J . Phys. Chem. 1985,89, 1269-1278
I
'I
0.4
8
0
i
10-5
[Fer]
(M)
Figure 6. Limiting currents (panel A) and half-wave potentials (panel B) for steady-state(10 mV/s) voltammograms of ferrocene at 1-pm- (0) and IO-pm- ( 0 )diameter microelectrodes in M Et4NC104/acetonitrile plotted vs. ferrocene concentration. Numbers in brackets indicate
Nerstian slope for voltammograms (top numbers, bottom numbers, 1-pn electrodes).
10-pm
electrodes;
moved from the permeation data by referring measured at polymer-coated electrodes to E I l 2measured at naked microelectrodes in the same experiment, as is done in the formulation of eq 5 and 6.
1269
Finally, experiments comparing 1- and 10-rm-diameter (naked) microelectrodes support the above conclusions. Figure 6A shows that the limiting currents for ferrocene oxidation in M Et4NC104a t both microelectrodes remain strictly proportional to ferrocene concentration even when the latter is 100 times larger than the electrolyte concentration. At the larger ferrocene concentrations (with larger currents), a positive (Ohmic potential) shift in E l / 2is induced (right-hand points in Figure 6B), more so for the 10-pm microelectrode (larger radius, larger current) than the 1-pm microelectrode. Importantly however, the E I l 2 becomes the same for the two electrodes when the ferrocene concentration equals the electrolyte concentration at M. Under the latter condition, the ferrocene oxidation wave also exhibits a strictly reversible shape (which is assumed in formulating eq 5 and 6) as shown by linear plots of potential vs. log [(ili,,,i / i ) ] with the ideal 59-mV slope (indicated parenthetically in Figure 6B). Higher slopes are observed at the higher ferrocene concentrations. These results support the conclusion that the microelectrode and solute/electrolyte concentration strategies adopted in this work minimize the effects of Ohmic potential losses and migration effects in the permeation study.
Acknowledgment. This research was supported in part by a grant from the National Science Foundation. We gratefully acknowledge helpful discussion with Dr.C. Chidsey and Prof. R. P. Buck and the sharing of unpublished theoretical results47 by Profs. A. J. Bard and J.-M. Saveant. Registry No. ( [ R ~ ( v b p y ) ~ ] 81206-05-5; ~+, TCNQ, 1518-16-7; TCNQ-, 34507-61-4; ferrocene, 102-54-5; ferrocenium, 12125-80-3.
Laser Pyrolysis/Laser Fluorescence Studies of High-Temperature Reactlon Rates: Description of the Method and Results for OH 4- CH,, C,H,, and C3H, Gregory P. Smith,* Paul W. Fairchild,? Jay B. Jeffries, and David R. Crosley Chemical Physics Laboratory, SRI International, Menlo Park, California 94025 (Received: September 20, 1984)
A new method is presented for measuring bimolecular reaction rates of radicals in the 800-1400 K temperature range: pulsed infrared laser heating, using SF, as the absorber-bath gas, is coupled with laser-induced fluorescence detection of radical concentrations. Detailed diagnostic experiments and calculations concerning the laser heating process are described. Extensive measurements of the hydroxyl/methane reaction rate agree well with previous determinations. The rate constant for OH with propane measured at 1075 K is 2.2 X lo-" cm3 s-l. The rate constant for OH with propylene is 4.5 X cm3 s-l at 960 K and 9 X at 1210 K. The results, mechanisms, and extrapolations of reaction rates with temperature and pressure are discussed in the context of transition-state theory.
I. Introduction Accurate modeling and proper understanding of combustion processes require knowledge of the appropriate rate constants and reaction products at high temperatures. When such measurements are coupled to the theoretical framework of chemical kinetics, reliable extrapolations to many other conditions can be made. A limited number of direct high-temperature rate studies exist, mainly using three methods. Shock tube investigations can cover wide temperature ranges but have low duty cycles. Heated flow reactor or flash photolysis methods feature accurate rate measurements using low radical concentrations but can be complicated by reaction during the relatively slow heating process and are usually limited to temperatures below lo00 K. We have developed ,
Present address: TWR Space and Technology Group, Redondo Beach, CA 90278.
0022-3654/85/2089-1269$01.50/0
a new laser pyrolysis technique as another alternative for measuring high-temperature reaction rates. A pulsed COz laser is used to irradiate a mixture of SF6absorber molecules, N2 bath gas, H202as the OH radical precursor, and hydrocarbon reactant. After energy transfer collisions heat the mixture and the H202 decomposes thermally, the reactive decay of OH with time can be followed by laser-induced fluorescence (LIF). A temperature range of 800-1400 K is attainable, as determined from OH rotational level populations measured by LIF. All our experiments have been performed with OH, but other radicals such as N H 2 and C H 3 0 are good candidates. This new method of rate constant measurement offers the advantages of fast heating, cool surfaces, high repetition rate, and real-time detection. Its limitations lie in temperature and density uncertainties and a limited range of operating pressures and reaction times. Described here is a comprehensive study of the 0 1985 American Chemical Society
Smith et al.
