10316
J. Phys. Chem. 1992, 96, 10316-10322
Temperature Dependences of CH, @A,) Removal Rates by Ar, NO, H2, and CH2C0 In the Range 295-859 K G.Hancock* and M. R.Heal Oxford Centre for Applied Kinetics, Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 JQZ, U.K. (Received: June 24, 1992; In Final Form: September 16, 1992)
Absolute rate constants for the removal of CHI (H'A,) by Ar, NO, H2, and CH2C0have been measured over the temperature range 295-859 K by the method of long-path kinetic absorption spectroscopy. For quenching to the ground X3BIstate by Ar, the rate constant rises by a factor of 3 over this range from its room-temperature value. Both the absolute values and their increase up to -500 K can be explained by a mixed-state model of quenching, in which fractional populations of singlet states perturbed by nearby triplet levels and the relaxation of the corresponding triplet levels contribute to the measured removal rate. Above 500 K, there is a significant deviation between experiment and calculation, suggesting that additional high-energy perturbed singlet levels are affectingthe decay process. In contrast, removal by H2 and NO, both considered to be predominantly by reaction, shows no temperature variation over this range, while removal by ketene shows a negative temperature dependence. The implications of the results to singlet methylene quenching and reaction processes at combustion temperatures are discussed.
Introduction The methylene radical, CH2,the simplest of the carbene species, has long been studied because of the significant role it plays as a reactive intermediatein synthetic pathways or in complex kinetic systems such as hydrocarbon combustion and planetary atmospheres.'s2 The chemistry of methylene depends strongly on its electronic structure, and the existence of two low-lying electronic states separated by only a relatively small energy gap has ensured that the radical has become an important model system for understanding singlet-triplet interactions and reactivity. The uncertainty over the exact difference in energy between the triplet ground state (g3B,) and the first excited singlet electronic state (H 'Al), hereafter abbreviated to 3CH2and 'CHI, respectively, has recently been eliminated following direct spectroscopic observation of transitionsbetween the two states, and a value of 37.65 kJ mol-' has been ~ b t a i n e d . ~This , ~ small energy difference, of approximately the same order of magnitude as thermodynamic activation energies, means that the reactions of these two lowest electronic states cannot be treated independently and this becomes increasingly more important at elevated temperatures. Exploitation of laser techniques has facilitated the direct measurement of absolute room-temperature rate constants for 1CH2S-15 and 3CH21619removal by a large number of reactants. For CH2, reaction is generally very fast and approaches gas kinetic collision efficiency for many hydrocarbons, while the corresponding rate constants of 3CH2are 5 or 6 orders of magnitude smaller. The kinetic behavior of the ground state has additionally been thoroughly investigated over the temperature range 295-700 K using a discharge flow apparatus to produce the radical and far-infrared laser magnetic resonance (LMR) absorption as det e c t i ~ n . ' ~Until ' ~ recently, however, there has been no such systematic investigation of the temperature dependence of the reactions of 'CH2. In a preliminary paper, we have reported the rate constants for lCH2removal by Ar, NO, and H2 in the temperature range 295-431 K.14 The technique of continuous wave (cw) laser resonance absorption was used to monitor the time evolution of an individual 'CH2 rotational level following production of the radical by pulsed photolysis of ketene (CH2CO) in the near-UV. The present work extends these measurements up to a maximum temperature of 859 K and includes the temperature dependence of the removal of lCH2 by CH2C0 itself. Only one other study has been published for 'CH2 removal at temperatures other than ambient,13in which rate constants at the three temperatures 210,295, and 475 K only were evaluated for removal by He, Ar, N2,and H2 and the four hydrocarbons CHI, C2H6, C2H4, and C6H6. For the total removal of 'CH2 by a reactive species R, there may also be a component of removal by physical quenching to
the ground electronic state. It is important to know the contribution of this channel to the total removal rate at different temperatures for a full understanding of methylene chemistry. Removal of lCH2 in the presence of an inert quencher can only proceed by the physical quenching pathway of spin-forbidden colliiion-induced intersystem crossing to 'CH2, and the data obtained in this work with Ar as the collision partner afford an important test of theoretical models developed to explain this process. These in turn may then lead to predictions of trends in reactive rate constants and branching ratios at higher combustion temperatures.
