Modeling the pressure effect on the multiphoton absorption and

Sep 1, 1986 - C. A. Rinaldi and J. C. Ferrero , M. A. Vázquez, M. L. Azcárate, and E. J. Quel. The Journal of Physical Chemistry 1996 100 (23), 9745...
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J . Phys. Chem. 1986, 90, 4562-4568

are also substantially smaller than the corresponding rate constants for CHClF, reported in part 2. Statistically the difference from CHCIF, is highly significant, but a theoretical discussion is beyond the scope of this work. Concluding Remarks. The results of this and the two preceding papers show that relaxation during IR absorption can be measured by relatively simple and inexpensive means. The relaxation times are physically well defined and accurate enough to justify traditional kinetic analysis. In the presence of even mild vibrational excitation, the kinetics of relaxation becomes dominated by resonant v-V exchange. Although resonant v-v exchange is ~ e l l - k n o w n , 'its ~ importance as an autocatalytic collisional

mechanism for overcoming optical saturation has not been adequately appreciated in recent computer modeling of IR absorption. Under the relatively mild conditions of the present experiments, the molecular vibrations remain within the familiar domain of low-energy vibrational spectroscopy.6 In principle there is no reason why, under more drastic conditions, the method should not be extendible above the low-energy domain. However, the validity of the assumptions made in part 1 must then be reexamined carefully. Registry No. CHC12F, 75-43-4.

Supplementary Material Available: Tables SI-SIV of results for CHC1,F at 1057, 1080, and 1090 cm-' and vibrational excitation at statistical equilibrium (4 pages). Ordering information is given on any current masthead page.

(13) Schwartz, R. N.;Slavsky, 2. I.; Herzfeld, K. F. J . Chem. Phys. 1952, 20, 1591.

Modeling the Pressure Effect on the Multiphoton Absorption and Dissociation of CDF,. Collisional Energy Transfer B. Toselli, J. C. Ferrero,* and E. H. Staricco Instituto de Investigaciones en Fisicoquimica de C6rdoba (INFIQC), Departamento de Fisico Quimica, Facultad de Ciencias Quimicas, Universidad Nacional de CGrdoba, Sucursal 16, C. C. 61, 5016 C6rdoba. Argentina (Received: January 30, 1986)

A simple model based on the solution of the master equation, but including rotational effects in the first discrete levels, has been used to model the uL(@) and reaction probability results for CDF3 in a wide range of experimental conditions. We investigated the role played by collisions in order to overcome restrictions to the absorption processes, which is a striking feature of small molecules. By solving the rate equations we have been able to obtain information about the rotational relaxation rate of CDF, by collisions with CDF3,CHF3,and Ar as well as information about the average energy transferred by collisions between the different buffer gases and the vibrationally excited CDF,. For CDF, (CHF3) as collider the values determined are k,,(CDF,-CDF,) = k,,,(CDF3-CHFJ = (3.0-6.0) X ns-' Torr-' and ( A E ) d= 3 kcal mol-', and for Ar as bath ns-' Torr-' and ( A E ) , < 0.7 kcal mol-'. gas, k,,,(CDF,-Ar) = 6.7 X

Introduction The transference of vibrational energy from highly excited molecules to a bath gas has been studied mainly by chemical activation' and more recently by direct t e c h n i q ~ e s . ~Also ~ ~ some attempts were made to obtain information on energy transfer from the multiphoton decomposition of molecules in the presence of a bath gas by modeling the experimental results with a master equation form~lation,"~ as well as in nonreactive condition^.^' Probably one of the most comprehensive studies in this direction was made by Gilbert et al. on ethyl acetate.' As this is a large molecule, the high density of vibrational states assures the resonant condition and thus all of the irradiated molecules absorb the laser radiation and can be excited to energies above the reaction threshold, while competing with collisional deactivation during the pulse. Whereas this is true for large molecules, in the case of small molecules only a fraction of the total population is in ( 1 ) Tardy, D. C.; Rabinovitch, B. S . Chem. Rec,. 1977, 77, 369. (2) Barker, J. R. J . Phys. Chem. 1984, 88, 1 1 . (3) Hippler, H.; Troe, J.; Wendelken, H. J. Chem. Phys. Letr. 1981, 84, 257; J . Chem. Phys. 1983, 78, 6709, 6718. (4) (a) Stone, J.; Thiele, E.; Goodman, M. F.; Stephenson, J. C.; King, D. S. J . Chem. Phys. 1980, 73, 2259. (b) Stephenson, J. C.; King, D. S . ; Goodman, M. F.; Stone, J. J . Chem. Phys. 1979, 70, 4496. (5) Baldwin, A. C.; van den Bergh, H. J . Chem. Phys. 1981, 74, 1012. ( 6 ) Jalenak, W. A,; Nogar, N. S. J . Chem. Phys. 1983, 79, 816. (7) (a) Eberhardt, J. E.; Knott, R. B.; Pryor, A. W.; Gilbert, R. G. Chem. Phys. 1982,69,45. (b) Brown, T. C.; Taylor, J. A.; King, K. D.; Gilbert, R. G. J . Phys. Chem. 1983,87, 5214. (c) Zellweger, J. M.; Brown, T.C.; Barker, J. R. J . Chem. P h p . , in press.