1270 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 Transient Digitizer PDP 11/02
Boxcar Integrator Recorder
Monochromator
10.6-pm C 0 2 laser beam of energy per pulse 11.2 J/cm2 and 1-ws duration. We obtained uniform fluence in the irradiated region by selecting only the center of the infrared beam using a thick, 1-cm-diameter aperture -20 cm before the cell. Because of minor diffraction effects and the fluence dependence of the SF6 absorption coefficient, the edges of the irradiated region will not be precisely sharp (as assumed in the calculations described below), but they are sufficiently well-defined for our purposes. The infrared radiation is reflected back on itself after traversing the cell, ensuring a more even absorption by the SF, than would a single pass. Within a few microseconds, rapid energy transfer collisions have heated the mixture in this volume to a temperature T’, 900-1 500 K, selected by the value of the infrared laser energy and SF6pressure. This causes some thermal decomposition of H202. The heated volume, now at higher pressure, expands and 0001s to temperature Tin 10 ps. This is accomplished by a sonic expansion wave traveling inward from the boundary and then outward again. At the same time a compression wave propagates outward through the unheated gas. The final pressure after the expansion waves pass is near its original value Po, the temperature, T, is roughly 200 K below its peak T’, and further H202decomposition is effectively stopped. Only slow cooling by thermal conductivity follows, and stable conditions over the next -200 NUSwill permit measurement of OH decay rates from bimolecular reaction with a hydrocarbon in the gas m i x t ~ r e . ~ A frequency-doubled, Nd:YAG-pumped dye laser beam of 2-mm diameter crosses the C 0 2 laser beam axis perpendicular to and 4 mm out from the center of the heated region. The laser probes molecules situated about halfway out in the heated cylinder, where the OH signal is reasonably large and density fluctuations were found to be minimal. The laser is tuned to the P,6 line of the OH A-X (0,O)band at 3 10.7 nm and is fired at an adjustable delay time At after the C 0 2 laser. Fluorescence is monitored, perpendicular to both lasers, through a monochromator tuned to the 309-nm Q head of the same band, and the signal is processed by a boxcar integrator. Under our conditions, following the expansion, the LIF signal is proportional to the O H density. By scanning the laser through various OH lines, we can deduce rotational level populations and thus the temperature T . We normally used the P16, P25, Q211, Q112, and Q,13 lines, carefully avoiding optical saturation. Typical errors of f50 K were obtained from the fits. Temperatures were usually measured before adding hydrocarbon but were observed not to decline significantly (> A , in fact, S is proportional to the OH mole fraction. The results of ref 5, at various delay times and cell positions, were nearly but not quite in this limit. The temporal behavior of S at cell center showed a rapid rise and then some indication of the expansion cooling. At the edge of the initially heated region (about halfway to the edge of the postexpansion region, and where we typically measure rates), a delayed rise was seen. This reflected the outward movement during the expansion of regions where more OH was produced via longer time at the highest temperature T'. After this, S then remained constant, as neither OH ( N o )nor total density varied. By directly measuring the quenching rate of the OH signal, we can directly measure the total gas density p of the LIF-probed volume for various At. For these experiments a transient digitizer with 10-ns resolution was used (see Figure 1). The OH fluorescence signal acquired in this fashion is given by
+
-
+
+
+
-
+
S ( t ) = CN, exp[-(A
lt
+ Q)?]
where A = 1.43 X lo6 s-I and Q = kQp. Thus, the time decay of s(t)a t a particular delay At gives Q = p(A.t)kq. Figure 4
Figure 5. The measured cell density as determined by measuring quenching rates vs. At, the delay between the C 0 2laser heating and the LIF probe. The size of the points for At > 20 ps is indicative of the statistical error. The lines are drawn for ease of reading.