Experimental Section The laser flash photolysis cw resonance absorption apparatus has been described in detail elsewhere,I4and only the main points are given again here. An advantage of this technique over pulsed timeresolved LIF is that an entire kinetic trace is obtained at each measurement. The output of a Lambda Physik EMGlOl XeCl exciplex laser at 308 nm was dincted along the length of a reaction cell by means of a dichroic mirror. The single-photon photolysis of CH2C0at this wavelength generates a "clean' source of 'CHI with near unity quantum yield20-22 without interference from the additional production of 3CH2ground-state radical. A cw probe beam from an argon-ion laser-pumped dye laser (Coherent Innova 70/CR599) was multipassed up to 12 times through the cell in the same plane as the volume swept out by the photolysis beam. An intracavity etalon in the dye laser narrowed the output bandwidth to -0.2 cm-I. The lCH2 radicals were detected in absorption by recordii the transient difference in signals between the probe beam after pasing through the cell and a reference beam split off prior to it entering the cell. The probe laser was tuned to a specific rovibiationaltransition in the pQIJ(J)subbranch near 590.5 nm in the b 'B,(0,14,0) H 'Al (O,O,O) vibronic band.23 The transition from the 414 rotational level of H 'A, (O,O,O) was used since this gave rise to the strongest absorbance signal in this region. Both the reference and probe cw beams were incident on identical fast-response S1223 Hamamatsu photodiodes with a rise time of 5 ns, The signals from the photodiodes were subtracted, and the transient difference signal produced at each photolysis pulse was amplified and taken to a 20-MHz digitizing board (Markenrich Corp. WAAG card) of a persona1,computer for subsequent analysis. Absorbance traces were collected and averaged over typically 50-100 laser shots. Calibration of the probe beam was achieved by reference to known peaks in the iodine absorption spectrum recorded by directing part of the beam through a second cell containing iodine vapor. A disadvantage of the absorption technique is that to obtain measurements of removal rates at greater than room temperature,
-
0022-3654/92/2096-103 16$03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No.25, 1992 10317
Temperature Dependences of CH2 (HIAl) Removal Rates the gas mixture over the entire absorption path length must be maintained constant at the elevated temperature. To achieve this, the reaction cell was mounted on a cradle inside a long cylindrical steel oven with end plates and heated by two heating tapes (Hotfoil Type G1) wrapped evenly around the outside of the cylinder. The whole apparatus was insulated using a 1-in. blanket of ceramic fiber. For the preliminary experiments,14the reaction cell was constructed of stainless steel (length 46 cm,internal diameter 4 cm)with Brewster angled quartz windows fmed at either end with Viton O-ring seals. The operating temperature of this cell was limited to 431 K and lower owing to thermal degradation of the O-rings and cracking of the quartz windows by expansion strews. A second cell of similar dimensions (length 50 cm, internal diameter 3.8 m)and constructed entirely of quartz with the windows fused directly onto the cell was therefore used in the majority of the experiments. Temperature measurement was provided by four calibrated type-K thermocouples attached to the body of the cell at the same level as the multipass plane and equally spaced along the length. The quartz cell was used for temperatures of up to 860 K with, at worst, a temperature gradient of 30 K along the length. This gradient diminished considerably for lower op erating temperatures. A limiting factor for the apparatus was refraction of the cw detection beam caused by fluctuations in the refractive index of the air by strong convection currents near the cell. In all experiments, a static gas sample was employed, and pressures were measured with a calibrated Datametria 0-10-Torr capacitance manometer located on the gas inlet line just outside of the heated oven. Ketene for photolysis was prepared by the pyrolysis of acetone24and purified by multiple trap-to-trap distillations between liquid nitrogen and dry ice/trichloroethylene slush baths, followed by pumping on the sample in a liquid nitrogen/isopentane-cooled trap at 113 K. Product purity was always confirmed by taking a mass spectrum and quantitatively assessed from a UV absorption spectrum between 200 and 400 nm.2s The ketene was stored frozen at -196 OC between experiments or at low pressures in a darkened bulb during experiments to prevent polymerization. Nitric oxide (NO) was also purified by repeated trapto-trap distillation. Hydrogen (H2) and argon (Ar) were obtained from BOC (with stated purities of 99.99% and 99.99596,respectively) and used as received. ResulQ
The experimental conditions were always chosen so that the removal of lCH2 obeyed first-order kinetics. Since only a very small fraction of ketene was photolyzed per shot (0.045%), this condition held even when ketene itself was the only reactant. Typical absorbances were always less than about 0.596, even for a total absorption path length of up to 6 m. For small total abeorbancea, the BemLambert law may be readily approximated without lass of accuracy to a form in which the transient Werence in signal between the reference and probe signals (Io - I) can be taken as proportional to the concentrationof the absorbing species in the probed path length. For measurements of removal rates with Ar, H2, or NO, the partial pressurs of ketene was kept constant at a value in the range 50-300 mTorr (depending on the cell temperature), while the pressure of the reactant gas was varied in the range 0-8 Torr for Ar and 0-700 mTorr for NO and H2. An example of the temporal evolution of absorbance from the 414 level under typical conditions is shown in Figure 1 and indicates the high level of signal to noise that was routinely obtained for the data. A pronounced exponential rise to the absorption trace was always observed, of much longer time scale than the 10-ns photolysis pulse length. It was therefore necessary to fit a double exponential of the form Y = A, [exP(-A2t)
- exp(-A301
(1)
to the data, where A, and A2 are the rise and fall rates, respectively, for the absorbance and Al is a scaling constant. Since the absorbance is directly proportional to the concentration of 'CH2, the constants A3 and A2 can be directly related to the rates of
0
2
4
6
8
10
Time / ps Figure 1. Example concentration of H IAl CHI in the 414rotational level of the (O,O,O) vibrational state as a function of time following the 308-nm photolysis pulse. The conditions were 160 mTorr of ketene, 1.80 Torr of Ar, 519 K with 50 shots averaged. The solid line corresponds to a least-squares fit to the data of a function with exponential rise and fall rates of 5.9 X lo6 and 9.2 X lo5 s-I, respectively.