0022-3654/86/2090-4562$01.50/0

resonance with the laser field and the extraction of the amount of energy transferred per collision requires either a knowledge of the fraction of excited molecules or experimental data in conditions where this rotational fractionation could be neglected. So far the results obtained for small molecules were not in all of the cases coincident. The reason can be attributed to the fact that the information was obtained by fitting only the reaction probabilities data, while it is at present well established that a reliable use of the master equation requires a fit to both the reaction probabilities and the absorption cross sections as functions of the incident Also, the convergence of the solution with decreasing grain size was not confirmed and when fractionation was included it was introduced as an adjustable parameter and without considering its intensity dependence during the pulse. Clearly, the wider the range of experimental conditions the master equation results fit, the more confidence can be assigned to the calculations. In this sense, one of the small molecules that received more attention is CDF,, mainly because the selective absorption of COz laser radiation relative to the normal species, CHF,, makes this molecule a candidate for laser enrichment of deuterium.I0 We have recently reported a modeling study which satisfactorily (8) Toselli, B.; Ferrero, J. C.; Staricco, E. H. J . Phys. Chem. 1985, 89, 1492. (9) Jang, J. C.; Setser, D. W.; Ferrero, J. C. J. Phys. Chem. 198!5,89, 414. (IO) (a) Herman, I. P.; Marling, J. B. Chem. Phys. Lett. 1979,64,75. (b) Tuccio, S . A.; Hartford, Jr., A. Chem. Phys. Lett. 1979,65, 234. (c) Marling, J. B.; Herman, I. P.; Thomas, S. J. J . Chem. Phys. 1980, 72, 5603. (d) Evans, D. K.; McAlpine, R. D.; Adams, H. M. J. Chem. Phys. 1982, 77, 3 5 5 1 .

0 1986 American Chemical Society

Multiphoton Absorption and Dissociation of CDF, accounts for the MPA and MPD processes of CDF3 in two extreme situations, namely, collision free and with a large excess of buffer gas added.8 In our model we demonstrated that the master equation can be used to model uL(9) and the reaction probabilities data so long as fractionation is considered. This intensity-dependent fraction, which was calculated from spectroscopic data, consequently varies according to the Rabi frequency and depends on the distribution of rotational states and the anharmonicity of the pumped vibrational mode. Thus, rotational and anharmonic bottlenecks are specifically considered in the collision-free regime. In the case of CF,I, this fraction of active molecules has recently been measured." In our previous work, the master equation was used to fit reaction probabilities and absorbed energies data obtained in a wide range of experimental conditions so that a model for the microscopic absorption cross sections could be extracted with reasonable certainty. In the present work collisions are included. The central idea is largely based on previous work in the l i t e r a t ~ r e and ~ ~ is ~ ~similar ~ ' ~ to the model recently reported by Herman for CTCI3,I4although independently developed and with some differences. The model is based on the fact that as pressures is increased rotational relaxation should increase the number of molecules interacting with the IR field and hence overcome the restrictions to absorption; this means that as a result of collisions, the molecules change their rotational states and are brought into resonance with the laser radiation. As a consequence, the rotational hole is destroyed and the molecules can be pumped to energies above the reaction threshold. Also, collisions with the bath gas produce a vibrational deactivation of the excited molecules and, as a result, a decrease in the reaction yield. While proper modeling of this process seems to be promising to obtain information on energy transfer in large molecules, a similar development has not been achieved for small molecules and further studies seem to be desirable. We now report an extension of our previous model for CDF, to consider collisional processes and obtain data on vibrational energy transfer from this kind of experiments. Our main goal was to model the multiphoton processes for CDF, and to analyze the validity of the master equation in relation to the transference of energy, with proper consideration of the factors affecting its solution. In this sense, we explore the possible deficiencies associated with the energy grain size and the effect of the pulse shape as well as the pressure regions where the rotational fractionation is important to the solution of the master equation.

Method of Calculation Rate Equation Formalism. In the rate equations formalism,I5 the temporal evolution of the populations of level i , Ni, is given by eq 1. In this equation ui+l,iis the microscopic cross section dNj/dt = Z(t)[ui,i-lNj-I + ~i,j+lNj+l - ( ~ j + l , j + ~i-l,i)Nj] + ~ z P i , Nj w N ~- kiNj (1)

+

for absorption of laser energy from level i to i 1 and it is related to the stimulated emission cross section by detailed balance; Le., ui,i+l= (gi/gi+l)ui+l,i, where gi is the degenerancy of level i. The microscopic RRKM rate constant is ki, w is the collision frequency, and PY is the collision transition probability from levelj to i. Z ( t ) is the intensity of the pulse. We have previously shown that the master equation can be used for this molecule in collision-free conditions only if it is considered that not all the population of the ground vibrational state is in resonance with the laser radiation, but only a fraction,f(t). Then, (1 1) Bagratashvili, V. N.; Vainer, Yu. G.; Doljikov, V. S.; Letokhov, V. S.; Makarov, A. A.; Malyavkin, I. P.; Ryabov, E. A.; Silkis, E. G.Opt. Lett. 1981, 6, 148. (12) (a) King, D. S. In Dynamics of the Excited State; Lawley, K. P., Ed.; Wiley: New York, 1982. (b) Fuss, W.; Kompa, K. L. Prog. Quuntum Electron. 1981, 7, 111. (13) (a) Letokhov, V. S. Nonlinear Laser Chemistry; Springer: New York, 1982. (b) Doljikov, V. S.; Kolominsky, Yu. R.; Ryabov, E. A. Chem. Phys. Lett. 1981, 80, 433. (14) Magnotta, F.; Herman, I, P. J . Chem. Phys. 1984, 81, 2363. (15) Jang, J. C.; Danen, W. C. In Laser Induced Chemical Processes; Steinfeld, J. I., Ed.; Plenum: New York, 1981.