illustrates the change in this fluorescence decay as the time between the heating and probing lasers is varied. The region probed is midway between the center and edge of the initially heated region. The rapid decay in the top trace reflects the high density and rapid collisional quenching before the expansion cooling. The lower trace has a much slower, nearly purely radiative, decay and is indicative of the density drop yielding less collisional quenching after the expansion is complete. The density decrease in the cooling expansion was measured by observing Q at At = 4 ps, before point A in Figure 2, and by measuring Q at At = 72 p s , well beyond point C in Figure 2. The small quenching rate constant3 for OH by SF6is exploited by performing this experiment in 9 torr of SF6and only 5 torr of N,. This gives a range of quenching rates easily measured by our 10-ns resolution: Q(At = 4 ps) = 1.85 X lo6 s-l and Q(72 ps) = 0.42 X lo6 s-' (note A = 1.43 X lo6 s-l). The temperature T'at 4 ps was measured to be 1375 K and T a t 72 ps to be 1210 K. The simple expansion formula predicts T = 1225 K, while code calculations (see Figure 2) would yield values near 1200 K, in fine agreement with experiment. The density at 4 ps still reflects the initial 298 K density. The ideal gas law predicts an expansion of 4.06, and we measure 4.40, an 8% difference. This assumes a constant value of kq at both 1375 and 1210 K, whereas with a constant quenching cross section we would expect a 6% drop in the rate constant k, as the temperature drops and a 2% difference between the predicted and observed expansion. Thus, the measured expansion cooling agrees well with the simple model. The full computer calculations give slightly larger expansions of -4.5 a t long times. The absolute value for k measured before the expansion also agrees (6%) with the value kQ reported previously3 in the postexpansion region. The density in the LIF-probed volume measured by this technique is plotted in Figure 5 as a function of ht. The dashed curve was taken with a 3-mm-diameter UV beam positioned to overlap the center of the heated region. Note the expansion, the
07
1274 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 fluctuation near 50 ps, and some minor later variations. The solid curve was taken with a 2-mm-diameter UV beam positioned near the edge of the initially heated region; this is the same as the UV probe location used for kinetics measurements. The fluctuations in the total density are less than flO% over the 40-160-ps range which was used for the kinetics measurements. These direct density measurements contribute significantly to our confidence in the reaction rate determinations. The variation of OH rotational temperature with At had been previously measured for At d 120 N S . ~Those measurements at cell center agreed with the simple adiabatic formula, showed greater cooling for 75% N2, and even suggested the dip in T a t -30 ps predicted in Figure 2. The range of At has been extended here to nearly 2 ms. For 30 6 At < 400 ps, T measured a t the edge of the initially heated region (i.e. about halfway from center to boundary in the postexpansion) is constant to within the 50 K measurement uncertainty. At 1.5 ms T has cooled by -160 f 70 K or 0.11 f 0.05 K/ps, in agreement with the rough 0.07-0.14 K/ps cooling rate (100-200 K) calculated above. The 0.4 K/ps rate observed from IR fluorescence8 was faster, but it included contributions from the cells near the edge which cool off faster. These relatively slow cooling rates suggest one must take into account decomposition reactions occurring in this “low-temperature tail” during LP relative unimolecular reaction studies of relative rates.’ To examine the question of whether the vibrational modes have equilibrated with the rotational ones before rate measurements are made, we examined the OH vibrational populations via LIF. If this high-frequency mode (AGl12= 3570 an-’)reflects the same temperature as rotation, one can be assured the vibrational degrees of freedom in the system have properly equilibrated. We measured the relative rotational line intensities1° from a (0,O)band excitation spectrum at 50-ps delay and extracted a rotational temperature of 1240 f 50 K in U” = 0. The relative intensities of the rotational lines in the (1,l) band from the same scan yielded a rotational temperature of 1260 f 50 K in u” = 1. The natural logarithm of the ratio of the least-squares intercepts of the two rotational temperature Boltzmann plots gave the relative vibrational level populations, from which we determined a vibrational temperature of 1180 f 150 K. This indicates the existence of vibrational equilibration as well as rotational equilibration to the same temperature in each vibrational level. The translational temperature, and those of other molecular vibrations in the gas mixture, should also be the same. D. Sources of Error. One difficulty with the present experiment concerns operation with optically thick conditions for the infrared heating pulse. Beam quality requirements with our current laser configuration confine us to non-line-tuned operation at P(20) of the 10.4-pm eo2band, thus limiting us to SF6as the sensitizer. For operation at reaction temperature T d 1150 K we can use 10-torr SF6/30-torr N2 mixtures and vary the laser fluence to obtain the desired temperature. The upper limit here is imposed by SF6 decomposition, discussed later, These gas mixtures absorb -25% of the I R in a single pass, and a 75 K initial temperature gradient from front to rear of the cell is calculated via Beer’s law for our retroreflected case. Higher temperature and higher pressure runs must be done with more SF,, resulting in larger initial temperature gradients. This could cause three problems: transport of OH, reaction products, or heat transport from the hotter front area of the cell to the 2-mm-diameter volume being probed; an axial shock wave traversing the cell from window to window producing density and temperature fluctuations; and the uncertainty caused by these conditions in the appropriate reactant density needed to calculate the rate constant from an observed decay. Diffusion is too slow for transport of radicals or heat to have an impact on the kinetic measurements, a fact reflected in the calculation. As we have previously observed,’**an optically thick cell and the resulting temperature and pressure inhomogeneity ~