production and relaxation for the 'CHI in the 414 rotational level being probed, where production is some fast process populating the level immediately after photolysis and relaxation is the slower total removal of population in collisions with reactant molecules. Deconvolution of the exponential rise from the absorbance trace yields the exponential decays associated with the removal of thermalized CH2 (H'A,). The linear relationship that is obtained for a plot of first-order rates for the rise (A3)against reactant pressure for a given reactant and temperature implies that a considerable proportion of the population of the 4,, level must build up through bimolecular relaxation of the initial population of photolysis rather than be the product of direct dissociation. In the presence of CH2C0 only at 303 K, such a plot yields a production rate constant for the probed rovibrational level of (7.7 1.0) X 10-locm3 molecule-' s-l. An exponential rise to the absorbance trace remained even at the highst temperature of 859 K investigated with this apparatus, indicating, therefore, that the nascent rotational temperature of lCH2produced in the photolysis of CH2C0 at 308 nm must still be considerably greater than this. A linear dependence of initial 'CHI concentration upon the photolysis fluence was observed and is entirely compatible with a single-photon proem being responsible for the formation of the lCH2 (O,O,O). Removal r a t a of other rotational or vibrational levels of lCH2 were not investigated in this work. Evidence from cw "eabeorption "entsof removal rates from other individually resolved transitions in the same pQIJsubband as that used in this study indicates that rotational equilibration must be fast on the time scale of collisional removal? as demonstrated by the fast bimolecular relaxation rate derived from the observed rises to the absorption traces. A further measurement by Langford et a1.6 using the 211(0,150) lol (0,l.O)transition indicates that vibrational relaxation within the H state is unimportant on the time scale of collisional removal. The rate coefficients kR for collisional removal of lCH2 were extracted in the standard way from the definition of the experimental fmt-order decay rates (A2)obtained from the fits to the absorbance profiles,
*
-
A2
kCH~CO[CH2COl+ kR[Rl
(2)
Typically, absorption profiles covering 10 different pressures of each reactant at each temperature were collected and analyzed. A least-squares linear regression fit to a plot of the decay rates A2 vs [R] was employed for decay rates covering the reactant pressure ranges already indicated, where kcH2co[CH2CO]was kept constant for removal with R (=NO, H2, and Ar). Example fint-order plots for removal by Ar at two different temperatures are illustrated in Figure 2. The slope of the fits yielded values of kR, where molecular rate constant units (cm3 molecule-' s-')
10318 The Journal of Physical Chemistry, Vol. 96, No.25, 1992 2
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Argon Concentration/ (IOi6 atoms cm")
18
20
Figure 2. First-order decay rate, A2, plotted as a function of concentration of Ar at two temperatures, 298 K (triangles) and 519 K (squares),
at constant partial pressures of CH2C0. Statistical error bars on indi-
vidual points, obtained from the fits to data such as thosc shown in Figure 1, were $58(la). The straight lines correspond to rate constants for cm3molecule-l s-' at 298 ICH2removal by Ar of 5.8 and 11.4 X and 519 K,respectively (error limits are discussed in the text), and the
intercepts are due to the component of 'CHI removal by ketene.
0
0
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.4
,'$L-----0250
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0
A
300
350
400
500
450
550
600
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i
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Temperature / (K) Figure 4. Rate constants for the collisional removal of H IAl CHI by H2 ( 0 ) Prcsent results, steel cell at temperatures < 430 K. (0) Present results, quartz cell at temperatures up to 680 K. Also shown are the room-temperature measurements of Ashfold et a1.5 ( 0 )and Langford et aL6 (+), together with the only other reported temperature-dependent measurements of Wagener" (A). Error bars are discussed in the text. _.I
-
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300 350 400 450 500 550 600 650 700 750 800 850 900
Temperature / (K)
Figure 3. Rate constants for the collisional removal of 5 'Al CH2by ketene. ( 0 )Present results, steel cell at temperatures < 430 K. (0) Present results, quartz cell at temperaturesup to 850 K. Also shown are
the room-temperature measurements of Langford et a1.6 (+) and Staker et al.ls ( 0 ) .The dashed line is the best fit to the data of an expression = A(T/295)", where A = (2.0 0.2) X cm3 of the form,k molecule-l s-l and n = -0.33 i 0.08. Error bars on the present data are discussed in the text.
