6316
J . Phys. Chem. 1990, 94, 6316-6320
the more accurate of the experimental values. In the present case, we believe that this was the laser result. A considerable simplification of the complications of high-temperature pyrolysis experiments can thus be achieved. The agreement between the modeling of the thermal rate constants, based on the measured laser results, and the measured thermal rate constants generally was within a factor of 2. Only for isopropylbenzene and tert-butylbenzene were discrepancies of about a factor of 3 observed. The incomplete knowledge about the dissociation energies in some cases left some uncertainties. However, in general, the present work showed a possibility to circumvent mechanistic difficulties in thermal dissociation experiments by using the related laser photolysis measurements. It
should be mentioned that the simplified SACM formalism, fixing the a / @ratio at its universal value of 0.5, in spite of the remaining artifacts of the method and the uncertainties in the potential energy surface, apparently predicted the rate constants within about a factor of 2 accuracy without parameter fitting. Acknowledgment. Financial support of this work by the Deutsche Forschungsgemeinschaft (Sonderforschungbereich 93 "Photochemie mit Lasern") is gratefully acknowledged. Registry No. Toluene, 108-88-3; m-xylene, 108-38-3; o-xylene, 9547-6; p-xylene, 106-42-3; mesitylene, 108-67-8; ethylbenzene, 100-41-4; isopropylbenzene, 98-82-8; ieri-butylbenzene, 98-06-6; methyl, 222907-4.
C-C and C-H Bond Splits of Laser-Excited Aromatic Molecules. 2. I n Situ Measurements of Branching Ratios K. Luther, J. Troe,* and K.-M. Weitzel Institut fur Physikalische Chemie der Universitat Gottingen, Tammannstrasse 6, 0-3400 Gottingen, West Germany (Received: August 17, 1989; In Final Form: February 14, 1990)
CH3 yields have been measured by multiphoton ionization in the laser-induced dissociation of toluene and ethyl-benzene under collision-free conditions. At an excitation energy near 53000 cm-I, about 17% of toluene dissociate by C-C bond split whereas 83% decompose by C-H bond split. Analysis of this result by unimolecular rate theory leads to thermal branching ratios for C-C bond split which rise from 13% at 1000 K to 47% at 2000 K. The importance of rotational effects in the specific rate constant k(E,J) is discussed with respect to the branching ratio.
-+
C~HSCH, C ~ H S C + H ~H
1. Introduction
The unambiguous identification of the products of elementary chemical reactions and, in the case of branching processes, of their relative yields often presents difficulties. Under high temperature combustion conditions this problem may become particularly serious when the branching ratios of competing dissociation channels become temperature- and pressure-dependent and the products give rise to different mechanisms of secondary reactions. In this situation a method for the direct identification of primary dissociation fragments and their yields appears desirable. The present work describes such a technique which is applicable under the condition that the dissociating molecule is characterized by suitable photophysical properties. We consider alkylbenzenes as examples of the present method. After laser irradiation at 193 nm these molecules undergo rapid internal conversion from excited electronic states to the electronic ground state such that high vibrational excitation arises. Similar energy levels as in high-temperature pyrolysis are populated; however, in photolysis the dissociation process can be studied under isolated molecule conditions. Dissociation rates and the identity of the dominant dissociation products have been determined in this way in part 1 I of this series. The accuracy of these measurements, however, did not allow characterization of the minor channels. This requires, instead, a direct identification of the minor products such as done in the present work. Multiphoton ionization with mass spectrometric identification is used for the detection of these species. A quantitative determination is achieved by actinometric calibration of the ion signals. In addition to this, the method allows one to specify the yields of various product vibrational states and to study the energy partitioning during the dissociation. The described technique is applied to the dissociation of toluene with the competing channels ( I ) Brand, U.; Hippler, H.; Lindemann, L.; Troe, J . J . Phys. Chem., preceding paper in this issue (part I ) .