Smith et al. along the cell axis produce an axial compression and expansion wave traveling at roughly the speed of sound. In our 1-cm-thick cell this will produce temperature and density fluctuations with a -35-ps period for SF6. The rate measurement thus averages over these variations. Calculations reveal that even for a 1100 K temperature at the center and 600 K a t the far window, only a 60 K variation within the probed region would occur, which is below our observation limit.5 Although the density fluctuations will be larger, their effect is averaged out over the kinetics decay measurements. The measurements of density in the LIF-probed region confirm that such axial-shock-induced fluctuations are confined to f5%. The presence of these inhomogeneities and shock waves does introduce some uncertainty in the density value used to determine rate constants. The calculation^'^^ upon which the values are based use a uniformly heated volume, but they also show the final density is well approximated by an ideal gas law calculation ( P = P,/RT, within -lo%, using T measured at 40-1s delay). This suggests the same simple expression will be valid for systems of more than two regions, Le., the optically thick situation. This view is also confirmed by our measurements on the benchmark OH CH, reaction as discussed below and our measurements of the cell density. The simplified, operational view here, confirmed by the diagnostics above, is one of pressure equilization of all regions, via rapid shock phenomena, with that of the surrounding unheated gas at the initial cell pressure. An additional problem to be avoided in these experiments is the production of large numbers of F atoms from the thermal decomposition of SF6. The subsequent reaction of atomic F with H 2 0 , H202, OH, and hydrocarbons, plus any resulting chain reactions, may perturb the kinetics measurements severely. Symptoms of this condition which we have observed include chemiluminescence from the cell, a varying (usually falling) OH signal with time, and the inability to reach higher temperatures and signal levels by increasing the C 0 2 laser power. A good diagnostic for the problem is replacement of H202with H 2 0 ,since then any OH LIF signal will indicate the occurrence of the F H20reaction. This problem sets the practical upper temperature limit of our system to be 1300-1400 K. Use of a more strongly bound sensitizer such as SiF, could extend this range (given a tunable C02laser), but the use of inert, inexpensive SF, with P(20) excitation is convenient. In 20 torr of SF6 at 1600 K initial temperature, with an estimated decomposition rate constant” of 20 s-I, approximately 5 mtorr of F will be produced before expansion cooling. This roughly equals typical OH concentrations, and at the estimated rate constantI2 of 3 X lo-” cm3/s, could remove the OH in 1 ms. In the measurements reported here great care was taken to avoid the production of F atoms by minimizing initial temperatures. For example, T’ = 1600 K gives T = 1460 for pure SF6 and 1260 K for 20% SF6 in N,. Thus, high temperature without F is best achieved at high SF6fractions. A uniform CO, beam free of hot spots and good shot-to-shot intensity stability of the pulses are required. The decrease in SF6 absorption of the P(20) CO, radiation with increasing laser fluence mitigates this difficulty somewhat. The principal sources of error in kinetic rate constants measured by LP/LF are due to limited ranges of delay time and reactant concentrations. During the time between initial heating and the shock expansion the reactant concentrations are roughly 4 times larger and the gas temperature is 200-400 K hotter than the quiescent postshock period when the kinetic decays can be measured. Thus, a large loss of the initial OH concentration due to reaction occurs in this first few microseconds. Additionally the reactant is often an efficient quencher of the O H excited state, which also decreases the LIF signal. Thus, we are limited to modest kinetic decays of a factor of 2-10 instead of the more common decays of 10-100-fold for each reactant concentration. These limitations reflect themselves in the statistical scatter of the measurements. Laser fluctuations and drift in intensity will
+
+
-
~~~
(10) I . L. Chidsey and D. R. Crosley, J . Quant. Spectrosc. Radial. Transfer, 23, 187 (1980).
(11) J. L. Lyman, J . Chem. Phys., 67, 1868 (1977). (12) W. E. Jones and E. G . Skolnik, Chem. Rev., 76, 563 (1976).
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1275
Laser Pyrolysis/Laser Fluorescence Studies
TABLE I: OH
+ Hydrocarbon Rate Constants'
L
Ak
reactant CH4
C3Hg CIH6
T 1030 930 975 1400 1412 1150 1120 870 830 1200 1176 966 1240
10IZk,cm3/s 1.33 1.55 2.1 4.4 4.2 1.7 3.6 2.25 1.25 3.3 2.35 2.0 2.9
statistical
total
n
0.1 0.35 1.o 0.5 0.5 0.2 0.4 0.8 0.1 0.4 0.4 0.4 0.2
0.5 0.7 1.2 0.8 0.8 0.7 0.9 1.0 0.6 1.0 0.7 1.0 0.35
3 3 2 2 3 2 2 3 2 2 2 2 5 6
1074
21.9
4.1
6.0
960 1180 1210 1090
4.5 7.0 8.9 5.8
0.4 0.6 0.6 0.9
0.7 1.0 1.2 1.1
c
iij
I
0
r
1 50
4
3 8 3
'Ak is the error estimate, and n is the number of separate determinations.
