Transfer and storage of vibrational energy in liquids: collisional up

John C. Deàk, Stuart T. Rhea, Lawrence K. Iwaki, and Dana D. Dlott. The Journal of Physical Chemistry A 2000 104 (21), 4866-4875. Abstract | Full Tex...
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J . Phys. Chem. 1986, 90, 1604-1 6 10

1604

Transfer and Storage of Vibrational Energy in Liquids: Collisional Up-Pumping of Carbon Monoxide in Liquid Argon Deon S. Anex and George E. Ewing* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: September 25, 19851 Isotopically enriched carbon monoxide (88% I3Ci6O,12% l3CI8O)dissolved in liquid argon was optically pumped to the = 1 level by a CW CO laser. This energy was then redistributed by collisional up-pumping to higher vibrational levels. Fluorescence from vibrational levels up to u = 20 of the heavier isotope was observed from the steady-state distribution. The features of the population distribution are discussed in terms of the strength of optical pumping, carbon monoxide concentration, translational temperature,and the pertinent rate constants for energy transfer. For some conditions the populations of the vibrational levels are inverted. The potential for these solutions to store vibrational energy is discussed. L)

Introduction Strongly vibrationally pumped systems of anharmonic oscillators have received considerable attention in the study of energy transfer of highly vibrationally excited molecules, lasing media, and isotope separation.l-l3 In these systems, energy is redistributed to higher vibrational levels when the rate of vibrational to vibrational (V-V) energy transfer exceeds the rate of loss due to radiation, vibrational to translational (V-T) relaxation, or quenching by impurities. The distribution of vibrational populations in the limit of fast V-V transfer was described by Treanor, Rich, and Rehm.I4 Distributions in which V-T and radiative processes also play a role have been described analytically by LamIs and numerically by Caledonia and CenterI6 and by Rich.17 Discussion of up-pumping experiments have included both quasithermodynamic descriptions’s and surprisal ana1y~is.I~ For optically pumped systems, uppumping to u = 42 has been observed in gas-phase CO at 300 K,334 overpopulation of levels up to v = 4 in matrix-isolated CO in Ar and N e at 8 K has been reported,2 as well as molecules excited to the u = 23 level and a pronounced population inversion in pure solid C O in the 20-35 K range.’ In a recent experiment, uppumping in matrix-isolated C O has produced vibration to electronic energy transfer.” The present work has extended the study of collisional uppumping in optically pumped systems to C O in liquid Ar. This work was based on a number of studies of the transfer and storage of vibrational energy in cryogenic liquids done in this laboratory. Specifically, with respect to CO, it was found that a carefully purified solution of CO in Ar was quite stable to V-T relaxation.*’ For dilute solutions relaxation was found to be purely radiative, with a lifetime of 18 ms. By increasing the concentration of CO, radiation was trapped by self-absorption and the lifetime was extended to 1 s. The long lifetime of vibrational energy, coupled (1) Legay-Sommaire, N.; Legay, F. IEEE J . Quantum Electron. 1980, QE16, 308. (2) Dubost, H; Charneau, R. Chem. Phys. 1976, 12, 407. (3) Rich, J. W.; Bergman, R. C.; Williams, M. J. Calspan Report No. WG-6021-A-1, Calspan Corp., Buffalo, NY, 1977. (4) Bergman, R. C.; Homicz, G. F.; Rich, J. W.; Wolk, G . L. J . Chem. Phvs. 1983. 78. 1281. 1 5 ) Brechignac, Ph. Chem. Phys. 1978, 34, 119. (6) Brechignac, Ph.; Taieb, G.; Legay, F. Chem. Phys. Lert. 1975, 36, 242. (7) Powell, H. T. J . Chem. Phys. 1973, 59, 4937. (8) Smith, I. W. M.; Wittig, C. J . Chem. SOC.,Faraday Trans. 2 1973, 69, 939. (9) Hancock, G.; Smith, I. W. M. Appl. Opt. 1971, 10, 1827. (10) Horn, K. P.; Oettinger, P. E. J . Chem. Phys. 1971, 54, 3040. (1 1) Galaup, J. P.; Harbec, J. Y.; Charneau, R.; Dubost, H. Chem. Phys. Lett. 1985, 120, 188. (12) Farrenq, R.; Rossetti, C.; Guelachvili, G.; Urban, W. Chem. Phys. 1985, 92, 388. (13) Farrenq, R.; Rossetti, C. Chem. Phys. 1985, 92, 401. (14) Treanor, C. E.; Rich, J. W.; Rehm, R. G. J . Chem. Phys. 1968, 48, 1798. ( 1 5 ) Lam. S. H. J . Chem. Phvs. 1977. 67. 2577 (16) Caledonia, G. E.; Cente; R. E. Chem. Phys. 1971, 55, 522. (17) Rich, J. W. J . Appl. Phys. 1971, 42, 2719. (18) Shamak, I.; Flynn, G. J . Chem. Phys. 1978, 69, 2474. (19) Huddleson, R. K.; Weitz, E. J . Chem. Phys. 1977, 66, 1740. (20) Chandler, D. W.; Ewing, G . E. Chem. Phps. 1981, 54, 241

i.

with fast V-V transfer, makes these cryogenic solutions good candidates for observing collisional up-pumping. In this paper the experimental arrangement and results are described. This is followed by a discussion of the observed population distributions. First, they are discussed in terms of the Treanor model, which is applicable in the limit of fast V-V transfer. Next, a semiquantitative argument is presented, explaining the gross features of the distributions and deviations from the Treanor model. These arguments are then supported by numerical calculations of the distributions. Finally, potential applications of these systems are discussed.