0022-3654/90/2094-6316$02.50/0
(1)
C6H5 CH3 (2) The relative yields of channels 1 and 2 have been the subject of discussions in thermal dissociation studies suggesting either channel 12-5 or channel 26 to be dominant. The temperature dependence of the ratio k , / ( k , + k,) was discussed recently,' suggesting values of 0.9 at 1000 K, 0.5 at I500 K, and 0.32 at 2000 K. In the laser experiments from part l 1 and refs 8-12, benzyl radicals and hydrogen atoms were identified as being the major products. The difference in the conclusions about a dominance of channel 1 or channel 2 in the pyrolysis could have been induced by mechanistic problems under the complicated thermal pyrolysis conditions. In the present work we detect CH3 radicals under isolated molecule conditions by multiphoton ionization. The CH3 channel has been detected before in molecular beam studies of the p y r o l y ~ i s , ~ ~ ~ ' ~ although details of these measurements have not yet been pub-+
(2) Brouwer, L. D.; Muller-Markgraf. W.; Troe, J . J . Phys. Chem. 1988, 92, 4905 (and references cited therein). (3) Rao, V. S.; Skinner, G.B. J . Phys. Chem. 1984, 88, 4362. (4) Braun-Unkhoff, M.; Frank, P.; Just, Th. Symp. ( h r ) Combusi. (Proc.) 1988, 22, 1053, and unpublished data 1986-1989. ( 5 ) Colket, M. Symp. (Int.) Combust. (Proc.) 1984, 20, 1032. ( 6 ) Pamidimukkula, K. M.; Kern, R. D.; Patel, M. R.; Wei, H. C.; Kiefer, J . H. J . Phys. Chem. 1987, 91, 2148. (7) Rao, V. S.; Skinner, G . B. J . Phys. Chem. 1989, 93, 1864 (and references cited therein). (8) Hippler, H.; Schubert, K.; Troe, J.; Wendelken, H. J . Chem. Phys. Leu. 1981, 84, 253. (9) Ikeda, N . ; Nakashima, N.; Yoshihara, K. J . Chem. Phys. 1985, 82, 5285. (IO) Kaji, Y.; Obi, K.; Tanaka, I.; Ikeda, N.; Nakashima, N . ; Yoshihara, K. J . Chem. Phys. 1987, 86, 61 15. (1 I ) Hippler, H.; Lindemann, L.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 440. (12) Bersohn, R.; Tsukiyama, K. J . Chem. Phys. 1987, 86, 745. ( 1 3 ) Krajnovich, D. J.; Buss, R . J.; Lee, Y. T. Con/ (Inz.) Phorochem. (Stanford) 1982. (14) Brudzinsky, R. J.; Felder, P.; Buss, R. J.; Lee, Y . T. Conf. (Int.) Radiaiionless Trans. (Newpor? Beach) 1984. Brudzinsky, R. J. Ph.D. Thesis, Berkeley CA, 1987.
0 1990 American Chemical Society
C-C and C-H Bond Splits of Aromatic Molecules lished. The derived fragment translational energy distributions from the beam experiments are complemented, in the present work, by determinations of CH3 vibrational distributions. Although the characterization of channels 1 and 2 by the described laser methods is straightforward, the application to the thermal dissociation requires further discussion. The branching ratio may be strongly energy-dependent such that the single-energy laser excitation experiments may have provided insufficient information. An energy dependence of the branching ratio results in a temperature dependence in thermal dissociation. Therefore, the laser result not necessarily gives the adequate answer for pyrolysis experiments. A theoretical analysis solves this problem. The investigation of alkylbenzene dissociation rates1 as well as of the fragment energy distributions indicates statistical reaction behavior. Modeling by the statistical adiabatic channel model (SACM)15.16of the two competing channels with energy E- and angular momentum J-dependent specific rate constants k,(E,J) and k2(E,J),after calibration with the laser experiment at a single energy E , then allows for a complete characterization of the branching. For the toluene system, e.g., an increasing importance of the minor channel at higher temperatures is predicted. The consequences of this behavior for high-temperature pyrolysis will be discussed.