100
150
Delay Time (Microseconds)
Y r
~~~~
also contribute to this scatter. The doubled dye laser intensity was continuously monitored, as was the COz laser power in recent experiments. For most experiments, long-term stability was ascertained by repeating signal level measurements at the initial delay after each delay and measuring T both before and after each experiment. We estimate such drifts can increase the uncertainty of the rate measurement by 10%. To minimize this problem, measurements were done rapidly a t a limited number of delay times. The observed 10% density variation (with time, and from the gas law value) discussed previously contributes another 10% uncertainty to the rate constant. Our typical statistical deviation (see the latter data table) is 10%. If we include the aformentioned other sources of error, by summing the variances (u2),we get an estimated l a accuracy of 1 5 2 0 % for these LP/LF rate constant measurements (or 20-25% keeping the density determination uncertainty separate). This method will be used to assign uncertainty to the forthcoming results. One goal of our efforts on the relatively well-characterized OH CHI reaction was to examine whether there were significant inherent inaccuracies in the method and whether the accuracy and precision could be improved statistically by accumulating results. Other sources of error and inconvenience, typical of high-temperature kinetics studies, however, are absent. These include heterogeneous reaction processes on hot surfaces, complex chemical mechanisms during slow heating process, or lack of time resolution. LP/LF provides a new, alternative method for measuring or confirming high-temperature rate constants.
-
+
+
111. OH CH4 These diagnostic and theoretical explorations of the LP/LF technique suggest sufficient understanding for its application to high-temperature bimolecular kinetics. Nonetheless, the fairly well-studied, and prototypical, OH CH4 reaction is a good initial choice. It provides a test for the accuracy and precision of this new method and an opportunity to extend direct rate measurements to higher temperatures. The existing data are well summarized by Cohen13 and include reliable flash photolysis meaand Zellner surements up to lo00 K by Tully and Ravi~hankara'~ and Steinert.I5 A few higher temperature (>I200 K) values have been derived from flameI6 and shock tube" experiments. Also,
+
(13) N. Cohen, Inf. J . Chem. Kiner., 14, 1339 (1982); 15, 503 (1983); private communication. (14) F. P. Tully and A. R. Ravishankara, J. Phys. Chem., 84,3 126 (1980). (151 R. Zellner and W. Steinert. Inr. J. Chem. Kinet.. 8. 397 (1976). (16j G. Dixon- Lewis and A. Williams, Symp. (Inr.) Combusr. [ P r d . ] ,l j , 1966, 951 (1967). (17) J. Emst, H.G. Wagner, and R. Zellner, Eer. Bumenges. Phys. Chem., 82, 409 (1978).
0 0
3
6
[CHql (1015cm-3)
Figure 6. (top) Logarithmic plot of the decline in OH LIF signal vs. delay time for various partial pressures of added CH4: triangles, no CH,; squares, two separate runs at 0.37 torr; crosses, 0.57 torr; open circles, runs at 0.74 and 0.80 torr. The experiment was performed at 1240 f 50 K in 47 torr of N2and 10 torr of SF6. (bottom) Decay rate of OH vs. CH4 concentration from the above data, with least-squares-fittedline.
Madronich and Felder'* recently used a heated flow tube to measure this rate constant from 300 to 1500 K. ZellnerI9 presented a simple expression for k(T), and CohenI3 has developed a transition-state theory (TST) expression for the temperature dependence which depends only on the experimental results at 300 K. We have made 13 LP/LF measurements of the OH CH4 rate constant at temperatures from 850 to 1400 K, using two or three distinct methane concentrations at each temperature. Mixtures of 10 torr of SF6and 30 torr of Nz were typically used, but some experiments a t high temperature used 30 torr of SF6. The results are summarized in Table I where both the statistical uncertainty or precision and our best estimate of the total uncertainty or accuracy of each measurement are presented. Data at 1240 K are shown in Figure 6;the upper four traces show the exponential decays of OH density (LIF intensity) with best fits, for added CH4 partial pressures of 0, 0.37, 0.57, and 0.77 torr. The resulting loss rates are plotted in the lower panel vs. the corresponding CH4 postexpansion densities. Note that this measurement, which was made after all the above diagnostics were understood, has an accuracy of 12%, whereas measurements with less refined apparatus and technique had much larger uncertainties as indicated in Table I. (The refinements which have been implemented include improvements to flow control and mass flow measurement, simultaneous UV and I R power monitoring, and temperature measurement after each kinetic decay. These results also indicate how we may realistically implement the potential5 for further improvement by automated data sorting according to the power of the C 0 2 and dye laser on each shot.) The least-squares line shown corresponds to k = (3.0 f 0.2) X cm3/s. Note in this case the run with no added methane is flat, within statistical precision. An alternate method of data
+
(18) S.Madronich and W. Felder, Symp. (Int.) Combust. [Proc.],20, in press. (19) R. Zellner, J. Phys. Chem., 83, 18 (1979).
Smith et al.