The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4563

the actual population of level i evolving in time is N: = f;:(t)Ni. This fraction, which depends on the number of rotational states within the power broadened line width, was calculated, for the ground vibrational state, from the reported spectroscopic data.I6 Rotational fractionation of higher vibrational levels was not considered, as it has no practical consequences in the computations.s Then, in the absence of collisions, a rotational hole is produced which plays a significant role in controlling the absorption to higher levels. Also, due to the temporal profile of the laser pulse, the fraction of molecules in resonance increases with time from zero up to its maximum value and then begins to decrease. Solution of the master equation also requires the choice of a suitable model for the energy-dependent microscopic absorption cross section, ui+l,i.In our previous work" we found that only a cross section that decreases with internal molecular excitation and depends on intensity through f i ( t ) , i.e. was able to fit the data reported in a wide range of experimental conditions. In this equation the broad-band absorption cross section was taken as ul0 = 3.1 X cm2 molecule-' at 980 cm-'. Even though the multiphoton absorption results of Evans et exhibit no apparent "red shift" in the band profile as the absorbed energy increase, it is necessary to include restrictions imposed by the anharmonicity of the v5 mode of CDF,, X S s ,to account for the dependence of uL(9) on fluence, i.e., the break in the decreasing trend of q(@)that occurs at 9 > 1 J/cm2. The incorporation of anharmonicity into the model was made by considering that the population of the first excited vibrational level could not further absorb unless the power broadened line width was larger than the anharmonic shift, 2x55. The fraction of absorbing molecules of this level was then calculated as (3) In this equation wR is the Rabi frequency and wI is the laser bandwidth which was always taken as 0.03 cm-I. From these computations we could estimate that a value of -0.57 cm-' for X,, produced the best fit. This value is in reasonable agreement, within the experimental uncertainty, with those reported in the literature, considering the simplicity of our modeL1'-I9 Our model incorporates, in a simple way, most of the phenomena that could be important in multiphoton processes. A more fundamental approach to the problem has been extensively described in the literature.20 The multiphoton processes of CDF, could be represented as transition from case C to B, and the theory should account for the experimental observation without the use of semiempirical fractionation. An application of this theory to 1,1,2-trifluoroethane has recently been reported and, with proper parametrization, fully accounts for the experimental The time dependence of the laser intensity, which is required to solve the master equation, was simulated as before, with a Gaussian function. This pulse profile represents only a smooth envelope to the real situation, which consists of a series of spikes. To clarify whether this simplified pulse shape has any effect on the calculations, some integrations were also made dividing the 2-11s fwhm pulse in spikes 0.4 ns wide and separated by 0.6-11s intervals in which the intensity was zero. The intensity of the spikes, which had also a temporal Gaussian dependence, was 2.5 times higher than the smoothed pulse, so that the fluence was the same. The Role of Collisions. Description of the Model. The model previously developed to describe the multiphoton absorption process of CDF3 in the absence of collisions will be extended here to (16) Qingshi, Zhu; Steinfeld, J. I. J . Mol. Spectrosc. 1981, 89, 405. (17) Ruoff, A.; Burger, H.; Biedermann, S. Spectrochim., Acta, Part A 1971, 27A, 1359. (18) Kirk, R. W.; Wilt, P. M. J . Mol. Spectrosc. 1975, 58, 102. (19) Harradine, D.; Foy, B.; Laux, L.; Dubs, M.; Steinfeld, J. I. J . Chem. Phys. 1984, 81, 4261. (20) Quack, M. J . Chem. Phys. 1978,69, 1282.

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analyze the effects of collisions on both q(@) and the dissociation yield of CDF3. Collisional effects during the pulse can be detrimental, due to vibrational deactivation,21or may result in an enhancement of the multiphoton processes through removal of the rotational and anharmonic bottlenecks in the discrete region.22 The primary mechanism through which these bottlenecks are overcome is the rotational hole filling and the compensation of the anharmonicity of the lower transitions by changes in the molecular rotational energy. In order to incorporate the effects of rotational relaxation in our model based on the master equation we must calculate the number of molecules that as a result of collisions are brought into resonance with the laser radiation. The rate of filling of the rotational hole in the ground vibrational state in the presence of a collision partner of density NT is given by (4)

In this equation k,,, is a relaxation constant for the rate of filling of the rotational hole, but not necessarily a true rotational relaxation constant. Note that when the pulse length is larger than l/krot all the molecules can change their rotational states by collisions during the pulse. N1* represents the population in rotational states off-resonance with the laser radiation, and Nl*is the same number if the Boltzmann distribution would have been reestablished; that is, N,*- = [l -f(t)]N1, where N1 is the total population of the ground vibrational state. Then, N 1 * - N,*" is the number of molecules that as a result of collisions might repopulate those rotational states which were emptied by optical pumping. For the first excited vibrational level, the initial population is less than 1.8% of the total and so it has no importance in the calculation at t = 0. However, as the laser pulse progresses, molecules that reach this level by absorption of one laser photon cannot further absorb due to anharmonicity. Now, the role of collisions is to produce a change in the rotational energy of the molecule as to overcome the anharmonicity of the vibrational mode. The rate of change of the number of molecules in resonance with the laser, in this level, was calculated as dN2/dt = k,,,(N,* - NzR)NT where N2* represents the number of molecules that cannot absorb the laser radiation, in the absence of collisions, if the anharmonic shift is larger than power broadening, and NzRis the small number of molecules that even in the absence of collisions may be in resonance with the laser field and it is calculated with eq 3. Restriction to absorption for higher vibrational levels was not considered as exploratory computations indicated that the results were essentially the same as without fractionation. In addition to removal of the rotational and anharmonic bottlenecks, collisions also produce a change in the populations of the vibrational states that has to be considered in modeling the effect of pressure and can be used to obtain the amount of energy transferred per collision. As there are still no general predictive theories, the stepladder and the exponential models for the transition probabilities between vibrational levels have been widely used to obtain the amount of energy transferred per collisions. Even though the stepladder model seems more adequate to explain the transference of energy between polyatomic collision partners, while the exponential model is better for mono- and diatomic molecules, we have used the former in our calculations, mainly because the computer requirements are lower and also because the differences should not be significant compared with the experimental error. Then, the elements Po required were calculated as P, = 1.0- P,l for i-j = ( a E ) d a n d P i , = Ofor i-j + ( A E ) d where ( L L E )is~ the average down-energy loss per collision. The up-transition probabilities were calculated by detailed balance, and the completeness conditions were also imposed on the tran(21) Papagiannakopoulus, P. J.; Kosnik, K.; Benson, s. W. f n t . J . Chem. Kinet. 1982, 14, 327. (22) Stone, J.: Thiele, E.; Goodman, M. F. J . Chem. Phys. 1980, 73. 2259.