*
were obtained by using the molecular density for the given temperature. Care was taken to mure a co118i8tcI1cy in measurements camed out with both of the reaction cells by performing at least two experiments with the quartz cell for each reactant in the 295-431 K overlap temperature range attainable with the steel cell. The rate constants obtained using both cells at a given temperature in the coincident temperature region were always equal to within experimental error. The temperature-dependent rate constants obtained for removal by each of the four collision partners (up to a maximum of 859 K) are shown in Table 1 and illustrated in Figures 3 4 The room-temperature (295 K) rate constants for removal of 'CH2 by CH,CO, H2, NO,and Ar are (210 f 20) X 10-12, (99 f 9) X 10-l2,(160 f 10) X 10-l2, and (5.5 f 0.5) X cm3molecule-' s-', respectively. Previously reported values for rate constants are additionally illustrated in Figures 3-6 for comparison. Error Andy& In general, the double-exponential fits to the experimentally obtained absorption traces converged readily so
-
1
I
I
I
250
300
350
400
I
450
I
I
I
I
500
550
600
650
0
TemperatureI (K) Figure 5. Rate constants for the collisional removal of H !Al CH2by NO. ( 0 )Present results, steel cell at temperatures < 430 K. (0) Quartz cell at temperatures up to 650 K. Also shown is the room-temperature measurement of Langford et a1.6 (+). Error bars on the present data are discussed in the text. that statistical uncertainty ( i l u ) in the decay rates at a given temperature and pressure is limited to f5% of the fitted value at most. However, two important source8 of systematic error that may affect the analysis of the absorbance trace3 are the diffuion of the *CH2radical from the path of the probe laser beam and consecutive shot depletion of CH2C0during the course of up to 100 averages. An excimer laser output of 90 d pulse-' distributed over a beam cross section of 4 X 1.5 an2dissociates only 0.045% of the CH2C0 contained within the photolysis volume per shot, when the one-photon absorption cross section of CH2C0 at 308 nm is taken as 2 x 10-20 cm2.25The photolyzed volume constitutes -40% of the total volume of the reaction cell, and diffusion in the time between laser shots (100ms) is sufficient to remix the gases completely. Ketene is also removed by subsequent reaction with 'CH2 produced in the photolysis, and at worst, when only CH2C0 is present in the cell, only a further equivalent fraction of 0.02% total CH2C0 will be removed in this way per shot. For 100 consecutive laser shots,therefore, the total CH2CO depletion will never exceed 4%. Experimental checks showed the absorption to be invariant with the number of laser shots over the range employed. Application of diffusion e q ~ a t i o n s ~demonstrates ~.~' that diffusion of 'CH2 out of the probe beam ia W b l e on the time scale of collisional removal for all but the most extreme case,
Temperature Dependences of CH2 (PA1) Removal Rates
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10319
TABLE I: ExpcliwatdRate ColgCIllQ k p for the Bimolecular Removal of CHI (i*A,) by KetHydrogea, Nitric Oxide, unl Argon as I Fuwtlon al Tempmturs (a) ketene (b) hydrogen (c) nitric oxide (d) argon TIK kCHs0 T/K kH2 TIK kNO TIK 4, 300 198 i 18 29 3 100i9 296 162 i 10 295 5.2 f 0.5 98 i 9 216 i 19 301 296 152 i 10 298 5.8 i 0.5 303 97 i 9 155 i 1 1 198 18 325 324 325 6.6 i 0.6 316 7.5 i 07 339 345 167 f 12 92 f 8 204 i 18 339 334 90 i 8 165 f 13 345 367 7.2 f 0.7 174 i 16 346 343 365 180 i 18 363 94 f 9 173 i 14 375 7.3 i 0.7 354 88 i 9 382 381 367 187 i 19 163 f 15 364 8.2 i 0.8 387 389 174 i 16 82 f 8 405 169 i 17 7.3 i 0.8 375 405 402 92 i 9 157 i 14 172 i 17 7.6 i 0.8 43 1 379 423 423 479 163 i 16 98 i 10 164 i 16 8.9 i 1.0 402 87 i 10 475 423 11.4 f 1.4 166 i 17 163 f 16 519 428 493 108 i 13 172 f 17 166 f 16 558 11.6 i 1.4 529 428 9 3 i 11 172 f 17 645 566 165 i 18 11.8 i 1.4 605 498 633 9 7 f 12 162 i 18 12.5 i 1.5 646 534 676 81 f 1 1 160 f 18 12.4 f 1.7 660 573 168 i 20 10.3 f 1.8 669 615 155 f 19 14.3 f 2.0 716 673 135 i 18 14.9 i 2.1 760 714 14.4 i 2.1 135 i 19 804 806 14.9 f 2.2 147 i 22 859 855
*
"All rate constants are in unis of in the text.
an3molecule-l s-I, and the error limits are the combination of statistical and systematic errors as described
18
250300350400450500550600850700750800850900
Temperature I (K)
Figure 6. Experimental values (points) of bimolecular rate constants for collisional quenching of H 'A, CH2 by Ar as a function of temperature.