Experimental Section The apparatus is shown schematically in Figure 1. Light from a C W CO laser is focused with a CaF, lens into a cryogenic cell containing a solution of carbon monoxide in liquid argon. Fluorescence was collected at right angles by a spherical mirror and focused onto the entrance slit of a Perkin-Elmer 210B monochromator with a grating blazed at 3.75 Mm. After passing through the monochromator, the light was collected by an ellipsoidal mirror and focused onto a liquid nitrogen cooled indium antimonide photovoltaic detector (Infra-red Associates). The signal from the detector then went through a preamplifier ( X 1000) to a signal averager or to a lock-in amplifier. Two types of measurements were made. The fluorescence lifetime was determined by tuning the monochromator to the fluorescence feature of interest and mechanically chopping (C, in Figure 1) the laser light before the cell at 5-15 Hz. The decay signals were passed to a FabriTek 1074 signal averager, which was triggered by a reference pulse from the chopper. Typically 1024 decays were averaged and the resulting decay trace sent to a chart recorder. The fluorescence spectrum was measured by chopping (C, in Figure 1) the emission from the cell at 667 Hz with a Princeton Applied Research (PAR) 120 mechanical chopper while continuously exciting the sample. The signal was measured with a PAR 120 lockin amplifier using the reference signal from the chopper. The spectrum was then output to the chart recorder while the monochromator was scanned. The C O was isotopically enriched carbon- 13 C O from Monsanto with reported isotopic composition (in atom percent) 99.4% carbon-13,0.6% carbon-12 with 88.0% oxygen-16 and 12% oxygen-18. The stated gross composition with (in mol %) 99.12% CO, 0.12% COz, 0.69% Ar, 0.02% H,, and 0.05% He. For low ) on the C O concentrations (8.8 X 10” molecules ~ m - a~ finger C O reservoir bulb was submerged in liquid nitrogen for at least 1 h before preparing a sample to trap impurities (predominantly CO,). For the higher concentration samples (7.1 X lOI9 molecules ~ m - an ~ )additional purification step was taken. Before being placed in the reservior bulb, the CO was passed through a series of liquid nitrogen cooled traps.*’ The entire reservoir bulb was then submerged in liquid nitrogen for 1 h before the samples were prepared. The extra purification step did not affect the results ( 2 1 ) Hayes, J., private communication

0022-3654/86/2090-1604$01.50/00 1986 American Chemical Society

Collisional Up-Pumping of CO in Liquid Ar

The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1605

\ T + - L l CRYOGENIC

MONOCHROMATOR

PREAMP

I

-I 1

CHART RECORDER

Figure 1. Schematic drawing of the experimental apparatus.

at the lower concentration but was required in order to get consistent results at the high concentration. The argon was Matheson purity (stated purity 99.9995%, with less than 0.5 ppm of hydrocarbons) and was passed through a dry ice cooled molecular sieve (Linde 4A) before condensation. The cryogenic cell, which is described elsewhere,22was made of brass, fitted with sapphire windows and was attached to the cold tip of a closed-cycle helium cryostat (Air Products Displex), controlled by an APD-E digital temperature controller (Air Products). LiF plugs were inserted near the entrance and exit windows of the cell to prevent attenuation of the laser light outside the region viewed by the collection optics and to minimize reabsorption of the fluorescence. The liquid samples were prepared by filling the cell and a portion of the vacuum line of known volume at room temperature to a calculated pressure of C O from the reservior bulb. The cell was then cooled to 85 K and argon was condensed into the cell. For the more dilute solution the concentration was confirmed by taking the absorption spectrum with a Perkin-Elmer 476 infrared spectrophotometer. For the more concentrated solution the concentration was calculated from the pressure and volume measurements and by application of Rauolt’s law. The validity of this method was confirmed by using the infrared spectrum for the lower concentration. The excitation source was a flowing CO-N2-He gas discharge laser operating on rovibrational transitions near P( 10) for several vibrational levels (u < 10). It was constructed following the design of L e g a ~ .The ~ ~ laser cavity consisted of a 3-m glass tube with CaF2 Brewster windows and external gold-coated Pyrex mirrors. One mirror was flat and totally reflecting and the other was concave with a radius of curvature of 20 m and had a 3-mmdiameter drilled hole in the center that was used as the output coupler. To operate the laser on the lower vibrational transitions, the laser tube was submerged in liquid nitrogen and the C O was cooled by passing it through a coil submerged in the same nitrogen bath. The gas concentrations were adjusted to maximize the power on the low u transitions. This was done by optimizing the power measured with a power meter (Scientech 36-000 disk calorimeter) through a band-pass interference filter that passed the 1-0 ( u = 1 u = 0) and 2-1 ( u = 2 u = 1) transitions. The spectral profile of the laser was then measured with a Perkin-Elmer 467 infrared spectrophotometer in single-beam mode to scan an attenuated portion of the laser output. The total power was measured with the power meter and the power of each transition deduced from the relative intensities of the lines of the spectrum. Typically the total output was in the range 0.8 to 1.2 W, with

-

-

(22) Lupo, D.; Abdel-Halim, H.; Ewing, G. E. Chem. Phys., in press.