lo-2

lo-'

1 Fluence

IO

(J/cm*>

Figure 1. Calculated laser absorption cross sections vs. fluence for the 2-11sfwhm pulse at different pressures including P = 0 Curves (---) were obtained by using k,,(CDF3-CDF3) = 3.0 X lo-' n b ' Torr-' and curves (-) with k,,, = 6.0 X lo-' ns-' Torr:'. The full line represents experimental results obtained by using the MPA parameters of ref 10d. The numbers indicate the pressures in Torr. (.e.).

sition probabilities, as before.23 In all the calculations, the time increment used in the integration of the master equation was 1/3000 of the pulse length. Results In modeling the experimental results of multiphoton processes we have to consider two different, but complementary, pieces of data: the laser absorption cross sections, uL(@),and the reaction probabilities as functions of fluence, pulse length, and pressure. The experimental variation of aL(CP)with fluence'O" shows a strong dependence on pressure, when irradiation is performed with either a 2- or 6-11s fwhm pulse. At every pressure the uL(CP) initially decreases as ab,where b ranges from -0.6, at 1.6 Torr, to -0.3, at 10 Torr of CDF3 pressure, and at a given @ starts to increase. This change in slope occurs at @ = 1 J/cm2 for the 2-11s pulse and at CP 2 J/cm* for the 6-ns pulse, and it seems to be independent of the total pressure. The model calculations satisfactorily predict these experimental observations for CDF3. In Figure 1 we show calculations of uL(@) for the 2-11sfwhm pulse at different pressures, including P = 0. As previously,*the uL(CP) reported in ref 1Od were multiplied by 3.3 to agree in the absolute values with those of Marling et al.'& This was made because even though the two groups of researchers have reported the same dependence on fluence, the data of Evans et al. seem to be too low to justify the dissociation probability per pulse. These calculated results were obtained with a rotational relaxation constant for collisions between molecules of CDF3, krot,of 6 X ns-' Torr-I which implies Prrot= 167 ns Torr. Some calculations were performed with k,, = 3 X 10-3 ns-' Torr-' (Pr,,, = 333 ns Torr) and are also shown in Figure 1. These are the values of k,, that simultaneously produce the best fit to all of the experimental data (vide infra). Evans et al. also studied the wavelength and fluence dependence of MPA of 5.5 Torr of CDF, irradiated with a 6-11s fwhm pulse.'" Figure 2 shows the results of our computations using the above values for Ps,, together with calculations assuming collision-free conditions along with the experimental data of Evans et al. In this figure we clearly see the important role of collisions in order to overcome the restrictions to the MPA, especially in the region near the center of the band, where the fraction of molecules that can interact with the laser is lower than in the wings. Regarding (23) Arbilla, G.; Ferrero, J. C.; Staricco, E. H. J . Phys. Chem. 1983, 87, 3906.

Multiphoton Absorption and Dissociation of CDF,

\

The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4565

L P

d x a

L

"

t

@:1

Ar

Pressure (Torr)

1

J/cm'

lo-'

F 880

875

Wavenumber

870

(cm-')

Figure 2. Laser absorption cross section at different wavenumbers and at two fluences. (e) and (m) are the experimental values (ref 10d) for a 6-11spulse and 5.5 Torr of CDF,, (0)and (0)are the calculated results with k,,,(CDF,-CDF,) = 6.0 X lo-, ns-' Torr-'. At 0 = 1 J/cm2 are also shown results obtained with k,, = 3.0 X lo-' ns-l Torr-' (E), and (A) are the calculated results assuming collision-free conditions.

the effect of collisional relaxation on the MPD process, we have also modeled the experimental reaction probabilities when different pressures of buffer gas are added to a fixed pressure of CDF,, for 2- and 90-ns fwhm pulses. The two bath gases, Ar and CHF3, have different effects on the reaction probability and will be considered separately. For the short pulse Marling et al.'& have reported results for 2 Torr of CDF3 and Q = 20 J/cm2, with a pressure of added Ar varying from 98 to 1030 Torr. The experiments show that the reaction probability increases with the pressure of Ar up to 750 Torr of inert gas. Also, these experimental results suggest that vibrational deactivation is not important and then, only the rotational relaxation needs to be considered. (However, see below.) By incorporating the collisions of CDF, with Ar to the model we could obtain results which are in good agreement with those reported. Both results, experimental and calculated, are shown in Figure 3a. The dashed line represents the calculated results for the dissociation probability during the laser pulse, F R , and the full line is F R plus the molecules which are above the threshold energy at the end of the pulse, FRO. It is obvious that F R O is the highest limit to the dissociation probability. In the computations we considered the influence of both rotational and vibrational relaxation in the system. To do this we had to estimate the value of the rotational relaxation rate constant and also the mean vibrational energy transferred by collisions. Several computations were made and the best fit was ~~ obtained with k,,(CDF,-Ar) = 6.67 X lo4 ns-' Torr-' ( P T , = 1500 ns Torr) and neglecting vibrational deactivation. When this process was incorporated into the calculations with a stepladder model, the calculated results showed a pronounced deviation from experiment, clearly indicating that V-T relaxation is not important under these experimental conditions. Notwithstanding, calculations with several different values of (AE), are shown in Figure 3a a t P = 530 Torr and suggest that should be smaller than 0.7 kcal mol-' for Ar as the bath gas. A further improvement to obtain this value was not pursued as it would require a much finer graining with the consequent increase in computation demands.