1276 The Journal of Physical Chemistry, Vo1. 89, No. 7, 1985 TIKI
1500
10-1'
6
1200
"
1000 900
800
j
600
700
500
20
15
10 1WO/T
Figure 7. Arrhenius plot for the OH + CH4 reaction: solid circles with error bars which reflect the accuracy of each measurement, this work; squares, ref 14; triangles, ref 15; asterisk, ref 20; shaded region, ref 17; open circles, ref 18; circled dot, ref 16. The solid line is the expression of ref 19, and the dashed line is the transition-state theory calculation of ref 13.
analysis, which we actually used to determine our rate constant values, involves averaging the values obtained from each decay plus the zero run. (This weights the zero methane density point the most heavily.) The result of this procedure is the same, k = (2.9 f 0.2) X 10-l2 cm3/s. Another 10% uncertainty, attributable to the density determination, must be added in quadrature with these uncertainties for the total accuracy of these rate constants, giving a typical -30% uncertainty in the CHI experiments (with experience, the run in Figure 6 and most of the later CzHzruns4 were better, 1 5 2 5 % ) . Figure 7 is a portion of the Arrhenius plot for OH CH4which presents our results with error bars, along with other studies previously mentioned. The formula of ZellnerIg (or alternatively the more recent expressions of Cohen and WestbergZoor Madronich and Felder18) is also shown as a consensus representation of existing data. Cohen's transition-state theory resultsI3 are also given. The error bars reflect statistical deviations plus the uncertainties discussed previously and are 1u values obtained by summing the variances. Good agreement is seen, a t both ends, with lower temperature flow tube?, and higher temperature shock results. (The high values of ref 15 are discussed in ref 14.) Our value^,^ which represent the first direct measurements of the OH CH, reaction rate above 1000 K, also agree with the recent results of Madronich and Felder,I8 who used flash photolysis/resonance fluorescence in a heated reactor to cover a wide temperature range. Furthermore, while our values, as expected from error estimates, show a 35% root-mean-square deviation from Zellner's fit, the average, signed deviation is only 3%. Thus, the scatter is random. A small yet significant temperature dependence follows from our data alone, although it appears the LP/LF method is a poor one for direct activation energy determination for this reaction. These results confirm the suitability of laser pyrolysis for reliable high-temperature bimolecular rate constant measurements, albeit with greater uncertainty than welldeveloped lower temperature methods. They support the use of the existing empirical expressions'8*20for k( 7') up as high as 2000 K. Note also from Figure 7 that Cohen's revised TST expressionI3 also fits other data and our higher temperature measurements well. Cohen's procedure is to derive k(7') = AT" exp(-E/R7') from TST: k = ( k T / h ) exp(AS*/R) exp(-AH*/R7'), where AS* is estimated by an assumed activation complex structure and AH* is fixed by the experimental 300 K rate constant at 300 K. (Here
-
+
+
(20) N. Cohen and K. R. Westberg, J . Phys. Chem. Re$ Datu, 12, 531 ( 1983).
(21) A. Szekely, R. K. Hanson, and C. T. Bowman, Fall Meeting Western States Section, Combustion Institute, Los Angeles, 1983.
1
2 lOOOil
3
Figure 8. Arrhenius plot of the OH + C3H8reaction: solid circle with error bars giving l a statistical uncertainty, this work; crosses ref 27; triangles, ref 21; open circle, ref 23. The solid line is the theoretical calculation of ref 13, while the dashed line shows the result of a linear extrapolation.
k = 7.3
X 10-177"0.7e-15w/RT cm3/(molecule s).) The estimated 2-eu error in AS* and hence that in AH* (0.6 kcal/mol) can produce 50% errors in k above 1000 K.I3 Noting the sharp high-temperature effect caused by a small error in estimating the need for data near 1000 K becomes clear. With two such well-separated experimental values, one can determined both AHs and AS*, calculate the curved TST Arrhenius plot, and extrapolated successfully as far as 2000 K. The fact that a good TST fit was obtained essentially from the one point a t 300 K suggests a very good a priori understanding of the structure of the OH CH, transition state. Although tunneling should be important at low temperatures, its explicit inclusion appears unnecessary. (The addition of a temperature-independent tunneling reaction would require a larger barrier and AH* to fit the 300 K data, given AS'. A sharper temperature dependence than that observed would then be predicted.)
+
IV. OH+CJHB To further test this theoretical approach and provide such a higher temperature point, we briefly examined the propane reaction. Propane is a good choice among the reactant partners whose rates were calculated in ref 13, because a large curvature in the Arrhenius plot was predicted, but no high-temperature measurements which would show this curvature existed when we undertook these experiments. Runs were done in 25-30 torr of SF6. The rate constant at 1075 K is (2.2 f 0.4) X lo-" cm3/s, from an average of six measurements. This large rate requires low propane pressures of -50 mtorr. Care was taken to operate at sufficiently low OH concentrations to ensure pseudo-first-order conditions. This result is shown in the Arrhenius plot of Figure 8, along with the existing temperature-dependent data,22*23 below 790 K.