2. Experimental Technique In the present work, alternatively toluene and ethylbenzene were irradiated by 15-11s flashes at 193 nm of an ArF excimer laser (Lambda Physik EMG 101 MSC) with a pulse energy of about 0.7 mJ in an unfocused beam of 4.5 mm diameter, corresponding to an intensity of 0.3 MW/cm2. The molecules were irradiated at a pressure of 4 X 1 0-3 mTorr in the ionization chamber of a time-of-flight mass spectrometer. At variable delay times after the excitation pulse, methyl radicals arising from the dissociation of toluene were ionized by resonance-enhanced multiphoton ionization (REMPI). Pulses of about 1 mJ from an excimerlaser-pumped dye laser (Lambda Physik EMG 101/FL3002, wavelength calibration by optogalvanic effect1') were focused with a quartz lense of 40 mm focal length into the photolysis region. The ions were extracted, accelerated, and detected by a multichannel plate detector (Varian 89462s). The ion signals were recorded with a fast transient digitizer (LeCroy TR8828B, 200 MHz) and handled numerically on a multichannel analyzer (LeCroy 3500 SA). A complete mass spectrum was distributed over 2500 channels with a recording time of 5 ns/channel. Typically 100-200 experiments were averaged. Between two experiments the gas in the reaction chamber was nearly completely exchanged by a flow of unreacted molecules through the cell. All further details of our experimental set up are described in ref 18. The detection of CH, radicals was done by the 2 + 1 REMPI technique where, by absorption of two photons, a Rydberg state is populated and the absorption of a further photpn leads to i~nization.'~The two-photon transition 3p2Ap X2AT is not observed by single-photon absorption.20 The 0; vibrational transition at X = 333.5 nm is strongest, indicating similar geometries of excited and ground 2 A F states. The 21 transition is shifted by 3.8 nm to the blue, Le., found at X = 329.7 nm. The shift corresponds to a higher bending frequency of the excited 2A2" state compared to the ground state for which ij = 606 cm-l was determined.21 Under the present collision-free photolysis conditions, the 0and the 1-1 bands have different half-widths, being equal to 0.15 and 0.8 nm, respectively. Figure 1 shows the corresponding REMPI signals of the two transitions from the dis-
-
(1 5 ) Quack, M.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974. 78. 241 J. J.. Chem. Phws. 1983. 79. 6017. (16), Troe. ~~,~ . ,~ ~. (17) King, D.S.;Schenck, P. K.; SmyihlK. C.; Travis, J. C. Appl. Opt. 1977, 16, 2617. Turk, G.C.; Travis, J. C.; de Voc,J. R.; OHaver, T. C. Anal. Chem. 1978, 50, 817. (18) Weitzel. K.-M. Doctoral Thesis, Gottingen, 1989. (19) Di Guiseppe, T. G.; Hudgens, J. W.; Lin, M. C. J . Chem. Phys. 1982, 76, 3337; 1983, 79. 571. (20) Herzberg, G. Molecular Spectra and Molecular Structure III; Van Nostrand Reinhold: New York, 1966. (21) Hirota, E.; Yamada, C. J . Mol. Spectrosc. 1982, 96, 175. ~
~
~
~
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6317
.."""
333
2
1
3
4
333.5 6
I
8
9 334
hinm "1"
"9.
m-
-
..
/o
5
2MO
-
c
.
=! IO00 c
u
I
1
1
1
Probe 333 5nm.15 GW/cm*
Y) 0 c *
c
~
Pump ond Probe At = 310 ns
Figure 2. Ion signals generated by pump (A), probe (B), and pump + probe (C) laser pulses.
sociation of ethylbenzene such as recorded 300 ns after the photolysis pulse. No rotational fine structure was resolved similar to the observations with thermalized CH, from the pyrolysis of di-tert-butyl peroxide at 1100 K from ref 19. Rotational fine structure of the 0-0 band has, however, been resolvedzz with jet-cooled CH3 radicals at a temperature near 40 K. The different widths of the 0-0 and 1-1 bands have also been observed in ref 19. The relative ratio of the 0and 1-1 signals will be interpreted later on in terms of the internal energy distribution of CH, radicals originating from the photolysis. The absolute reaction yields of CH, in the present work, are determined by comparing signals from ethylbenzene and toluene photolysis. Such experiments have been done under identical conditions, once with ethylbenzene, once with toluene in the reaction cell; see below. Before the CH, REMPI signals can be uniquely attributed to the photolysis being under investigation, any ion signals originating from the photolysis and probe pulses alone have to be identified and subtracted. At the lowest intensities (0.3 MW/cmz) of the 193-nm photolysis pulse, without the REMPI probe pulse, some ions at the masses 106 and 91 were detected as well as smaller fragments like CH,+ (n = 1, 2, 3). At the chosen sensitivity of the mass spectrometer, these signals, however, can be ignored; see Figure 2. Increasing the photolysis pulse intensity up to about 2 MW/cm2 on the one hand increases these ion signals and on the other hand induces multiphoton dissociation of the parent (22) Chen, P.; Colson, S. D.; Chupka, W. A.; Bersohn, J. A. J . Phys. Chem. 1986, 90, 2319.