200 CHF)

400 600 Pressure (Torr )

Figure 3. Reaction probabilities for 2 Torr of CDF, as a function of added bath gas for a 2-ns fwhm laser pulse at = 20 J/cm2. The experimental points (e) were extracted from ref 1Oc. (a) Calculated results as a function of Ar added. The full line represents FRmand the dashed line FR. The results were obtained by using a value of kIot(CDF3-Ar) = 6.67 X ns-l Torr-' and neglecting vibrational deactivation. The solid triangles at P = 530 Torr are the calculations with different values of (A,??),(kcal mol-') as indicated in the figure. (b) The same as above, but using CHF, as buffer gas (---) and (-) are the calculated results for FR and FRm,respectively, using k,,,(CDF3-CHF3) = 6.0 X lo-, ns-l Torr-' and different values of (AE),,; and are the calculationsof FR and FRO obtained with a value of k,,, = 3.0 X lo-' ns'l Torr-'. At pressures below those indicated by the arrows, the lines represent extrapolation of the calculated reaction probabilities. (e-)

(-.-e-)

In the same figure (part b) the experimental as well as the calculated results for Q = 20 J/cm2 are shown, but for the case of CHF, as buffer gas. The dependence of reaction yield on the pressure of CHF, has very important practical consequences, as in the actual photochemical enrichment of deuterium a large excess of CHF3 will always be present since the CDF, natural abundance is typically 150 ppm.'& In the computations the best fit was ns-' Torr-' for k,,,obtained with values of (3.0-6.0) X (CDF3-CHF3), which is the same as determined by fitting the q ( Q ) data, and 3 kcal mol-' for the mean down vibrational energy transferred per collision. Also, the computations considering only rotational relaxation are shown in Figure 3b. Note that at variance with Ar, vibrational deactivation by CHF, is very important. With these values of rotational relaxation constant and ( h E ) d we have also modeled the effect of pressure for a 90-ns fwhm pulse and 0.065 Torr of CDF,, which are generally understood as collisionless conditions.Ih However, the model calculations (Figure 4) show a large difference in the reaction probabilities when computations are performed in collisionless conditions as compared with the results at 0.065 Torr of CDF, and with k,,, = (3.0-6.0) X lo-, ns-' Torr-'. The agreement between calculations and experiment confirms our previous assertion that even at this low pressure collisions were occurring to some extent.* In Figure 5 we show the dependence of CDF3 decomposition on laser fluence for Ar pressures ranging from 0 to 30 Torr for the 90-ns pulse, using the same rotational relaxation constant as done previously. Note that these are predicted results and show an excellent coincidence with experiments.

4566 The Journal of Physical Chemistry, Vol. 90, No. 19, 1986

Toselli et al.

-

hS/B

h3/2

/

C

hVl0

0

Grain

Lo 0

Figure 6. Calculations of reaction probabilities for a mixture of 230 Torr of CHF, and 2 Torr of CDF3as a function of the grain size for a 2-11s fwhm pulse. The full line represents FR- and the dashed line FR.

K

-

I

100

50

Fluence

(J/cm*

150

)

Reaction probabilitiesvs. fluence for a 90-ns fwhm pulse and 0.065 Torr of CDF3. The symbols ( 0 ) represent the experimental measurements from ref loa. Curve A is calculated by using the master equation in the case thatf(t) = 1 and X,, = 0; curve B is calculated with kr,,,(CDF3-CDF3) = 6.0 X IO-’ ns-’ Torr-’; curve C is calculated with k,,, = 3.0 X ns-l Torr-’; and curve D is calculated assuming collision-free conditions. In these calculations F R = F R - . Figure 4.

I

I

I

10

20

30

Ar

/

pressure ( T o r r )

Reaction probabilities for a 90-11sfwhm pulse and 0.065 Torr of CDF, as a function of Ar added at three fluences. ( O ) , (m), and (A) are experimental results from ref loa, and the curves are the calculations with the same value of k,,, as in Figure 3a. Figure 5.

In all of the above calculations the temporal dependence of the pulse intensity was considered as a Gaussian envelope. As mentioned before, some calculations were also made dividing the 2-11s fwhm pulse in spikes 0.4 ns long. Calculations at a fluence of 20 J/cm2, not shown, were essentially the same as those represented in Figure 3b. Also, calculations at @ = 15 J/cm2, with reaction probabilities quite different from those at 20 J/cm2, produced the same result. For example, at 570 Torr of CHF3,

Size

the calculated reaction probabilities were 0.030 and 0.033 for both kinds of pulses. These calculations confirm previous finding^^^,^^ that a continuous function is a convenient way of representing the time dependence of the pulse intensity, but are at variance with other r e s ~ l t s . ~ Some calculations were also made to analyze the influence of the grain size on the solution of the master equation, as Eberhardt et al.7afound it had an important effect on the calculated reaction yields. In Figure 6 we show a plot of reaction probabilities for different grain size values, for a mixture of 230 Torr of CHF, and 2 Torr of CDF,. These results show that convergence is rapidly achieved and also that the change in the reaction yield is probably smaller than the experimental error. Discussion