(23) Legay, F., private communication.

about 50 mW for 1-0 and 150 mW for 2-1. It is the 1-0 and 2-1 laser transitions which fall in the absorption profiles of I3CI6O and 13C’*0in argon solution. The total power was also measured after the laser light had passed through the cell containing the more dilute CO-Ar solution along with similar measurements for the cell filled with liquid argon only. These were used to determine how much power was absorbed by this CO-Ar solution, with the effects of reflection and absorption losses by the windows eliminated. Approximately 40 mW was absorbed. The strongly pumped (“s”)and weakly pumped (“w”) cases in the results to follow were achieved by changing the laser power and focusing conditions to the liquid solution. The external collection optics, the monochromator, and the detector housing were purged with nitrogen to reduce interference from atmospheric water in the C O overtone region. The monochromator was calibrated in the C O overtone region by using the first overtone spectrum of 1 2 C ’ 6 0(4300 to 4200 cm-l) and the atmospheric water fundamentals (4000 to 3450 cm-I). Calibration in the CO fundamental region was done by using the I2Ck6O fundamental (2200 to 2100 cm-I). The calibration was found to be accurate to 0.5 cm-I. The spectra in the first overtone region were taken at a 12-cm-] spectral slit width. The accuracies of the CO solution frequencies were limited by the uncertainty in locating the maxima of the diffuse features and is estimated to be f 1 cm-I.

Results The fluorescencedecay of each sample was measured as a check of the amount of quenching impurities present. It has been shown that for a solution of C O in Ar the observed rate, in the absence of self-absorption and quenching impurities, is the purely radiative rate, 55 s-I for 12C160.20 Small concentrations of molecules that quench vibrational energy dramatically increase the observed rates in these systems.24 The observed rate of fluorescence decay for the I3CI6O1-0 feature in the dilute (8.8 X 10” molecules ~ m - ~ ) solution after low power laser excitation is 50 f 2 s-l. This agrees well with the observed radiative rate for l2CI6Owhen it is corrected for the dependence of the radiative rate on the cube of the transition frequency,25giving a predicted radiative rate of 5 1 s-I for I3CI6O. From this it is concluded that the level of quenching impurities is too low to affect the populations of the lower vibrational levels. For the higher concentration samples (7.1 X lOI9 molecules ~ m - the ~ ) observed rate was shortened to 33 s-I due to self-absorption effects. Fluorescence was observed in both the fundamental and first overtone regions. For quantitative measurements of the population distribution the emission spectra were taken in the overtone region to avoid absorption by the sapphire windows below 2000 cm-l and to eliminate interference from scattered laser light. A representitive spectrum is shown in Figure 2. As indicated, fluorescence is observed from the 2-0 and 3-1 transitions, of the lighter isotope (I3CI6O)and from the 2-0 through 16-14 transitions of the heavier isotope (13C’80).It will be shown below that the other transitions of the lighter isotope (4-2, 5-3, etc.) make a negligible contribution to the spectrum. The positions of the features in the overtone (Au = -2) region were shifted by -5 cm-’ from their gas-phase values.26 The frequencies, v, in cm-’ were fit to the equation”

to determine the spectroscopic constants we, and wy,. These spectroscopic constants were used to calculate all the energy levels when modeling this system using the relation

(24) Abdel-Halim, H.; Ewing, G. E. J . Chem. Phys. 1985, 82, 5442. (25) Herzberg, G. Spectra of Diatomic Molecules; Van Nostrand: New York, 1950. (26) Dale, M.; et al. Can. J . Phys. 1979, 57. 677.

1606 The Journal of Physical Chemistry, Vol. 90, No. 8, 1986

Anex and Ewing

c.

E~

c

01

L -

I

1

3400

3600

3800

4000

4200

view- ) Figure 2. Representative fluorescence spectrum, [”CO] = 8 8

X

10” molecules cm-3 in liquid Ar ( T = 8 5 K).

I

L ’ i

c

1

I

1’

‘00

4

8

12

16

20

24

U

101

4

’

8

’

1I2

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’

1I6

’

20

’

’

24

Figure 3. Population distribution for 13C’80 in liquid Ar at 85 K. [l3C0] = 8.8 X 1OIs molecules ~ m - [13C180] ~, = 1.1 X lo1*molecules cm-’. The closed circles represent data. T h e solid lines are the results of the numerical model and the dashed line is the continuation of the Treanor model fit to the lower levels. The two sets of curves differ by the intensity of laser pumping of the L‘ = 1 level. For the curve labeled ”s”, 8, = 1255 K. For “w”, 0, = 1025 K

Figure 4. Population distribution derived for ‘3C180in liquid Ar at 85 K. [I3CO]= 7.1 X lOI9 molecules ~ m - [13C’80] ~, = 8.5 X I0l8 molecules cm”. The closed circles represent data. The solid lines are the results of the numerical model and the dashed line is the continuation of the Treanor fit to the lower levels. The two sets of curves differ by the intensity of laser pumping of the c’ = 1 level. For the curve labeled “s”, 8 , = 1105 K . For “w”, 8, = 1010 K .