(0) Present results, steel cell at temperatures < 430 K. (0)Present results with quartz cell at temperatures between 300 and 859 K. Error bars on these data are discussed in the text. Also shown are the only other temperature-dependent measurements of WagencrI3(A) and previous measurements at room temperature by Ashfold et aL5 ( 0 ) and Langford et a1.6 (+). The solid line is the theoretical prediction using the mixed state model, scaled to the present experimental value at 295 K, as explained in the text. The dashed line is the best fit to the data of an expression of the form kA, A(T/295)", where A = (5.9 i 0.5) X 10-l2 cm3 molecule-l s-I and n = 0.93 i 0.12.
-
Le., at the lowest pressure of CH2C0 used and at the highest temperatures. The vertical depth of the excimer photolysis beam profile along the reaction cell was never less than 15 mm, and the multipass plane was arm@ to always pass through the center of this profile. The photolysis profile extended a c r w the entire width of the reaction cell, but the outermost passes of the probe beam in the multipaw plane were always greater than 6 mm from the walls. This considerably reduced the effect of unwanted deactivation of 'CH2 by collision with the walls of the cell. The diffusion equation appropriate for onedimensional diffusion from a cross-sectionalprofile of width much greater than the diffusion dimension shows that the concentrationof 'CH2 radical along the midline of the profile (the multipass plane) has decreased by leas than 9% over a 1 0 - c ~period ~ even for a calculated diffusion mtlkient up to 1 m2 F',the largestdcuiated diffusion coeficient applicable to any experiment reported here. A lower temperature, heavier collision partner, or increased reactant pressure all sig-
nificantly reduce the concentration depletion in the multipass plane. The effects of diffusion are further diminished because of the inherent rapid removal of 'CH2 with all of the collision partners studied. All first-order decay rates measured in these experiments were significantly greater than 3 X lo5 s-', a value which implies three lifetimes of exponential decay in 10 ccs or over 95% removal of 'CH2 in the same time period before diffusion starts to become significant. The final conclusion, therefore, is that errors introduced into the analysis of absorbance decays due to the loss of 'CHI through diffusion amount to only a few percent at temperatures greater than around 650 K and are entirely negligible in all other cases. In all experiments, a static sample of gas was employed, with the required partial pressure of ketene initially introduced into the cell followed by the reactant gas. Several minutes were allowed before photolysis to ensure thorough mixing and thermal equilibration of the gases. Errors in the measurements of partial pressures of the gases using the capacitance manometer are estimated as f1%. Although the pressure gauge was situated on the (cool) inlet gas line exterior to the heated oven, the use of a static sample of gases ensured a constant pressure of gas throughout, despite the obvious gradient in molecular density. Although the thermocouples for the cell had been calibrated, the accuracy in temperature measurement was restricted by the consistency of the temperature profile along the length of the cell. This could be maintained to within about 5 K for temperatures up to around 400 K,increasing to about 30 K for the highest mean temperatures attained of over 850 K, a contribution to total error on a sliding scale between 1.5% and 3.5%. The error is important because it propagates in the use of a temperature value to convert decay rates into molecular rate constants (cm3 molecule-' d). We estimate our total error in reported bimolecular rate constants to be f9% at ambient temperature, rising to f15% at the highest temperatures of -850 K.
Discu~.qion (a) Comparison witb Previoua Results. Comparison of roomtemperature rate constants derived in this work with those obtained by other direct spectroscopic measurements following pulsed production of the radical is mostly very good. There is general lies in the region (2.1-2.7) X cm3 agreement that ,k molecule-' s-',6J5J8 with the value of Langfordet al.,6 at the upper end of this range, being some 25% higher than this work. The cm3 molecule-' s-l reported value of kH2= (1.0 f 0.1) X here agrees well with the similar resonance absorption measurement by Langford et a1.,6 with both these being slightly lower
10320 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
than the two values around 1.3 X cm3molecule-' s-I derived using timeresolved LIF on the 'CH2 r a d i ~ a l . ~There J ~ is complete cm3molecule-' s-' for the agreement on a value of 1.60 X rate constant kNObetween this work and the single other previous direct determination of this constant by Langford et a1.6 Finally, cm3 our room-temperature value of kAr= (5.5 f 0.5) x molecule-' s-I agrees well with the values of (6.0f 0.5)X cm3molecule-' s-',~ cm3molecule-' s-' and (5.8 f 0.5)X but all three are somewhat higher than the recent measurement of Wagener,I3who reports a quenching rate constant for 'CH2 cm3 molecule-' s-I, using conwith Ar of (4.65 f 1.0) X ventional UV photolysis and time-resolved LIF. No correction for diffusive loss out of the LIF probe region has been applied by Wagener, and this may partially account for his lower value Of kAr.