6318
Luther et al.
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
2woi
2000 Ln
p
I
0 00
0 25
0 75
050
100
125
lsool-.
I
01
ao
0.5
At/pS
2.0
2.5
P t / p
Time dependence of CH3 ion signals during photodissociation of ethylbenzene: pump pulse at 193 nm, probe pulse at 333.5 nm, solid line representing best fit of the data to a double exponential. Figure 3.
molecules such as discussed in part 3.23 The REMPI probe pulse, in the absence of the photolysis pulse, because of its higher intensity (of the order of 15 GW/cm2) produces ion signals. Figure 2 shows these ion signals for m / e = 12-1 5. In addition, signals at m / e = 24, 25, 26,27, and 39 from the ions C2+,C2H+,C2H2+,C2H3+, and C3H3+are obtained. In the presence of the photolysis and the REMPI probe pulse (delay time of the probe pulse 200 ns), the CH, signal at m / e = 15 is greatly enhanced while the signals at the other masses remain unchanged; see Figure 2. This demonstrates that the unavoidable background ion signals can be safely subtracted. Since we always deal with photon densities, which are orders of magnitude larger than the density of molecules in the ionization region, the probe laser pulse is only absorbed to a minor extent. At a pressure of 4 X IO-, Torr, an effective ionization volume of 1.5 X cm3 and 6% of excited molecules, about 150 CH, radicals will be formed by every pump laser pulse. On the other hand, the observed CH, REMPI signals (see Figure 2), at a detector gain of IO6, correspond to about 150 ions. This estimate shows the high detection efficiency of our apparatus. The small total ion numbers are of importance for ruling out spacecharge effects. In the following, the difference of the signals from pump and probe and from probe pulses only will be discussed. While some CH3+signal is generated from the parent molecules toluene and ethylbenzene by the probe pulse, only minor additional contributions are expected from hot radical products such as phenyl and benzyl. After multiphoton excitation, these species probably undergo internal conversion and decompose by analogy to the thermal dissociation. The corresponding fragments are known to be more of the C,H, type than hydrogen-rich like CH,. In addition, we could not detect CH, signals from benzene under our conditions. 3. Experimental Results 3.1. Time Dependence o j C H , Formation. The time dependence of the CH, signal arising from the photolysis of ethylbenzene at I93 nm, monitored with variable delay times between photolysis and probe pulses, is shown in Figure 3. The photolysis is rapid, with a rise time of the CH, signal of the order of 50 ns. The decay of the CH, signal is attributed to the much slower disappearance of the radicals by flying out of the probe volume. Figure 3 shows a fit of the ion signals S(t) to the function s(t)= S,[eXp(-kbt) - exp(-kat)] (3) The parameters So = 15 000 f 1500 (arbitrary units), k, = (2.0 f 0.4) X IO7 s-', and kb = (2.6 f 1) X IO3 s-l are derived. Figure 4 shows the time dependence of the CH, signal arising from the photolysis of toluene a t 193 nm. The rise time of the signal is about a factor of 10 larger. The full line corresponds to a fit following eq 3 with the parameters So = 2500 f 800 (arbritrary units), k, = (2.2 f 1) X IO6 s-l, and kb = (1.3 f 1) X IO5 s-l. I t should be emphasized that the parameters Soare (23) Hippler,,H.;Riehn, Ch.; Troe, J.; Weitzel, following paper in this issue (part 3).