where higher-order terms have been neglected. The intensity distributions of the observed Av = -2 transitions (e.g. see Figure 2) are used to obtain the relative population distributions of the vibrationally excited CO molecules. This was accomplished by scaling the intensity distributions by the u-dependent spontaneous emission coefficients for the various transitionsn The same coefficients were used for each isotope since the correction to the relative values is small (6% at L; = 20). The integrated intensity of each peak was taken to be proportional to the peak height, since the shape of each feature was the same and the features are well enough separated so that error introduced from overlapping features is minimal. The system photometry response was taken to be constant from 4200 to 3400 cm-’. Figure 3 shows population distributions for [13C’80(u)] in molecules cm-3 for the lower concentration sample. Figure 4 shows population

distributions of [13Ci80(u)] for a higher concentration CO solution. In both Figure 3 and Figure 4 the closed circles are the data and the two curves labeled “s” and “w” are for different laser pumping conditions. The lines are theoretical models for the distributions and the dashed line is the continuation of the Treanor distribution fit to the populations of the lower levels. These will be discussed later as will the details for extracting the absolute distribution of [ i 3 C ’ 8 0 ( u ) ] from the relative distributions. Three regions are indicated in Figures 3 and 4. With increasing quantum number, the population drops off quickly in region I, becomes flat in region 11, and then falls off quickly in region 111. In some cases the distribution near the end of region I passes through a minimum. For example, there is a population inversion in the lower curve of Figure 4. In general, the distribution at the end of region I becomes flatter with increased laser pumping intensity. In addition, the inverted region is more pronounced for the higher concentration sample. These observations will be interpreted in the following section.

( 2 7 ) Lightman, A. J.; Fisher, E. R. Appl. Phys. Lett. 1976, 29. 593.

Collisional Up-Pumping of C O in Liquid Ar

The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1607

Discussion The quasiequilibrium established by anharmonic oscillators with an excess of vibrational energy in the limit of fast V-V transfer has been described by Treanor, Rich, and Rehm.14 Their approach neglects processes that lose quanta of vibrational energy (V-T, radiative, impurity quenching) compared to fast quanta-conserving (V-V) processes. Although quanta are conserved in V-V processes, there is an energy defect resulting from anharmonicity. This can be illustrated by considering the process

co(u=i) + co(u=j)

k

2c o ( u = i - l ) + c o ( u = j + l ) kr

(3)

corresponding to the exchange of one vibrational quantum. Using equation 2, but ignoring wy,, one can see that the energy change for process 3 in the forward direction is approximately AE = -2wex,(j-i+ 1 )

(4)

This is exothermic ( A E < 0) i f j 2 i. Processes that pass quanta to higher vibrational levels are favored energetically. The forward rate constant (k,) for process 3 is related to the reverse (k,) by the relation kf/k, = exp(-AE/kBT)

(5)

where AE is the energy change, kB is the Boltzmann constant, and T i s the translational temperature. A detailed balancing of the one vibrational quantum exchanges of eq 3 using eq 5 shows that all the rate constants cancel and a population distribution results given by

N , = No exp(uy) exp[-(E, - Eo)/kBTI

(6)

where N , is the population of vibrational level u, E, is its energy, and the y is a single parameter for all energy levels. When the vibrational energy is in equilibrium with the translational temperature y = 0. If there is an excess of vibrational energy, then y > 0 (this is opposite to the sign convention in the original paper). There is no single vibrational temperature to describe all the levels as there is for a harmonic oscillator, but pairwise temperatures can be defined. For L; = 0 and u = 1 NI

=

NO

exp[-(El - EO)/kBell

(7)

defines a vibrational temperature 8,. If eq 7 is equated to eq 6 for u = 1, the parameter y can be defined in terms of the vibrational temperature of the first level 7 =

[(El

- EO)/kB1(T1 -

el-1)

where eq 2, deleting the w d e term, was used to approximate the energy. For a given translational temperature, the minimum in the distribution moves to the lower u for stronger pumping, i.e. higher 81 or y. As shown in the Appendix of ref 14 the Treanor model is easily extended to a mixture of two diatomic molecules. An equation similar to eq 6 results for each species

(8)

When y in eq 6 is replaced by this expression a convenient result is obtained

Several features should be noted. When O1 = T (the vibrational energy is in equilibrium with the translational temperature) a Boltzmann distribution, Nu = No exp[-(E, - E o ) / k B n , for the anharmonic oscillator results. If E, - E, = u(El - Eo),then eq 9 becomes the distribution function for the harmonic oscillator with an excess of vibrational energy. This results in an exponentially decaying population distribution N , = No exp[-v(E, Eo)/kBSI]governed soley by a vibrational temperature 1 9 ~ For . the anharmonic oscillator, from eq 9, it is seen that the population of the higher vibrational levels is enhanced by strong pumping of the first level, Le. making 8, large. (Indeed, any level in region I can be pumped since vibrational energy is quickly redistributed.) An overpopulation with respect to a Boltzmann-like distribution is due to a combination of anharmonicity and low translational temperature compared to 0,. This treatment predicts a population inversion beyond some level urnin,which can be determined by differentiating eq 6 or eq 9 with respect to u. When the first derivative is equated to zero, eq 9 yields