The present results on the variation of these rate coefficients with temperature indicate a substantial (almost 3-fold) increase cm3 molecule-' s-' for in the rate constant to around 15 X physical deactivation of 'CHI by Ar (Table I and Figure 6). Only the recent work of Wagener13has reported values of kR at any temperature other than ambient. He has also noted an increase an3molecule-' s-l at 295 K to 7.0X in kk from 4.65 X cm3 molecule-' s-' at the single elevated temperature of 475 K. While the value reported here for kArat 475 K is around 8.8 X cm3molecule-' s-I, the significant point is that in both studies the fractional increase is approximately 50% of the respective room-temperature values. If a function of the form
(3) is fitted to the observed rate constants for collision with Ar, then a value of n = 0.93 f 0.12 (2u error limit) is obtained for the temperature-dependence power exponent, with A = (5.9f 0.5) X cm3molecule-' s-I. The exponent is in good agreement with the value of n = 0.75 f 0.25reported by Wagener." A slight to about 1.4 X cm3 decrease of 33% from 2.1 X molecule-' s-' is observed for the removal rate constant of 'CHI by CHzCO over the temperature range 295-855 K, and a similar fit of eq 3 to the kCHICO data yields a value of n = -0.33 f 0.08 cm3molecule-' s-I. (2u error limit), with A = (2.0 f 0.2)x Both of these parametric fittings are shown as dashed lines on at 475 K is about 22% Figures 3 and 6. The decrease in kCHzCO from the room-temperature value, and this compares to the reduction in removal rates with the four hydrocarbons investigated by Wagener" at this temperature, which range from 17% with C& to 41% with CH,. The corresponding values for the exponent n for these four hydrocarbons are similarly all negative, with magnitudes in the range -0.55 f 0.35 to 4.95 f 0.35. The to 0.93 X cm3 marked drop in kH, from 1.35 X molecule-' 9-l between 295 and 475 K reported by Wagener" has not been observed in the present work, although both values at 475 K are in agreement within quoted error limits. For both kH2 and kNO(Figures 4 and 5 ) , the present observations indicate no change in rate constant over the temperature range 295-675 K, and (1.63f 0.11)X with values of (0.94f 0.13)X cm3 molecule-' s-', respectively, encompassing all measured kR. It must be noted, of course, that the removal rate constants obtained by monitoring the decay in the absorption of 'CH2are for total removal of 'CH2 by all pathways involving contributions from either of or both of the channels of reaction to different products or physical quenching to the fc 3Bl ground state. It is therefore clear from these results that the temperature dependence of the physical quenching process is distinctly different from the other predominantly reactive removal rates. (b) Intersystem Crossing in Collisions with Ar. The spin-forbidden &onal quenching of 'Al CH2to the electronic ground state % 3Bl is clearly the only channel open for removal of the initially produced 'CH2 radicals on collision with Ar. Although the observed removal rate of 'CH2 by Ar is some 18 times smaller than removal by H2or 38 times smaller than removal by CH2C0, an intersystem crossing (ISC) rate at an average of 1 in 60 collisions can still be considered to be a fast process. The
Hancock and Heal methylene radical can be classified as being in the small-molecule limit for nonradiative electronic transitions, where there is an insufficient density of states in the fc 'B1 acceptor state for irreversible electronic relaxation processes to occur in the isolated radical. A standard quenching theory, in which the collider's spin-orbit interaction induces the singlet-triplet transition by perturbation of the adiabatic singlet and triplet eigenstates of the isolated m01ecule,2~,~~ can be rejected owing to two major discrepancies with experimental observations. First, the ISC rate is predicted to be proportional to the square of the atomic number of the collider, and second, the crossing rate should show a large kinetic isotope effect3' Neither effect has been observed for experiments with *CHI and 'CD2 and a series of inert gas quencher~.~-~,~~-~~ Instead, an alternative "mixed state" model for ISC has been developed in which the existence of permanent intrinsic spin-orbit coupling interactions in the isolated molecule enables rapid exchange of energy between the two electronic states during a c o l l i ~ i o n . Certain ~ ~ * ~ ~eigenstates ~~~ of the free molecule have a mixed electronic parentage, and collision-induced ISC proceeds through the triplet perturbed "doorway" singlet levels of the ZI state which "borrow" some of the pure triplet rotational relaxation crw section. The singlet-triplet coupling implies crossover transitions with large cross sections into levels of the fc state and so the observed high efficiencies for ISC rates can in part be traced back to the high (near gas kinetic) rates of rotational relaxation processes within the X state. The population of methylene in these perturbed singlet levels and the rate of rotational relaxation within the particular acceptor vibrational state are the important quantities that determine the overall magnitude of the ISC rate and the way in which it will vary with temperature. The perturbed levels are described using simple linear combinations of the pure vibronic states. The rate constant k, for loss of population from a specific perturbed but predominantly singlet rovibrational level i is then simply given by the product of two terms37
w
ki = sin2 (Bi)k,,
(4) where sin2Bi is the square of the triplet mixing coefficient in the linear combination expression for the H level and k,,, is the bimolecular rate constant for loss of population by rotational quenching out of the perturbed but predominantly triplet acceptor level into other triplet levels. For comparison of calculated ISC rates with experimentally measured values of kR, the ki values are summed over all perturbed singlet levels i , with each one weighted in proportion to the population in that perturbed level, i.e., kIsc = kr0,Cwisin2 Bi i
