. 1991, 95, 2104-2107
An Experknental Exploration of the Energy Gap Law for Vibratlon-Transhtbn Energy Transfer. The I,* M System
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Hong Du,t Douglas J. Krajnovich,t and Charles S. Parmenter* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: October 31, 1990; In Final Form: December 17, 1990) New crossed beam inelastic scattering data have been obtained for the 12(B O,+)(u'=35) + M system where M = He, Ne, or Ar. The data are used to explore exponential energy gap law (EGL)scaling for vibration-translation (V-T) energy transfer over a range of collision dynamics and interaction potentials. Relative cross sections for Au changes in the vibrationally (and rotationally) inelastic scattering were obtained with center-of-mass collision energies (E,.,,) of 350 and 1500 cm-' for He, 1370 cm-' for Ne, and 2050 cm-' for Ar. When these experiments are combined with earlier beam and 300 K bulb experiments plus a classical trajectory calculation, the collisions range from nearly impulsive to nearly adiabatic and encompass E,.,,. distributions ranging from 300 K thermal to narrow crossed beam Gaussians. The trajectory calculations simulate monochromaticE , collisions. The various interaction potentials include both minimal and substantial attractive contributions. EGL scaling is a good representation of the V-T transition probabilities over all of these conditions.
Introduction Collisional molecular energy transfer processes are often modeled by an energy gap law (EGL)ld P W ) a exp(-M/B) (1) where the relative transition probability P scales exponentially against the energy AE switched between translation and an internal degree of freedom. B is a scaling parameter. For example, the EGL is often a successful representationof rotation-translation energy transfer data for atom-diatom collisions. The EGL is only one of many scaling laws used for rotational energy transfer, and extensive discussions of such scalings are a~ailable.'.~ The EGL is on far less secure grounds for vibration-translation (V-T) energy transfer even though it is frequently used. In these casts, attachment to data is rare. It usually appears in modeling of processes in which V-T transfer plays a role. There are few generalized theoretical treatments, and almost the only experimental demonstration of V-T EGL scaling has been provided by the 12* + M 300 K bulb experimentsof Steinfeld and c&workers? Their state-testate V-T study of u' = 43 in the B O,+ electronic state (I2*) with a variety of collision partners M gave singlecollision V-T cross sections that scaled well with an EGL. Three-dimensional classical trajectory calculations by Rubinson, Garetz, and Steinfeld'O have supported the scaling for this V-T system. Additionally, their development of the forced oscillator approach, MITFITS, also recovers EGL scaling, but not with such a good match to the data. Since the V-T EGL is so commonly assumed, additional experimental probes of the law's generality and its limits of a p plicability would be useful. This Letter presents some that are derived from vibrationally inelastic scattering of 12* from He, Ne, and Ar under a variety of crossed beam collisional conditions. Recently, we developed a new V-T experiment that moved the optical pumpdispersed fluorescence probe technique so long used with bulbs into the collisional environment of crossed beams. The switch from bulbs to beams replaces the broad center-of-mass collision energy (E,) distribution of thermal bulbs with a narrow Gaussian that can be tuned selectively inside the bulb distribution. Our first experiments" used the collision partners H2and D2 with 12*(u'=35)and gave relative scattering cross sections for Au = f l to Au = f 7 with E,.,,, near 800 cm-l. More extensive data were obtained'z" for scattering from each of three 12* vibrational states (u' = 15,25, and 35) with He at E,.,,, = 720 cm-I. All of these I2* + M beam data are well represented by EGL scaling Present address: Argonne National Lab, Chemistry Division, 9700 S. Cas8 Ave., Argonne, 1L 60439. *RaKntaddreas: IBM Almaden Research Cmter, 650 Harry Road, San Jw, CA 951 20. *To whom correspondence should be a d d r d .
0022-365419112095-2104$02.50/0
as demonstrated in Fig. 2 of ref 13. We have now extended the 12* studies to a much greater span of collisional conditions. An 12* + He study is in progress using tunable Ec.,,. values ranging from less than the 312 cm-' mean energy of a 300 K bulb to values above 1500 cm-l. We have also used heavier collision partners with interaction potentials s u b stantially different than those of H2, D2,and He. Some results are presented here. Together with the earlier work, they demonstrate the impressive persistence of EGL behavior over these various excursions of the collision dynamics.