where i labels the species and y is common to both species if they readily exchange vibrational energy. An expression similar to eq 9 can then be derived for each species. Note that the 81(i)are different for each isotope, but related. This can be seen by rewriting eq 8 for each species and equating them since the parameter y is common to both. The physical basis for the different is due to the energy defect when quanta are exchanged between molecules with different vibrational frequencies. The lower frequency molecule will be preferentially pumped by the higher frequency molecule. Note that this is also true for a mixture of two harmonic oscillators. We shall associate the population distributions expressed by eq 6,9, or 1 1 with the Treanor model. These distributions predict a population inversion beyond umin depending on the pumping conditions, anharmonicity, and the translational temperature as shown in eq 10. It should be stressed that this inversion depends on the Treanor model assumption that V-V processes that conserve vibrational quanta are rapid relative to dissipative processes (eg. V-T, quenching, or radiative) that result in losses in vibrational quanta. When dissipative processes become important population inversion may become less pronounced or disappear. The distribution in region I is well characterized by the Treanor model. For each observed population distribution u = 2, 3, and 4 levels for the heavier isotope were fit to the Treanor distribution from eq 1 1 to determine y or O1 by using the derived spectroscopic constants in eq 2 to calculate energy levels. The calculated values of 4 for I3Cl8Ofor the “s” (strongly) and “w” (weakly) pumped cases are given in the figure captions. Each y (or Ol(i)) was then for each isotope. used to calculate the population relative to A’,,(’) The relative populations of the u = 2 levels for the two isotopes were used to place the curves for the isotopes with respect to each other. The absolute distributions in molecules cm-3 was then calculated from the known density of CO molecules by using the calculated values of the populations for u = 0 and u = 1 of each isotope and the observed populations for the other levels. As a check of the consistency, the relative abundance of each isotope was calculated from the absolute distributions. In each case the error was less than 6% of the reported value from the 13C0 lot analysis. The calculated Treanor distributions for I3Ci8Oare shown in Figures 3 and 4. The agreement with the Treanor model is quite good in region I. In each case the heavier isotope is pumped by the lighter to an extent in quantitative agreement with the Treanor model. Application of eq 1 1 shows that the calculated distribution of the lighter isotope I3Ci6O makes a negligible contribution to the spectrum of the heavier isotope beyond u = 3 as was assumed in deriving the population distributions from the spectral intensities and as is evident from Figure 2. For the higher levels, the population distribution deviates from the Treanor model, given by eq 6, 9, or 1 1 as the dashed curves in Figures 3 and 4 show. For these higher levels relaxation processes which cause a loss of vibrational quanta become important and the distribution depends on the details of all the relaxation rate constants. This is in contrast to the distribution in the Treanor region, which is a consequence of the detailed balancing from eq 3 and 5 in which all the rate constants cancel to yield the final simple algebraic expressions for N,. In order to discuss the details of the distributions in regions I1 and 111, we must call on more complete treatments of vibrational energy This requires the solution of a large number of coupled rate equations describing the system. Although this

1608 The Journal of Physical Chemistry, Vol. 90, No. 8. 1986

L

-

C

0

m

6

3

4-

t h

O3

4

-

L

a

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L16

20 L

U

Figure 5. Pseudo-first-order rate constants: k$' [CO( I ) ] , -; k::f?; [CO(u)],----; k$,[M], - . - I . Two cases differing in the strength of the pumping of the lower levels are labeled ''w" and "s". The Treanor minima are indicated by the open circles. Also included for reference are the radiative rates: k:,$,, -.

is done numerically below, an understanding of the gross features

of the distribution can be gained by focusing upon a few dominant processes that a molecule in level u can undergo:

+ CO(u) CO(0) + CO(u+l) CO(u) + CO(u) + CO(u-1) + CO(u+l) CO(U) + M CO(C-I) + M CO(0) CO(U-1) + hv CO(1)

-+

+

(12) (13)

(14) (15)

These equations have the following significance for up-pumping CO to high u levels. Equation 12 in the forward direction promotes CO(u) to CO( u S 1 ) by using the plentiful supply of CO(1). The (pseudo) first-order rate for this process is kf$+'[CO(I)] (now iVc = [CO(u)]). This channel would be efficient for supplying CO to high u levels were it not for the fact that the rate constant k$' drops sharply as the energy gap widens. This energy gap given by eq 4 is exothermic in the forward direction with AE = -2uwexe and measures the nonresonance for the process. The efficiency for this channel for up-pumping C O is shown by the two solid curves in Figure 5 . W e shall discuss later the quantitative selection of k:$+;+' from theoretical calculations.** The two curves "w" and "s" correspond to the [CO(l)] concentrations of the weak and strong pumping conditions in Figure 4. The rate for uppumping, k$+'[CO( l)], declines rapidly a t high u levels due to the increasing nonresonance for the processes of eq 12 corresponding to the decline of k:$" as found by others.28 The two curves vary only slightly with pumping conditions because [CO(l ) ] changes little (see Figure 4). W e turn next to process 13, for the forward direction, which remains near-resonant with AE = -2w,x, for all u as eq 4 shows. Because of the nonvarying and small exothermic energy gap we expect, as found by others,29that k:;:?; remains large and slowly changing at high L! levels. Yowever, as the data in Figure 4 show the concentration of [CO(u)] depends dramatically on pumping conditions beyond the minimum of the Treanor distribution. Consequently, the two dashed curves for k$; [CO(u)] are widely separated a t high o levels. As the efficient pumping channel 1 2 drops below channel 13 the extent of up-pumping decreases. This occurs since process 13 essentially shuffles quanta back and forth (28) Cacciatore, M.; Billing, G. D. Chem. Phys. 1981, 58, 395. (29) Cacciatore, M : Billing, G. D Chem. Phys L e t f . 1983. 9 4 . 281.