The above results show that an extension of our previous model based on the solution of the master equation to specifically consider rotational and vibrational energy transfer satisfactorily accounts for the observed experimental results of MPA and MPD of CDF, in collisional conditions. We may compare some of these derived values for the rotational relaxation rates and average energy transferred by collision with CDF,, CHF,, and Ar to the values obtained in other studies. Considering the effect of pressure on the experimental dissociation yield data, the addition of bath gas initially produces an increase of the reaction probability for CDF3. This effect has also been shown to occur with several other molecules, as for example SF6,26CF3CH3,9i27CF2HC1,28and C2H4.29 This behavior has been associated with the existence of a rotational bottleneck in the absorption process, which is removed by collisions. In Figures 3 and 5 , we note that, with the addition of CHF3 or Ar to the system, the dissociation yield initially increases with pressure. Clearly, if rotational relaxation were the only important process, the yield would increase to reach the value obtained by solution of the simple master equation. Considering the results for Ar as bath gas, we note that, for pressures of about 400 Torr for the short pulse or 20 Torr for the long pulse, the yield is almost equal to the value obtained by assuming that all the molecules are in resonance with the laser, i.e.,f(t) = 1, and that there is no anharmonic shift for the absorption of the second level, Le., X 5 , = 0 (Figure 4). However, the behavior with CHF3-added is clearly different. When the pressure of CHF, increases above 200 Torr for the short pulse, the yield begins to decrease. This decrease in reaction probability with increasing pressure of CHF, is most likely caused by collisional vibrational deactivation of molecules which are excited in the quasi-continuum or continuum above the (24) Lawrence, W. D.; Knight, A. E. W.; Gilbert, R. G.; King, K. D. Chem. Phys. 1981, 56, 343. ( 2 5 ) Weston, Jr., R. E. J . Phys. Chem. 1982, 86, 4864. (26) Duperrex, R.; van den Bergh, H. Chem. Phys. 1979, 40, 275. (27) Jang, J. C.; Setser, D. W. J . Phys. Chem. 1979, 83, 2809. (28) King, D. S.; Stephenson, J. C. Chem. Phys. Lett. 1979, 66, 33. (29) Chekalin, N. V.; Letokhov, V. S.; Lokhman, V. N.; Shibanov, A. N. Chem. Phys. 1979, 36, 415

Multiphoton Absorption and Dissociation of CDF3

The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4567

dissociation energy30as the present model calculations show, and it is not surprising as polyatomic mdecules are much more efficient in V-V,T energy transfer than monoatomics. It is remarkable that extrapolation of this part of the curve to zero pressure yields the same value as that obtained with the simple master equation. This is the reaction probability that would have been obtained in collisionless conditions if all of the molecules were in resonance with the laser radiation. In Figure 3b are shown the results of computations considering that the only process that occurs is rotational relaxation. From these calculations, we realize that the rotational relaxation is complete for pressures of CHF3 in the range of 60-100 Torr (short pulse). With the values of k,,,(CDF3-CDF3) determined rotational relaxation times of 5.5, 2.8-3.3, and 1.7 ns can be calculated for both pressures, which compared with a total pulse length of about 6 ns means that all the molecules have changed their rotational states during the pulse. Therefore, for pressures of CHF, higher than 100 Torr, the simple master equation including vibrational energy transfer yields the same results as when considering fractionation with rotational relaxation. This is a very important fact associated with the predictive power of our approximation. With regard to the value of ( h E ) d transferred by collisions with CHF3, integration of the differential equations using various values of ( Le., 3, 6 , and 9 kcal mol-', yielded a series of straight lines of different slopes but passing through the same point on the ordinate (Figure 3b), as it should be. The value of ( h E ) d = 3 kcal mol-' produces the best fit to the experimental data. On the other hand, the estimation of the mean down energy < 0.7 kcal mol-', may be compared transferred by argon, ( with typical values of (AE)d0.5-1 kcal mol-' found in chemical a c t i ~ a t i o n ~and , ~ ' MPD In the latter case, however, the ( h E ) d values for collision of CF2HCI and CF,CFCl with Ar were determined to be 0.1 and 2.6 kcal mol-', respectively$v5 and -0.3 and 1.5 kcal mol-' for collisions of CTCI, and CH,CFCI also with Ar.l4,I6 This spread in the ( values may be due to deficiencies in the solution of the master equation or a fit to an insufficient amount of experimental data. Thus, in a study on the collisional energy transfer for vibrationally excited CF2HCI,5the master equation calculations showed that in order to fit the reaction probabilities vs. pressure, at different fluences, with a unique value of ( AE)d,the pulse had to be considered as consistent with a series of spikes. Calculations with a smoothed pulse resulted in different values of ( M ) d at every fluence. Our model calculations on CDF3 show that the same results are obtained, irrespective of whether a true pulse shape is used or only a Gaussian envelope. Moreover, even a simple rectangular pulse of constant intensity produced results that deviated no more than 30% from those obtained with the more real shapes. This is a very important point regarding the possibility of extracting ( AE)dvalues by modeling multiphoton absorption processes and certainly needs clarification. However, in the case of CFzHCI, the grain size was maintained as one IR photon, even in the collisional case, and that may be the reason for the observed behavior of the calculations. Regarding this point, it is certain that in order to keep computational tractability the energy grain size in the master equation has to be of about one IR photon. However, when modeling the effect of collisions with an inefficient partner, which removes small amounts of energy, we must use a grain size at least equal to ( h E ) d . This implies a strong increase in both the computational time and storage. Regarding this point Eberhardt et al.7aclaimed that the choice of the energy grain required for accurate computation must be much lower than the value of (&!?)d and they found an important effect in the calculated reaction yield in varying the grain size from hu to h v / 4 . For example, for 0 = 2 J/cm2 and 200 Pa of N, added to 2 Pa of ethyl acetate, the yield was 1.63% for a grain size of hv/4, 3.45% for hu/2, and 27% for