(5)
where wi is a Boltzmann weighting factor, including rotational and nuclear spin degeneracies, and k,, is now an averaged rotational relaxation constant. Analysis of spectroscopic absorption23-38 and LMR3 data at room temperature for the methylene electronic states has shown there to be four pairs of significantly perturbed levels up to 1033 cm-' above the H state origin. For ~7'6,818, 'CHI (O,O,O), these levels are denoted by N ~ = K431, and 945, while the respective perturbing triplet rovibrational levels are identified as (0,3,0)312,(o,3,0)615,(O,2,0)g3,,and (0,2,0)9,. Values of the coupling matrix elements are tabulated in ref 3. The first of these perturbed singlet levels is of para symmetry, and the rest are ortho, with nuclear spin degeneracies of one and three, respecti~ely.~~ Previous work has shown that the population of 'CH2 in the initial distribution formed on photolysis of CHzCO at 308 nm follows the expected statistical 3:l ratio for ortho and para rotational levels, re~pectively.~~ Since a bulk sample of CHzCO also has the same degeneracy of ortho and para forms, there must be a conservation of nuclear spin in the photodissociation process, in agreement with the results obtained by Moore and co-workers from the analysis of PHOFEX spectra.21 This observation of a statistical distribution for nuclear spin enables the individual contributions to kIsc from ortho and para levels to be combined into a single overall rate constant for the physical
Temperature Dependences of CH2 (H'A,) Removal Rates
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10321
deactivation of a bulk statistical sample. A value for k,, with different collision partners has been estimated by Bley et al.37*40 from measurements by LMR of the linebroadening parameters rotational transition. The final calculation for the 3CH2(lol-l at room temperature (295 K) for a statistical sample of 'CH2 gives an3molecule-' an overall ISC rate constant for kA,of 4.90X s-I. This theoretical value of kArrbased only on spectroscopic measurements and using no adjustable parameters, is in excellent agreement with the experimentally determined rate constant reported here. It is now important to determine wKat the effect of temperature will be on this mixed state model of collision-induced intersystem crossing. We follow the method outlined in the previous paper14 and assume that redistribution of population within the H-state manifold is fast enough to maintain a Boltzmann temperature. The effect of temperature is then just 2-fold: (i) to alter the relative proportion wiof H-state molecules in the perturbed levels i and (ii) to change the value of the rotational relaxation rate constant k, out of the perturbed acceptor triplet levels. The first of these is readily calculated by substitutingnew B o l t " factors and partition functions in the expression for the population weighting wiof each mixed singlet level. For the second quantity, an investigation by Temps and co-workers40 on pressure-broadening parameters of 3CH2at different temperatures reports a positive temperature dependence in k, of the form k,, when the collision partner is Ar. This calculated temperature variation in relative ISC rate constant for quenching by Ar is shown as the solid line in Figure 6,where the theoretical curve has been scaled to the present experimental value of kAr= 5.5 X cm3 molecule-' s-' at 295 K. The predicted increase in klsc with temperature is now more marked than that calculated in the previous paper,I4 where only the variations in w iwere included because of lack of experimental information on the temperature dependence of k,,,. The increase in kArwith temperature predicted by the solid curve is seen to be in excellent agreement with the present results up to a temperature of around 500 K. It predicts also that the rate constant at 210 K is some 47% lower than at 295 K, and this compares with the 20% reduction that has been experimentally observed by Wagener13from his lower value of kArat 295 K. Above 500 K, the theoretical ISC rate rises more slowly to a peak value of about 10.5 X cm3molecule-' s-' before beginning to decrease very slightly above around 900 K. The measurement of k, from line-broadening parameters was carried out only over the limited temperature range so caution must be exercised in extrapolating to of 235-373 K,40 the much higher temperatures reached in this work. An important point to note is that the nature of the collision partner enters into the calculations only through its influence upon the rotational relaxation term krOt. We now consider the deviations between experiment and theory at temperatures > 500 K. If we assume that the basic features of the mixed state model for methylene are correct, then the observation that experimental values of kh are up to 50% in excess of the calculated klsc at temperatures greater than 500 K may indicate the existence of further pairs of perturbed "doorway" levels at higher energies whose presence only becomes important when there is sufficient population in higher levels of the H-state manifold for them to make a siflicant contribution to total ISC pathways. The energy of the highest identified perturbed level in the H manifold used in these calculations was 1033.587 cm-' for (0,0,0)94s.At 295 K,this has a population of only 6% that of the (0,0,0)431 lowest identified perturbed level at 284.385 cm-1,23 and the contribution to ISC from higher levels will be negligible. At 900 K, however, this fraction has risen significantly to 64%, and population in yet higher doorway levels must be considered. The rotational term value of the 945level is -5 kT at 295 K, so in order to maintain an equivalent accuracy in the calculations at 900 K, the H-state manifold needs to be examined for strongly coupled levels up to term values of 3200 cm-'above the H-state origin. The vibrational frequencies of CH2 (ZL'A,) are v1 = 2806 cm-', v3 = 2865 ~ m - l , and ~ ' v2 = 1353 cm-1,42so at 3200 cm-I, the (l,O,O), (O,O,l), (O,l,O), and (0,2,0)I 'Al vibronic bands need