Anex and Ewing among the levels u i 1. The rates of the forward and reverse reactions of (13) are nearly equal since. the process is near-resonant. As channel 13 takes over at the expense of channel 12 we achieve concentrations of CO(u) essentially invariant with L'. This accounts for the plateau region characterizing region 11. Equation 14 accounts for the dissipation of vibrational quanta by impurity quenching and the sharp turn-down in the CO(u) distributions of Figures 3 and 4 which we have described as region 111. The curve representing k$,[M] in Figure 5 expressing this (psuedo) first-order process is hypothetical, illustrating the quantum dependence of this process that causes the sharp break in the distribution in region 111. We shall suggest an identification of M and calculations of kzo-l later. Finally, shown in Figure 5 is k$., whose specification we will discuss later. As we see Figure 5 the radiative process is inefficient relative to any of the other channels we have considered. Considering now some of the finer details of Figure 5 . For the higher concentration case appropriate to Figure 4 we see for the more strongly pumped case "s" that the Treanor region ends (first intersection of nonresonant k$' [CO(u)] and near-resonant k$,' [CO(u)] curves) after the Treanor minimum (open circle). A total inversion is predicted for a small range of levels. Region I1 then begins, dominated by near-resonant exchange which results in a flat population distribution. The flat region extends until k;.-, [MI becomes important, turning the distribution downward in region 111. In the less strongly pumped "w" case, the end of the Treanor region occurs farther from the minimum so there are more levels totally inverted. The beginning of region I11 occurs right a t the end of region I, so there is no plateau in this case. Similar arguments can be used to explain the lower concentration distributions appropriate to Figure 3. In summary, the large inversion for high vibrational levels predicted by the Treanor model depends on nonresonant collisions carrying vibrational energy from the pumped lower levels to the higher levels. The large energy gap in the process results in the forward process occurring to a much greater extent than the reverse, but the large energy gap also results in these nonresonant processes becoming less likely as the vibrational level increases. Near-resonant processes may become responsible for the transfer of vibrational energy for a range of vibrational levels. Near-resonant exchanges are less efficient in passing energy to higher levels since the reverse process occurs to an appreciable extent due to the small energy defect. If the point a t which the near-resonant transfer becomes more important than the nonresonant process occurs after the Treanor minimum, a total inversion is expected for a range of vibrational levels. After the end of the Treanor region. in region 11, the near-resonant exchange of vibrational energy is the most likely process. This results in a flat population distribution in region 11, extending until a process that removes vibrational quanta from the system begins to dominate. At this point the distribution turns downward, beginning region 111. Having just considered the gross features of the population distributions we turn now to a more complete discussion. The rate equations describing the system eq 3, 14, and 15 were solved in the steady-state by using an iterative scheme (described in the Appendix) to numerically model the population distributions. Notice that the more general form of one quantum exchanges, eq 3, is used which includes the special cases of eq 12 and 13. This calculation of the populations was performed to confirm the predictions of the general considerations given above and to identify the process causing the drop-off in the distribution in region 111. The V-V rate constants were taken from calculations by Cacciatore and Billing for gas-phase CO at 100 K. The rate constants for k$' are available from Table I1 and Figure 1 of ref 28 for u = 0-12, 19, 29. Rate constants for k$yT' are given in Figure 8 of the same reference for u' = 5 , 10, and 15 and in Table I of ref 29 for u = u' = 14, 18, 22, 24, 26, 28, and 30. Rate constants not explicitly presented were interpolated or extrapolated from the available calculations. The rate constants were not corrected to 85 K as this correction is small as shown in ref 29 Moreover, the calculated rate constants for ' 2 C ' 6 0were taken The relative Einstein coefficients to be appropriate for 13C180.

The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1609

Collisional Up-Pumping of C O in Liquid Ar

"I

I

U

Figure 6. Pseudo-first-order rate constants k&, [MI. The pseudofirst-order rate constant needed to turn the distribution down in region I11 is indicated by the shaded region. The method for calculation of k y L - , [ M ] for M = CH,, H,,C 0 2 ,or Ar is given in the text.

for spontaneous emission in C O are availablez7 to scale the observed rate constant, 50 s-l, for lzC'sO 1-0 to obtain k::, for higher vibrational levels. The modeled distributions are shown by the solid lines in Figures 3 and 4. The calculated shape of the distribution in region I11 has been forced to fit the observed shape by artifical adjustment of k y F l [ M ] .This set of rate constants was multiplied by a constant which was varied to improve the fit in region 111. The calculated curves for regions I and I1 are insensitive to the region 111distributions. The excellent agreement between the data and the theoretical curves for Figures 3 and 4 lends credibility to the myriad rate constants calculated by Cacciatore and Billing.28~z9Radiative decay, through k:L1, has no effect on the population distributions in any of the regions. All of the adjusted k$, [MI needed to fit the experimental results in Figures 3 and 4 fall inside the range indicated by the shaded area in Figure 6. Also shown in Figure 6 are calculated rates, k$, [MI for several species ( M = Ar, H,, CO,, CH,). Relaxation by H e was not calculated since it is less efficient as a quencher than HzS3l Self-relaxation by C O CO(u) + CO(0) CO(u-1) + CO(0) (16) is not efficient under the present conditions.z0-z8 For COz and CH, the processes considered were V-V transfer, specifically CO(U) + COz(OO0) CO(U-1) + COz(100) (17)

+ CH,(OOOO)

Future Work The population of high vibrational levels in a cryogenic liquid environment makes several interesting applications possible. Under the proper conditions the inversion may exceed the threshold for lasing. If this is the case, it is conceivable that a liquid-state cryogenic infrared laser can be developed. This laser would be tunable over the broad emission features present in the liquid. In addition, the liquid-state analogues to gas-phase experiments in strongly pumped systems may be p e r f ~ r m e d . ~For $ ~ *example, ~ solutions may be doped with known quantities of quenching species to study the relaxation of high vibrational level^.^ To study V-V transfer, double resonance experiments may be performed.s-6 In addition, if molecules in the liquid state are pumped to high enough levels, crossing into excited electronic states, dissociation, and chemical reactions may be observed."

Acknowledgment. This work was supported by a grant from the National Science Foundation.