hv. The difference in these results cannot be neglected and so we have tested the convergence of the solution of the master equation by decreasing the grain size up to hu/lO. Our results show a small change in the reaction yield with the graining. The reason for the discrepancy of these results with those of ref 7a is not clear, but it is probably due to the use of different transition probabilities models. All of our calculations were done considering a stepladder model, while in the case of ethyl acetate, the authors used an exponential model which is known to require a finer graining to produce satisfactory results, even in the chemical activation studies.32 In this work, due to the small dependence of the calculated reaction yield on the grain size we have used a value equal to hu in all of the calculations, except for added Ar as a bath gas. Considering the value of the rotational relaxation rate constant obtained with our model calculations, there are two other independent values to be compared. In one of the studies, McAlpine et aL3, were able to extract a value of k,,, with CDF3 as a collider of 2.66 X lo-, ns-' Torr-', which implies a PT,,~= 376 ns Torr. This result that was obtained by fitting their experimental results to an empirical equation is in good agreement with the lower value of k,,, determined by us. The other value comes from infrared double-resonance experiment^,'^ where the relaxation rate of the ground vibrational state was measured by using u2 0 transition and that of the excited state with the 2v5 u5 line. The values reported, with CDF, as collisional partner, were PT,,, = 24.5 ns Torr (v, 0) and 56 ns Torr (2v5 u 5 ) . With H e as collider PT,,was 109 ns Torr. Our value of PT,,, = 167 ns Torr for CHF, is in between the above results. Regarding the effect of Ar, there are no previous data on rotational relaxation of CDF3 with Ar to compare with our results. Our calculation yielded PT,,, = 1500 ns Torr which is an order of magnitude larger than that of ref 19 for He. Other experimental results that can be compared are PT,,, = 100 ns Torr (SF6-Xe) and PT,,, = 160 ns Torr (C2H,-Xe). Thus, all the experimental evidence suggests that the rotational relaxation constants should be larger than the values of k,,, extracted from our model calculations. These discrepancies can be attributed to the approximations used on the solution of the master equation but also to the fact that k,,, is a highly averaged value. In addition, as mentioned before, k,,, is a rate constant for the rotational hole filling that may require J J f n, with n > 1 , while there are evidences that rotational relaxation follows propensity rules such as J J f 1 .34 If this were the case, extraction of true rotational relaxation rate constants would require the specification of all the rotational quantum numbers, which would constitute a really enormous computational effort. Finally, we should remark that, after the pulse, the system may undergo pressure and temperature excursions that could have an influence on the reaction probabilities and energy-transfer processes. However, as our calculations show that most of the reaction postpulse effects can takes place during the pulse, Le., FR N FRm, be safely ignored, and thus, they were not included in the model.

(30) Ambartzumian, R. V.; Letokhov, V. S. In Chemical and Biochemical Applications of Lasers; Moore, C. B., Ed.;Academic: New York, 1977;Vol.

(32) Tardy, D. C.; Rabinovitch, B. S. J . Chem. Phys. 1968, 48, 1284. (33) McAlpine, R. D.; Evans, D. K.; Adams, H. M. J. Chem. Phys. 1983,

3. (31) Marcoux, P. J.; Setser, D. W. J . Phys. Chem. 1978, 82, 97.

+

-

-

+-

-

-+

Conclusions The present model calculations show that the master equation formulation of multiphoton processes can be applied to small molecules in the presence of collision during the pulse provided that the restrictions to absorption are properly considered. These restrictions are mainly due to the fact that only a fraction of the total population is in the proper rotational states from which absorption of the laser radiation can occur and also due to the anharmonicity of the pumped rotational mode. These rotational and anharmonic bottlenecks can be removed by collisional change of the molecular quantum states, thus enhancing the multiphoton process. However, at higher pressures, the vibrational deactivation of highly excited molecules results in a lower reaction probability.

78, 5990. (34) Oka, T. J . Chem. Phys. 1967, 47, 13.

4568

J. Phys. Chem. 1986, 90,4568-4573

When these two effects are incorporated to the master equation, the calculated results show a very good agreement with experiment in a variety of conditions, demonstrating the predictive power of the method. In regions where pressure is detrimental to the multiphoton decomposition, rotational relaxation is complete and then the simple master q u a t i o n without fractionation applies. Data in this region allow the extraction of the mean down vibrational energy removed per collision. The results also show that

the calculated reaction probabilities are independent of the shape of the laser pulse, in the sense that a smoothed Gaussian profile yields virtually the same results as when spiking is considered. AcknowfedgTent. We thank the Consejo Nacional de Investigaciones Cientificas y Tknicas (CONICET) for partial financial support. Registry No. CDF,, 558-22-5; CHF,, 75-46-7; Ar, 7440-37-1,

Exclmer-Laser-Induced Photochemlstry of Organometallic Compounds Monitored by Dye Laser Mass Spectroscopy: Dimethyl Dltetlurlde (CH,TeTeCH,) R. Larciprete and M. Stuke* Max-Planck-lnstitut fur biophysikalische Chemie, Department Laserphysik, 0-3400 Gottingen, West Germany (Received: February 3, 1986)

Dimethyl ditelluride, CH3TeTeCH3,is a suitable organometallic gaseous precursor of tellurium. We describe a detailed investigation of the laser-induced photochemistry of CH3TeTeCH3monitored by tunable dye laser multiphoton ionization time-of-flight mass spectroscopy with nanosecond and picosecond laser pulses. In the blue spectral region, we observe the formation of the Te atoms and CH3TeCH3molecules. With KrF excimer laser (248 nm) irradiation in the UV, however, the formation of metal dimers Te2is identified, and an estimation of the internal energy distribution of the Te2photofragments is given.