Laser Pyrolysis/Laser Fluorescence Studies Cohen's theory13 does a good job fitting all the results including our new point and thus is validated here as the choice for extrapolating to higher temperatures. Bott and Cohen's recent shock tube measurementz4 agrees very well with our result and the theory. They suggest" the calculated line be raised slightly (larger AS*)compared with that in ref 13, to fit the lower temperature data better. This raises the predicted value at 1200 K by the same amount, in good agreement with our experiment. Note that below 690 K little curvature is evident from the data, and a typical straight Arrhenius extrapolation would result in large errors in the predicted rate constant above 1000 K (see Figure 8). Such a procedure must not be used for bimolecular reactions with low activation energy, where curvature is to be expected. For OH alkane reactions, TST can and should be used to extrapolate rate constant measurements made at 300 K up to 2000 K within a factor of 2 accuracy. This error can be narrowed to -30% if a second measurement above 1000 K is available. However, if one simply uses this 1000 K value to determine a 7"'dependence for the rate constant without examining its consistency with theory and covariance with E,, large errors in an extrapolation to 2000 K can result. LP/LF is very suitable for the measurements of such fast high-temperature rates.
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1277 2000
7
lo00 700 I I I I I
T(KI 500
1
300 I
I
+
V. OH+CjHs Hydroxyl/hydrocarbon reactions can be categorized as the just-discussed exothermic hydrogen abstractions from alkanes or as the unsaturated systems such as acetylene4 which proceed by addition at low temperature and endothermic abstraction at high temperature. Propylene represents an interesting combination. Since the allylic hydrogen is relatively weakly bound, one would expect a fairly large low-temperature abstraction rate. Surprisingly, this does not occur. A product analysis study at 298 Kz5 indicates that the OH/propylene reaction proceeds by addition, cm3/s. This with an abstraction rate constant kAB< 4 X slow rate suggests little allylic enhancement over values expected for primary hydrogen abstractions (the ethane rate constantI3 is 3 X 10-13), despite the fact that 1-butene with secondary allylic at 298 K) than hydrogens shows faster abstractionz5 (6 X propane (1 X 1O-l2). Data on the addition channel include a recent 298 K pressure dependence study:6 a 298 K high-pressure (1 atm of N2) rate constantz7 of 2.9 X lo-" cm3/s, and lower pressure K. By analogy to the OH temperature d e p e n d e n ~ e to s ~-450 ~~~~ addition reactions with acetylene4 and e t h ~ l e n e ,one ~ ~ expects ,~~ the propylene addition channel to decline precipitously at higher temperatures and the abstraction rate to become larger and measurable. We have measured the OH/propylene reaction rate near 1200 K and at 960 and 1090 K, as shown in Table I and Figure 9. These measurements were made in 15 torr of SF6and 6-1 0 torr of Nz. The rate constant increases with temperature, in contrast to the observed behavior at 300-500 K, and suggests a direct, endothermic channel. We were unable to determine whether a portion of the measured value of 4.5 X cm3/s at 960 K still proceeds by the pressure-dependent addition mechanism, as was established in our acetylene results. Given that our uncertainties are 515%, many experiments would be needed to measure an accurate total pressure dependence at this temperature. These are hard experiments due to the rapid propylene quenching of OH LIF, the fast reaction at preexpansion temperatures, and the necessity to avoid thermal propylene decomposition or F atom reaction. Note that the rate constant measured at 960 K is much lower (22) F. P. Tully, A. R. Ravishankara, and K. Carr, Int. J . Chem. Kinet., 15, 1111 (1983). (23) N. R. Greiner, J . Chem. Phys., 53, 1070 (1970). (24) J. F. Bott and N. Cohen, Int. J. Chem. Kinei., in press. (25) H. W. Blermann, G. W. Harris, and J. N. Pitts Jr., J. Phys. Chem., 86,2958 (1982). (26) R. Zellner and K. Lorenz, J. Phys. Chem., 88, 984 (1984). (27) T. Ohta, J. Phys. Chem., 87, 1209 (1983). (28) R. Atkinson and J. N. Pitts, J . Chem. Phys., 63,3591 (1975). (29) R. H. Smith, J . Phyq. Chem., 87, 1596 (1983). (30) F. Tully, Chem. Phys. Lett., 96,148 (1983).
'4
I ,
I/
I/ 1
2
3
4
1000/T
+
Figure 9. Arrhenius plot of the O H C3H6reaction: solid circles with errors bars giving l a statistical uncertainty, this work; square, ref 26; open circles, in 50 torr of He, ref 27; crosses in 2 torr of He, ref 28. The lines drawn are the results of the calculations described in the text.