-

Appendix: Numerical Method The numerical method of solving the rate equations is based on the scheme outlined by Rich." The rate of change in the population of level u is described by

-

dN,/dt = C(-k$KT'N,Ni

4

CO(u)

used as described elsewherez4to calculate d , which was rounded off to the nearest integer. The following values for d were used: Ar, d = 5 ; COz, d = 4;Hz, d = 1; and CH4, d = 4. It should be noted that the same potential parameters, a and d , were used for all vibrational levels. While, a small change in the range parameter can have a significant effect on the rate constant, we only seek to understand the relaxation channels for our system. For this purpose we believe the calculations to be valid.,, The The . upper limit to density of Ar is 2.1 X loz2molecules ~ m - ~ the COz and H 2 impurity level was estimated at 1 ppm each. A 0.3-ppm concentration of CH, was used which is consistent with the manufacturer's upper limit for hydrocarbon impurities in Ar. We see from Figure 6 that relaxation of CO(u) by Hz, COz, or Ar is insignificant; however, even small amounts of a quenching impurity like CH4 easily compete with other energy-transfer processes at the higher levels. We note that because of the quantum dependence of k&, for CH4, concentrations near 0.3 ppm have no effect on the relaxation of C O ( l ) , consistent with our lifetime measurements. We believe CH4 (or another hydrocarbon) to be the likely quenching impurity affecting uppumping in our systems. Unfortunately it is not an easy task to remove the last traces of CH,. In spite of this, a population inversion was observed at the present impurity level.

CO(u-1)

+ CHd(0100)

(18) followed by fast V-T relaxation of COz(lOO) or CH4(0100). Both these processes are nonresonant for relaxation of CO(1) but are none-the-less rather efficient as we have demonstrated for reaction 18 e l s e ~ h e r e . ~ ,However, for higher u levels the vibrational spacings of CO close up and these processes become near-resonant and exceedingly efficient as we shall show directly. At u = 28 of 1 3 C 1 8the 0 vibrational spacing nearly matches v l = 1388 cm-' of COz and at u = 22 the spacing closely approaches u2 = 1534 cm-' of CH,. The rate constants shown in Figure 6 were calculated by the method of Thompson,30and described elsewherez4for the relaxation of two species interacting in a one-dimensional collision over a Morse potential. The Morse potential is described with the range parameter, a, and by the number of bound van der Waals vibrational levels, d , of the interacting species in the intermolecular cm-l, except potential well. In these calculations a = 2.0 X for H 2 where a = 1.7 X cm-I gave a better fit of available low-temperature data for relaxation of IzC'60(u=l).31 The well depths were taken from Hirshfelder, Curtiss, and Bird32and were (30) Thompson, S . L. J . Chem. Phys. 1968, 49, 3400. (31) Millikan, R. J . Chem. Phys. 1964, 40, 2594.

i'

i=O

+ kL$(LJVi-lN,+l + k$\NiN, +

where i* is chosen above the highest kinetically important level, in this case i* = 25. The other symbols are defined in the text. The forward and reverse rates are related by eq 9. Variables involving levels outside the range of the calculation are set to zero. The expression for N,, in the steady state, is obtained by setting ( A l ) to zero and is i*

N, =

C (kMifuNj-IN,+l + k ~ ~ $ N , - I N j ++l }kzI,,NMN,+I

i=O

'i

kl.",d,,N,/(C(kZ;"~'Ni + k$o+-]lNi}+ k&,NM i=O

+ k$l}

+ (A2)

For the purposes of this calculation the pumping of the low levels was mimicked by fixing the ratio of the populations of u = 0 to u = 1 according to the ratio defined by the Treanor parameter O1. An initial estimate of the population distribution was made. Equation A2 was then used for each level in turn, from u = 2 to (32) Hirshfelder, J . 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids: Wiley; New York, 1954.

J . Phys. Chem. 1986, 90, 1610-1614

1610

v = i*, using the current estimate for the population distribution. After each new population was calculated, it replaced the old value in the population distribution. After one pass through the levels, the distribution was normalized to the total number of molecules. These iterations were continued until the relative change in

was less than some prescribed value for all v. As a check of each solution, the "residual" rates were calculated from ( A l ) by using the final population distribution to make sure they were approaching zero as more stringent convergence requirements were applied. As an additional check of the method, the equations were- solved with only V-V terms, resulting in distributions predicted by the Treanor model. Registry No. CO, 630-08-0; "CO, 1641-69-6; '3C'80,35907-63-2;

('43)

Ar, 7440-37-1.

Multiphoton Ionization and Photochemistry of Chromyl Chloride in Supersonic Cluster Beams Robert G. Wheeler and Michael A. Duncan* School of Chemical Sciences, Department of Chemistry, University of Georgia, Athens, Georgia 30602 (Received: October 7, 198s)

Chromyl chloride and chromyl chloride clusters in a pulsed supersonic beam are probed with multiphoton ionization time-of-flight mass spectroscopy. At the excimer laser wavelengths used, both monomers and clusters exhibit strongly wavelength dependent MPI behavior unlike that typically found for inorganic or organometallic complexes. Chromyl chloride clusters ionize prior to extensive fragmentation,allowing consideration of ion fragmentation in a species with both inter- and intramolecular bonding.