1.5
1.0
K.-M. J . Phys. Chem.,
Figure 4. Time dependence of CH, ion signals during photodissociation of toluene: pump pulse at 193 nm, probe pulse at 333.5 nm, identical experimental conditions as in Figure 3, solid line representing best fit of the data to a double exponential.
derived from experiments under identical probing conditions such that their ratio can be evaluated in terms of relative CH, yields (see below). The derived values of k, are in good agreement with the corresponding values derived from the formation of benzyl radicals in the 193-nm photolysis: For ethylbenzene, k, = (2.3 f 0.4) X IO7 s-l was obtained in this way in part 1;' for toluene, k, = (1.9 f 0.3)X lo6 s-I was found. Since k, corresponds to the sum of the rate constants of the competing dissociation processes, the agreement of the present k, values with the earlier results confirms the validity of the present experiments. 3.2. CH, Yields. The photolysis of ethylbenzene in our work serves as the actinometer for the CH, signals. In order to derive the CH, quantum yield from toluene photolysis on the basis of this actinometer, the CH, quantum yield in the photolysis of ethylbenzene has to be known as well as the ratio of the absorption coefficients of the two molecules at 193 nm. Measurements of the decadic absorption coefficients in a Cary 17D spectrometer gave t = 5000 L mol-I cm-I for ethylbenzene and e = 4250 L mol-l cm-' for toluene. The determination of the benzyl yields in the laser photolysis of ethylbenzene, based on the known absorption coefficients of benzyl radials from the photolysis of benzyl chloride, in part I ' led to values of larger than 0.75. Furthermore, the thermal dissociation of ethylbenzene is known to lead predominantly to benzyl CH, p r o d ~ c t s . It~ should ~ ~ ~ ~be added that the present experiments used identical ethylbenzene and toluene pressures, and that multiphoton processes were small. The detailed investigation of multiphoton processes (part 323) allowed us to subtract this contribution in the present work. With CH, quantum yields of 0.75 in the photolysis of ethylbenzene, the corresponding yield for toluene from the ratio of So values from section 3.1 follows as 0.14. With a CH, yield of 1 in the ethylbenzene photolysis, a value of 0.19 would be derived. A final result 4(CH3) = 0.17 f 0.06 (4)
+
for the toluene photolysis encompasses the estimated errors from the present measurements and from the actinometer. As long as there are only the channels 1 and 2 in toluene photolysis, @(CH,) corresponds to the ratio k2/(kl k2). Our direct result agrees roughly with the other direct laser measurement in molecular beams from refs 13 and 14 which gave @ = 0.13 and 0.1 1, respectively. This, however, was obtained with slightly lower excitation energies (excitation of cycloheptatriene at 248 and 266 nm). 3.3. Vibrational Distribution of CH,. In the following, the ratio of the 0-0 and 1-1 band intensities will be analyzed briefly by comparison of the present results with the observations from
+
(24) Robaugh, D. A.; Stein, S. E. I n f . J . Chem. Kinef. 1981, 13, 445. Robaugh, D. A,; Tsang, W.; Fahr, A,; Stein, S. E. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 11. (25) Muller-Markgraf. W.: Troe, J. J . Phys. Chem. 1988, 92, 4414.
C-C and C-H Bond Splits of Aromatic Molecules
El
cm-' 45000 50000 55000 60000 70000 80000 90000
kl (E,J=O) 3.2 X 10' 5.4 X IO' 4.7 X IO6 2.6 X 10' 3.5 X lo8 2.2 X IO9 8.3 X lo9
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6319
k2 y2 kl k2 y2 (E,J=O) (E,J=O) (E,J=100) (E,J=100) (E,J=100) 2.0 X 10' 0.059 3.1 X 10' 2.5 X lo3 0.075 0.13 5.0 X 10' 8.3 X IO' 1.1 X 10' 0.18 1.2 X IO6 0.20 4.6 X IO6 1.5 X 106 0.25 8.5 X lo6 0.25 2.7 X lo7 1.1 X lo6 0.29 1.4 X IO8 0.29 3.6 X 10' 1.8 X 10' 0.32 9.4 X lo8 0.30 2.2 X lo9 1.1 X lo9 0.34 3.5 X IO9 0.30 8.8 X lo9 4.2 X IO9 0.34