-
-
to be considered, assuming there is significant Franck-Condon overlap with vibronic bands in the X state. (c) Reactive Removal. The negative temperature dependences observed for the removal of 'CH2 by ketene in this work and by hydrocarbons in the measurements of Wagener" suggest a different behavior when reactive channels are possible. Chemical reaction is dominant in these cases. For ketene, the chemical removal channel appears to be excl~sively4~ 'CH2 CHzCO C2H4 + CO
+
+
and estimates of the quantum yield of this ChaMel compared with all removal processes have ranged from a lower limit of 0.9* to a more recent value of 0.63 f 0.13.4s For hydrocarbons, direct measurements of 'CH2 removal together with 3CH2detection by LMR yielded chemical removal quantum yields in the range 0.7-0.9.& These measurements are in qualitative agreement with estimates of the nonchemical removal rates from ParmenterSeaver correlation plots4' for the deexcitation of 'CH2 by nonreactive partners M. Such a correlation takes the form
(7) where uMis the cross section for the purely deexcitation proctss, cMM is the well depth for the attractive potential between pairs of M species, and C and fl are constants. The linear relationship established at room temperature for collisions with rare g a m and N? also fits data for the deexcitation cross sections measured for the predominantly reactive hydrocarbom4 If this correlation is then taken as a predictor of the deexcitation cross section, then our measurement of the total removal rate constant with ketene suggests that the reactive channel (6)has a quantum yield of -0.9. All results are consistent with reaction being dominant (but not exclusive), and thus, the temperature dependence of the rate constant (Figure 3) at least near room temperature reflects a decrease in the reaction rate constant with increasing T. The implicationsof this are that if the temperature dependence of the singlet-triplet deexcitation process in collisions with ketene follows the same functional form as for Ar, then the quantum yield for chemical removal will decrease at higher temperatures, in a manner analogous to that discussed for removal by hydrmbons.l3 Such a prediction would depend upon similar mechanisms for the singlet-triplet crossing process for collisions with potentially reactive species and with Ar and would be invalidated, for example, in the mixed state model if the rate constant for rotational relaxation within the triplet manifold showed a pronounced negative temperature dependence. Total removal rate constants with both H2and NO are invariant with temperature over the measured range (295-676K). Braun et al.34and Bell and Kistiakowski4*have shown that the reaction with H2takes place via an excited methane adduct, not by direct hydrogen abstraction: 'CH2 + H2 CH4* CH3 H (8) +
+
+
and accounts for > 80% of the total removal rate. The Parmenter-Seaver correlation again predicts chemical reaction to dominate, and ab initio calculations indicate that there is no activation energy barrier along the optimum pathway for the insertion reaction.49 A number of thermodynamically favorable spin-allowed bimolecular reactions of 'CH2 with NO are possible, but no calculations on energy barriers have been reported: again, chemical reaction is predicted to dominate by the correlation argument. The differences in the behavior between these two small molecules and the more pronounced temperature decrease of removal with ketene and hydrocarbons may be due to the interplay of temperature-dependent preexponential factors reflecting the structures of the transition states and the partition functions of the reactants, existence of small barriers to reaction (for example, along nonoptimum pathways), and the temperature dependences of the deexcitation channel. The present results, although producing rate constants at temperatures approaching those of combustion interest, need to be combined with accurate quantum yield determinations before the relative importance of deexcitation vs chemical reaction can be assessed at high temperatures.
10322 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 conclusiolw The purely collision-induced intersystem cmssing rate from CH, ($A,) to CH2 (g3B1)with Ar exhibits a pronounced increase with over the temperature range temperature of the form 7".93M.13 295-859 K. While the agreement between experiment and a mixed state model theory for ISC involving energy transfer through perturbed doorway levels is extremely satisfactory for the lower half of the temperature range studied in this work, it is clear that further work is required to extend the usefulncss of the model. Measurements of relaxation rates in the triplet manifold as a function of temperature and a full characterizationof perturbation couplings between the H 'Al and 2 'BI rovibrational levels in methylene up to at least 3000 cm-' above the H state origin are needed. Removal rates of CH2 (%'Al)by H2 and NO show no variation with temperature in the range 295-676 K. In both cam, the removal is probably predominantly reactive and the zero activation energy for reaction with H2 is in agreement with theoretical calculations. The total removal of CHI (H'A,) by CH2C0 has in the a negative temperature dependence of the form To.33*0.0s range 295-859 K. If deexcitation by the potentially reactive collision partners shows the same temperature dependence as for Ar,then the branching ratio to reaction will decrease as a function of temperature. Acknowledgmenr. We are grateful to PowerGen for partial support of this work and to the SERC for a maintenance grant. We also acknowledge the assistance provided by P. Biggs, D. J. McGarvey, and A. D. Parr in the earlier part of this work. Re.gi8try No. CHI, 2465-56-7; Ar, 7440-37-1; NO, 10102-43-9; H,, 1333-74.0; CHZCO, 463-51-4.
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