Structured deposition of superconductors, metals, and semiconductors on various substrate materials and shapes can be achieved by using excimer lasers and organometallic compounds. MOCVD (metal organic chemical vapor deposition) seems to be the mast promising technique for the generation of well-defined layers of metals and semiconductors, since it combines the advantages of MBE (molecular beam epitaxy) and LPE (liquid-phase epitaxy) with a potential for mass production of electronic devices. For a review of MOCVD see ref 1 and references therein. Extending MOCVD by the use of lasers to laser-MOCVD, selective area growth can be achieved (see ref 2 therein). In the ideal case, one would like to induce photodeposition on various substrate materials and shapes only from selected adsorbate species and sites, controlled by the tunable laser wavelength and the intensity distribution impinging onto the surface. So far, however, only steps in this direction have been achieved when laser-enhanced deposition through a combination of thermal and photochemical effects3 was observed, or when UV laser photodeposition from adsorbate mixtures4 was induced. In the majority of applications up to now, thermal effects seem to be dominating. In addition to the generation of microstructures, the reduction of substrate temperatures is another promising feature of laserMOCVD when compared to the classical MOCVD technique. In special cases, the reduction of substrate temperatures may be achieved by using a less stable organometallic c o m p o ~ n d . ~But in general, the use of photon energy rather than thermal energy for the decomposition of the organometallic compounds may by far be more practical. Thus, photochemistry comes in. For a systematic and successful use of (laser) photochemistry of organometallic compounds for deposition processes, the identification and internal energy characterization of photoproducts is necessary for a detailed understanding and control of the (1) Metalorganic Vapour Phase Epitaxy 1984; Mullin, J. B., et al., Eds.; North-Holland: Amsterdam, 1984. (2) Laser Chemical Processing of Semiconductor Devices; Houle, F. A., Deutsch, T. F., Osgood, R. M., Eds.; Material Research Society: Pittsburg, PA, 1984. (3) Aoyagi, Y.; Masuda, S.;Namba, S.;Doi, A, A. Appl. Phys. Lett. 1985, 41, 95. (4) Ehrlich, D. J.; Tsao, J. Y . Appl. Phys. Lett. 1985, 46, 198. Higashi, G S.; Rothberg, L. J. Appl. Phys. Lett. 1985, 47, 1288. (5) Hoke, W. E.; Lemonias, P. J. Appl. Phys. Lett. 1985, 46, 398.

0022-3654/86/2090-4568$01.50/0

photochemical processes involved. Knowledge of the excimerlaser-induced photoproducts from a vast variety of organometallic compounds is needed for selection of the appropriate molecule, laser wavelength, and intensity for a given deposition process. The applications of lasers in (photo-) chemical analysis has brought tremendous advantages over classical techniques. Different from the purely spectroscopic techniques such as laserinduced fluorescence (LIF) and coherent antistokes raman scattering (CARS), laser mass spectroscopy gives both: the mass of the species to be detected and in addition spectroscopic information, which makes this technique unique for sensitive identification and characterization of stable and transient species. In addition, this technique has the potential for the exact evaluation of ultrafast kinetics: though this field is still in its infancy. In this respect, it is interesting to note that already in 1971 Jonah, Chandra, and Bersohn measured in an ingenious and elegant experiment’ the photodissociation of dimethylcadmium Cd (CH,), and-without using any laser-they could estimate the photodissociation kinetics to be on the femtosecond time scale. In general, however, the use of lasers will be necessary for a detailed understanding of the photoprocess: product identification, internal energy characterization of photoproduct atoms and molecules, and determination of the (ultrafast) kinetics involved. A recent review of the applications of lasers in chemical analysis is given in ref 8. Tellurium (and also selenium) is used in a vast variety of important group 11-VI (groups 12-16)17 compounds such as cadmium mercury telluride, an infrared detector material; in HgTe/CdTe superlattices; in phase-change-erasable optical data storage devices. Also some compact disk (CD) players use tellurium-containing layers. Dimethyl ditelluride, CH,TeTeCH,, is a suitable organometallic precursor of tellurium. In the following, we shall describe a (6) El-Sayed, M. A,; Gobeli, D.; Simon, J. In Ultrafast Phenomena; Auston, D. H., Eisenthal, K. B., Springer Ser. Chem. Phys. Springer: Berlin, 1984; Eds.; Vol. 38, 341. Greene, B. I.; Farrow, R. C. J. Chem. Phys. 1983, 78, 3336. Greene, B.I. In Ultrafast Phenomena; Ed. Auston, D.H., Eisenthal, K.B., Springer Ser. Chem. Phys. IV; Springer: Berlin, 1984; Eds.; Vol. 38, 308. Stuke, M. Proc. Con$ Laser Electroopt. (CLEO), June 1984, Anaheim, CA 1984, 254. (7) Jonah, C . ; Chandra, P.; Bersohn, J. Chem. Phys. 1971, 55, 1903. (8) Zare, R . N. Science 1984, 226, 298.

0 1986 American Chemical Society