kl k2 y2 kl k2 y2 (E,J=250) (E,J=250) (E,J=250) (E,J=490) (E,J=490) (E,J=490) 4.8 X lo3 2.7 X lo3 0.32 6.2 X lo2 1.00 2.0 X lo5 1.7 X 10' 0.45 1.3 X 10' 2.4 X lo5 1.00 2.7 X lo6 2.9 X IO6 0.51 3.7 X lo3 6.4 X 106 1.00 2.0 X 10' 2.3 X 10' 0.54 1.7 X 10' 6.0 X 10' 1.00 3.3 X lo8 4.1 X 10' 0.56 1.4 X lo7 1.0 X IO9 0.99 2.3 X lo9 2.6 X lo9 0.53 3.2 X 10' 5.4 X lo9 0.94 9.5 X lo9 8.7 X lo9 0.48 2.2 X lo9 1.5 X 10'O 0.87
"C-H bond split, k , ; C-C bond split, k2; k(E,J) in s-I. ref 19. The ratio of the apparent intensities I of the 1-1 and 0-0 transitions for ethylbenzene photolysis in our work was found to be I(l-l)/I(O-O) = 1/6 whereas this ratio for the reference spectrum from ref 19 followed as 1/9.5. The half-widths of the two bands were nearly identical in the two experiments. We now assume that the dissociation of ethylbenzene behaves statistically such as described by the statistical adiabatic channel model (SACM). We furthermore take into account that the energy distributions of individual oscillators in canonical and microcanonical ensembles of excited polyatomic molecules of the same average internal energies are nearly identical.2628 We now calculate the apparent temperature of the dissociation fragments by identifying the distributable energy of the dissociating molecules ( E ) with an average energy S&T. Here, ( E ) is given by the sum of the energy of a photon at 193 nm and the average thermal energy at room temperature reduced by the dissociation energy Eo = 26 9 10 cm-I; i.e. ( E ) = 26 050 cm-I. The effective number S,, of adiabatic channels, over which the energy ( E ) is distributed statistically, can be deduced in the simplest way from the energy dependence of the number of open channels W(E,J=O) whose energy dependence near ( E ) is expressed by W(E,J=O) a ( E The evaluation of the SACM calculations of part 1' for E = 50300 cm-l gave W(E,J=O) = 1.6 X lo7, for E = 55 300 cm-' gave W(E,J-0) = 1.2 X lo9, such that Seff= 23.7 and an apparent temperature of 1680 K arises. Under the assumption that the observed 1-1 transition corresponds to the excitation of the ground-state bending of CH3 with a characteristic temperature of 0 = 606 cm-I, i.e. hc/k = 872 K,the intensity ratio I(l-l)/ I(0-0) at 1680 K should be exp(-872/1680 + 872/1100) = 1.3 times larger than this ratio at 1100 K. Our experiments gave an intensity ratio which was about 1.6 times larger than that of the reference spectrum from ref 19. Since in the experiments of ref 19 the distribution may have relaxed slightly from that of the initial temperature of 1100 K, our measured intensity ratio of the 1-1 and 0-0 transitions within the experimental uncertainties appears consistent with a statistical energy redistribution over the dissociation channels. The intensity ratio in toluene dissociation, because of the smaller signals, was more difficult to measure. However, there, was also no evidence for deviations from statistical behavior. The translational energy distributions recorded in the molecular beam experiments of toluene d i s s ~ c i a t i o n ' ~also J ~ appeared consistent with statistical behavior, at least for the CH3 radicals.
4. SACM Representation of the Specific Rate Constants k(E,J) The specific rate constants k(E,J) of the major dissociation channels for toluene, Le., the C-H bond split, and for ethylbenzene, Le., the C-C bond split, in ref 1 have been constructed by the statistical adiabatic channel model (SACM). The simplified version of ref 16 was employed using an anisotropy ratio a/j3 = 0.5 and an empirical correction factor fixed by comparison with the measured (k(E,J)) values for a thermal rotational distribution. At the excitation energy of the laser experiment, the J dependence of k(E,J) was found to be only small. Therefore, the rotational (26) Quack, M. Nuovo Cimento SOC.Ital. Fis., B 1981, 638, 358. (27) Brouwer. L.; Hippler, H.; Lindcmann, L.; Troe, J. J. Phys. Chem. 1985, 89, 4608. (28) Dove, J. E.;Hippler, H.; Plach, H. J.; Troe, J. J . Chem. Phys. 1984, 81, 1209.