Introduction UV/visible laser photochemistry, multiphoton dissociation, and multiphoton ionization (MPI) of transition-metal complexes have been and continue to be active research areas.'-I4 Part of the interest in these areas is in the fundamental photophysical dynamics of these processes. Other motivations include the use of metal complexes for photoinitiated c a t a l y s i ~ , *for ~ ' ~photolytic production of gas-phase metal c l ~ s t e r s , ~and ~ , 'for ~ laser photo(1) L. Geoffrov and M. s. Wriehton. "Oreanometallic ~ ( a l, G. ~ , Photochemistry", Academic'Press, New York, 1679;(b) M. 5. Wrighton, Chem. Rev. 74, 401 (1974). (2) 2. Karney, R. Naaman, and R . N. Zare, Chem. Phys. Lett. 59, 33

(1978). (3) (a) M.A. Duncan, T. G. Dietz, and R. E. Smalley, Chem. Phys. 44, 415 (1979); (b) M.A. Duncan, T. G. Dietz, and R. E. Smalley, J . Am. Chem. SOC.,103,5245 (1981). (4) P. C.Engleking, Chem. Phys. Lett., 74,207 (1980). (5) D.P. Gerrity, L. J . Rothberg, and V. Vaida, Chem. Phys. Left.,74, l(1980). (6)S.Leutwyler, U.Even, and J. Jortner, J . Phys. Chem., 85,3026(1981). (7) (a) J. T. Yardley, B. Gitlin, G. Nathanson, and A. M. Rosan, J . Chem. Phys. 74, 361 (1981);(b) Nathanson, B. Gitlin, A. M. Rosan, and J. T. Yardley, J . Chem. Phys., 74, 370 (1981);(c) W.Tumas, B. Gitlin, A. M. Rosan, and J. T. Yardley, J . Am. Chem. Soc., 104,55 (1982). (8) (a) R.L.Whetten, K. J . Fu, and E. R. Grant, 3. Chem. Phys., 77,3769 (1982); (b) R. L. Whetten, K. J. Fu, and E. R. Grant, J . A m . Chem. Soc., 104,4270 (1982). (9) (a) J. A. Welch, K. S. Peters, and V. Vaida, J . A m . Chem. Soc., 86, 1941 (1982);(b) J. D. Simon and K. S . Peters, Chem. Phys. Lett., 98,53 (1983). (10) A. Gedanken, M. B. Robin, and N. A . Keubler, J . Phys. Chem., 86, 4096 - - (1982). ( 1 1 ) H. Hermann, F. W. Grevels, A. Henne, and K. Schaffner, J . Phys. Chem., 86,5151 (1982). (12) (a) A.J. Ouderkirk, P. Wermer, N. L. Schultz, and E. Weitz, J . Am. Chem. Soc., 105,3354 (1983);(b) T. A. Seder, S . P. Church, A. J. Ouderkirk. and E. Weitz, J . A m . Chem. SOC.,107, 1432 (1985). (13) D. G. Leopold and V. Vaida, J . Am. Chem. SOC.,105,6809(1983). (14)T.R. Fletcher and R. N . Rosenfeld, J . Am. Chem. Soc., 107,2203 (1985). \ - -

- - I

0022-3654/86/2090-1610$01.50/0

chemical vapor deposition of thin film^.'^-^* For all of these applications, detailed data are required on photochemical products and their wavelength dependence, the mechanism of dissociation or ionization, and the molecular electronic states involved. To obtain this kind of information, early experiments used photolysis of metal complexes in cryogenic rare gas matrices, followed by IR or UV/visible detection of photo fragment^.'^ More recent experiments have taken advantage of new technology, using techniques such as picosecond transient absorption ~pectroscopy,~ IR transient absorption,"9l2 and multiphoton ionization in supersonic molecular beam^.^,^ Metal carbonyls have received the greatest attention in these experiments, but a variety of other inorganic and organometallic species have also been studied (e.g. SII(CH,)~,HgBr2, ferrocene'O). In this report, we present new results on the UV photochemistry and photoionization of chromyl chloride (Cr02C12)and chromyl chloride van der Waals clusters probed with MPI mass spectroscopy. The interrelation of MPI mechanisms and molecular photochemistry has been studied extensiveIy.l0 One aspect of previous studies has been to determine when fragmentation can be described by maximum-entropy (statistical) theories.20,21 van der Waals complexes and other cluster species afford interesting opportunities (15) (a) S. D. Al1en.J. Appl. Phys., 52,6501 (1981); (b) S.D. Allen and A. B. Tringubo, J . Appl. Phys., 54, 1641 (1983). (16) A. R. Calloway, T. A. Galantowicz, and W. R. Fenner, J . Vac. Sci. Technol., A, 1, 534 (1983). (17) J. Y. Tsao and D. J. Ehrlich, J . Chem. Phys., 81, 4620 (1984). (18) R. M.Osgood and T. F. Deutch, Science, 227,709 (1985). (19) (a) R. N.Perutz and J. J. Turner, J . Am. Chem. Soc., 97, 4800 (1975);(b) J. K. Burdett, M. A. Graham, R. N. Perutz, M. Poliakoff, A. J. Rest, J. J. Turner, and R. F. Turner, J . A m . Chem. SOC.,97,4805 (1975); (c) R. N.Perutz and J. J. Turner, J . Am. Chem. Soc., 97,4791 (1975);(d) R. N. Perutz and J. J. Turner, Inorg. Chem., 14,262 (1975). (20)D.A. Lichtin, R. B. Bernstein, and K. R. Newton, 3. Chem. Phys., 75,5728 (1981);(b) J. Silberstein and R. D. Levine, J . Chem. Phys., 75,5735

(1981). (21)J. Silberstein, N.Ohmichi, and R. D. Levine, J . Phys. Chem., 88, 4952 (1984)

0 1986 American Chemical Society