Experimental Cooditions Most experimental procedures for data acquisition and analysis have been given earlierI2 with a discussion of 12* + He at EC.,,. = 720 cm-'. The principle modifications concern changes in the beam expansion conditions to achieve different E,.,,. for He collisions or to introduce Ne and Ar as collision partners. Briefly, the 12* + He collisions at = 720 cm-I were o b tained from skimmed pulsed beams crossed at No.The primary beam contained I2 seeded in He and was expanded from T = 360 K. The secondary beam was pure He expanded from 300 K. To achieve different E,.,, the secondary beam stagnation gas temperature was adjusted above or below 300 K with a liquid nitrogen heated coil system. Additionally, the secondary beam was run CW with a mechanical beam chopper and unskimmed. For 12* He with E,.,,. = 350 cm-' (43 mev), the secondary beam stagnation gas was at 180 K, and the 360 K primary beam expansion was changed to I2 seeded in Ar. The E, = 1500 cm-I (186 meV) collisions were obtained with a 730 K secondary beam
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(1) Troe, J. J . Chem. Phys. 1977, 66, 4745. Snider, N. fbid. 1986, 85, 4207. (2) Troc, J. J. Chem. Phys. 1982, 77, 3485. (3) Gilbert, R. G. Chcm. Phys. Lett. 1983, 96, 259. (4) Tardy, D. C.; Rabinovitch, B. S. J. Phys. Chcm. 1986, 90, 1187. (5) Forst, W. Chem. Phys. 1989, 131, 209. (6) Charutz, D.; Berman, M.; Levine, R. D. Chcm. Phys. Lcrr. 1989,161, 495. (7) Brunner, T. A.; Pritchard, D. In Dynamics of rhr Excired Store; Lawley, K. P., Ed.; John Wiley & Sons: N e w York, 1982; p 589. (8) Dexheimer, S. L.; Durand, M.; Brunner, T. A.; Ritchard, D. E. J . Chem. Phys. 1982, 76,4996. (9) Kurzel, R. 8.; Steinfeld, J. I. J . Chem. Phys. 1970, 53, 3293. (10) Rubinson, M.; Garetz. B.; Steinfeld, J. I. J . Chem. Phys. 1974. 60, 3082. (11) Krajnovich, D. J.; Butz, K. W.; Du, H.; Pannenter, C. S. J. Phys. Chem. 1988. 92. 1388. (12)-Gajn&ch, D. J.; Butz, K. W.; Du, H.; Parmenter, C. S.J . Chem. Phys. 1989, 91, 7705. (13) Krajnovich, D. J.; Butz, K. W.; Du. H.; Parmenter, C. S. J . Chem. Phys. 1989, 91, 7725.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2105
Letters stagnation gas and a 360 K primary beam expansion of I2 seeded in He. The scattering with Ne at EE.,,,= 1370 cm-I (170 meV) and with Ar at E,.,,. = 2050 cm-' (254 meV) used pure 300 K gas expansions for a pulsed secondary beam together with 360 K expansions of I2 in He for the primary beam. The nozzle diameter was 0.5 mm for all pulsed expansions and 0.1 mm for the CW He expansion. All collision energies were calculated, not measured.
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ReeulQ The four sets of relative cross sections presented in Table I describe vibrationally inelastic scattering from 12(B)',0 ( ~ ' ~ 3 5 ) with J 10. The initial rotational and vibrational selection was achieved by laser pumping within the 3 5 4 band. The cross sections are derived from fluorescence band intensities by procedures described earlier.'* The cross sections in each set are normalized to the Au = -1 cross section in the set. We do not attempt to relate the m a g nitudes of the various sets to each other. The values listed for Au = 0 refer to pure rotationally inelastic scattering within the u' = 35 level of 12*. The uncertainties given in Table I are based on consideration of "analysis errors" and of "data uncertainties" as discussed in our paper12on collisions with E, = 720 cm-'.The uncertainties in the present work arc larger due to lower S/N ratios. Most range from 10% to 30%. The largest are 50-8046 occurring for the Au = -5 cross sections. The Au = -3 cross sections for Ar and the Au = +4 cross sections for all gases are missing from Table I on account of spectroscopic interferences.
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Discussion We do not attempt here to relate our data to any specific theory or to trace the various conditions under which EGL predictions emerge from various theoretical treatments. One aspect common to many theoretical discussions, however, is the concept of adiabatic vs impulsive collisions, and it provides a convenient way to discuss our 12*+ M beam experiments. The collisional encounter may be described by a so-called This parameter is the ratio of "adiabaticity parameter", €.I4 collision time t, and the vibrational period t,, specifically F = 2 ~ ( r , / t , ) . For adiabatic collisions where € >> 1, a slow collision is outrun by a fast oscillator motion. For impulsive or sudden limit collisions where 4