102
50
60 70 80 90 E I lo3 cm-' Figure 5. Specific rate constants k(E,J) for C-H bond split ( k , ( E , J ) ) and C-C bond split ( k 2 ( E , J ) ) in the dissociation of toluene (SACM
calculations of this work, fitted to measured dissociation rate constant! and branching ratio from this work). average ( k ( E , J ) ) practically agreed with the k(E,J=O) value. The comparison of k(E,J) with respect to absolute value, energy and angular momentum dependence, in ref 1 was done for C-H and C-C bond splits in groups of different molecules with different properties. It, therefore, appears possible to make this comparison for C-H and C-C bond splits in the same molecule, Le., toluene in the present work. We again apply the simplified SACM version of ref 16. The details of the calculation for the dominant C-H bond split (1) were indicated in ref 1. The analogous calculation for the C-C bond split (2) was made using a/P = 0.5 and an empirical energy-independent correction factor such that our measured branching ratio of 0.17 is reproduced for J = 0. This calculation leads to the specific rate constants for the two channels, k,(E,J) and k2(E,J),respectively, which are shown in Table I and Figure 5. E- and J-dependent branching ratios
are also included in Table I. A number of points are worth noticing. First, one should keep in mind that the branching ratio only depends on the ratio of number of open channels W(E,J) whereas densities of states cancel from the specific rate constants k(E,J) used in eq 5 . Second, the branching ratio depends on the energy E and, even more strongly, on the angular momentum J . Our present experiments (near r c " temperature) correspond to a low average J value ( ( J ) near 40) where the J dependence of the branching ratio is still small and close to Y2(E,J=O). Hightemperature thermal experiments, however, have to take into account the strong J dependence; see next section. Any RRKMtype analysis neglecting the explicit J dependence of the specific rate constants k(E,J), therefore, will lead to incorrect interpretations of the high-temperature thermal branching ratios. The J dependence of the number of channels W(E,J)entering k ( E , J ) , and of the branching ratio Y(E,J),arises from several contributions in which the two channels show different behavior. There is, first, a different dependence of the threshold energies
6320 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 E o ( J ) on the angular momentum. Using a Morse potential and a linear, quasi-triatomic centrifugal model, for channel 1, we have obtained the J dependence Eoi(J)- Eoi(J=O) = CJ(J + 1) with C, = 0.054 an-'; for channel 2, the much smaller value C2= 0.015 cm-' was derived (for not too large J values). The difference in the Ci values is due to the strongly differing reduced moments of inertia of the fragments which arise from the different masses of the H and CH3 fragments. The different centrifugal barriers lead to a "rotational channel s ~ i t c h i n g " ; ~Le., ~ ~channel '~ 1 has the lower threshold energy for low J , whereas channel 2 has the lower threshold energy for high J . The J value, at which the channel switching occurs, depends on the different Ci values and the difference in the channel threshold energies Eoi(J=O). With the given Ci values and AEoi(J=O) = 36 0oO - 3 1 080 cm-l = 4920 cm-I, such as used in the present work, one predicts channel switching at a J value near J = 360. Although this value is high, channel-switching effects are becoming relevant for high-temperature thermal dissociation reactions; see next section. Second, there is a different number of rotational modes in the fragments of the two reactions which also have different moments of inertia. In the case of reaction 1, with dissociation into benzyl + H, the adiabatic channels of the dissociation lead to the 36 vibrational and 3 rotational modes of benzyl. In the case of reaction 2, they lead to the 27 vibrational and 3 rotational modes of phenyl and the 6 vibrational and 3 rotational modes of methyl. Treating benzyl + H as a spherical top + atom system, phase space theory ( E T ) gives the number of channels of the rotational modes asI6
Luther et al. TABLE 11: Thermal Branching Ratios Y1(T ) for C C Bond Split in the Dissociation of Toluene" Yl(r)
IOOOK
1200K
1400K
1600K
1800K
0.13
0.21 0.22
0.29 0.36
0.36 0.50
0.42 0.60
Y*(n 0.10
"This work, based on laser-induced dissociation. based on thermal dissociation results.
2000K-ref 0.47 0.68
u
6
Reference 7,
specific rate constants of the branching unimolecular reactions determine the thermally averaged branching ratio.29 We do not consider this range here, but concentrate instead on the highpressure range where Boltzmann distributions of excited states are established. In this case, the thermal rate constants k,( T ) for dissociation are given by thermally averaged expressions in which the densities of states cancel and only W(E,J) enter. With the described calculation of specific rate constants one obtains the following thermal rate constants of recombination in the high-pressure limit k,,-(300 K) = 2 X I O l 4 cm3 mol-] s-I for reaction 1 and k,,(300 K) = 2.5 X IOt3 cm3 mol-' s-l for reaction 2. For dissociation, we obtain kdiss,, = 10'6.26exp(-384 kJ mol-'/R7') s-' for reaction 1 and kdiss,..= 10i6.99exp(-414 kJ mol-'/RT) s-I for reaction 2. These values result in thermal branching ratios
such as given in Table 11. V2(7') markedly exceeds the values of Y2(E,J=O)and Y2(E,J=100)because of the contributions from higher J values, confirming the trend shown in Table I. for small J , and Table I1 compares our predicted thermal branching ratios with estimates from thermal dissociation experiments given in ref 7 . Wrot,l(E,J) 4(E - EOI(J))~/'/~B~/' (7) Our present laser results, which are consistent with the photolysis data from refs 1 , 13, and 14, predict somewhat lower branching for large J . Here, B is the geometrical mean of the rotational ratios Y2(T)than the estimated values from ref 7 . Also the constants of benzyl. In SACM-modified PST,3' the value of B temperature dependence is slightly different. However, in view in eqs 6 and 7 is increased up to an effective value chosen such of the various experimental uncertainties, the agreement appears that a measured k(E,J) is fitted.l Likewise, treating phenyl satisfactory. CH, as a system of two spherical tops, PST gives The advantage of the present determination lies in the fact that Wrot,z(E,J) = ( 2 J + 1)8(E - E O ~ ) ' / ' / ~ ~ B ~+B ~ [ B I (8) mechanistic complications as in thermal reactions do not occur. The accuracy of our measurements was quite good. The analysis for small J , and of the data in terms of unimolecular rate theory is relatively free WrO,2(E,J)= ( E - E o ~ ( J ) ) ~ / ~ B I ~ / ~ (9) B z ~ / ~from artifacts. Some dependence on the difference of the threshold energies Eo,- Eo,remains. (Here we used Eo,= 36000 cm-I for large J , where B , and B2 are the geometrical means of the and Eo, = 31 080 cm-], see ref 1 . ) We showed that the analysis rotational constants of phenyl and CH,, respectively. Again, B1 requires particular care with respect to J dependences of k(E,J). and B2 are increased in SACM-modified PST accounting for the RRKM treatments, which do not explicitly account for adequate "rigidity" introduced by the anisotropy of the potential. In order centrifugal barriers and angular momentum conservation, to obtain the total numbers of open channels, the expressions for therefore, have to be considered with caution. (The analysis of Wr,,(E,J)have to be convoluted with the numbers of states of 36 ref 7 combined an RRKM analysis with the experimental data oscillators in reaction 1 and of 27 + 6 oscillators in reaction 2. from refs 6 and 7 ) . The present analysis suggests that the C-H Obviously, the different behavior of the two channels (threshold bond split at T I 2000 K always dominates, in agreement with energies, energy dependence of Wrot, and product rotational the conclusions from ref 2. Nevertheless, with increasing temconstants) will lead to largely different E and J dependences of peratures the C-C bond split becomes increasingly important. In the specific rate constants and of the branching ratios. Following high-temperature experiments it, therefore, should always be taken the described approach, we have obtained the results of Table I into account. and Figure 5 which illustrate this behavior. Our present work, like part 1 , ' has demonstrated that laserexcitation studies of dissociation processes in the electronic ground 5. Thermal Rate Constants and Thermal Branching Ratios state can provide an essential help to understand complicated Branching ratios of two channel thermal unimolecular reactions thermal decomposition systems. are known to be strongly pressure dependent. At low pressures Acknowledgment. Financial support of this work by the the properties of collisonal energy transfer together with the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 93 "Photochemie mit Lasern") and the Stiftung Volkswagenwerk is (29) Just, Th : Troe, J. J. Phys. Chem. 1980, 84. 3068. gratefully acknowledged. (30) Troe. J In?. J. Mass. Spectrom. Ion Processes 1987, 80, 17. Registry No. CH3, 2229-07-4; toluene, 108-88-3; ethylbenzene, 100(31) Brouwer, L.;Cobos, C. J.; Troe, J.; Dlbal, H.R.; Crim, F. F. J. Wrot,i(E,J) = (2J + 1)(E - E o i ( J ) ) / B
(6)
+
~
Chem Phys 1987, 86,6171.
~~~
41-4.