than the value at 300 K and roughly equals the hydrogen abstraction rate constant for methane. At 1200 K (in 50 torr of SF,), the OH/propylene rate constant has increased to -9 X cm3/s. This indicates that the direct abstraction channel is operative a t these temperatures and that it behaves in a manner similar to the primary hydrogens of methane or ethane. That the allylic stabilization energy is not available to promote the abstraction reaction is a feature consistent with a lack of resonance energy until the hydrogen atom has partially departed, Le., beyond the transition state. The temperature dependence and low values for abstraction even suggest a small energy barrier exists here. However, iodine atoms abstract allylic hydrogens without an added energy barrier above the endothermicity, with a reasonable A factor.31 The contrast with the apparently fast abstraction of secondary allylic hydrogens by OH in 1-butene is also hard to explain. On the other hand, the hydrogen abstraction from propylene occurs at a rate like that observed for side-chain hycm3/s at 900 K) from toluene,32 drogen abstraction ( 5 X which produces the similarly stabilized benzyl radical. The question of whether the addition mechanism plays a significant role above 900 K under various pressure conditions can be addressed theoretically. We use a unimolecular rate theory approach previously applied to acetylene: with numerical values based on lower temperature data. The parameters needed for the falloff calc~lation,3~ and the values used, are the following: adduct vibrational frequencies 3600, 1300, 600, 300 and 200 cm-' plus those of propane; adduct moments of inertia 44,63, 106 amu AZ; a Lennard-Jones collision diameter of 4.1 A and well depth of 200 K; average energy transferred per collision with helium bath gas 0.24 kcal; the stability of the adduct, which largely determines the falloff, of 38 kcal/mol; and the decline with temperature of (31) D. M. Golden, A. S.Rodgers, and S.W. Benson, J . Am. Chem. Sac.,
88, 3196 (1966). (32) F. P. Tully, A. R. Ravishankara, R. L. Thompson, J. M. Nicovich, R. C. Shah, N. M. Krentter, and P. H. Wine, J . Phys. Chem., 85, 2262 (1981). (33) J. Troe, J . Chem. Phys., 66, 4758 (1977); J . Phys. Chem., 83, 114 (1979).
1278 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985
the high-pressure rate constant from the measured 298 K value.z7 This also is dictated by the data% at 50 torr of He and was taken (units of cm3/s and kcal/mol). to be k, = 9 X 10-11e+0.7/RT The good fit to the data is shown in Figure 9, except for the lowest temperature value of ref 29. Even the data of ref 28 appear to be slightly in the pressure falloff, although this becomes extremely difficult to discern experimentally because the rate constant in the pressure range studiedzs changes very slowly. This gradual approach to the high-pressure limit seems generally not well appreciated. The large k , values and their decline with temperature are indicative of a loose, hindered-rotation transition state.34 A fixed vibrational model, using low frequencies to give a high rate constant, would give a positive temperature dependen~e.~~ Zellner and Lorenz26 also applied this approach to their 298 K data and that of others between 1 and 100 torr. They used a significantly lower value for the low-pressure rate constant, but the two fits differ by less than 30%. We note that our fit is based on matching the 2-torr point at 458 K, where the system is most in the falloff and hence most sensitive to the low-pressure rate constant value and parameters. Any significant inaccuracy in this value could alter our fit, including our selection of k , and the degree of falloff for the 50-torr data. More measurements of the pressure dependence of this rate constant at temperatures near and above 500 K are needed. (Tully and Goldsmith35have recently begun such experiments. The recent kinetic study of Baldwin et al.36on propylene oxidation suggests addition predominates (5:l) at 720 K but abstraction (E,= 6 kcal/mol) becomes more important above 1200 K.) Figure 9 also presents an extrapolation of the addition rate to high temperatures for 200 torr of helium, which approximates the collisional efficiency of our highest pressure experiments. Within the considerable uncertainty this extrapolation entails, the results indicate addition should be only a minor part of our 960 K rate. At higher temperatures and combustion environments, addition is no longer important (as with acetylene4 and ethyleneZ6s3O). The exact temperature range where this change of mechanism occurs remains to be precisely determined, and more experiments and fits are needed. It is quite possible that a portion of our reaction rate at lo00 K is due to addition, and this would be more important at 1-atm pressure. This alternative would then give a higher activation energy for abstraction and a higher extrapolated rate at 2000 K. (A least-squares fit to our data gives an activation energy of 5.7 f 1.2 kcal/mol, with a large A factor of (8.4f 5.0) X lo-" cm3/s, but as noted earlier, the limited temperature range is not well suited for the determination of accurate activation energies.) It should be emphasized that this falloff approach must be taken when extrapolating addition rate constant values to the high temperatures of combustion mechanisms. For the analogous 0 C3H6 system,37 however, the greater adduct stability (85
-
+
(34) G. P. Smith and D. M. Golden, Int. J . Chem. Kinet., 10,489 (1978); M. Rossi and D. M. Golden, ibid., 11, 775 (1979). (35) F. Tully and J. E. M. Goldsmith, private communication. (36) R. R. Baldwin, M. W. H. Hisham, and R. W. Walker, Symp. (Int.) Combust., [Proc.],20, in press.
Smith et al.
+
kcal/mol) and the alternate decomposition to H C ~ H S O result in little falloff. Neglect of pressure falloff overestimates the importance of a reaction at high temperature, despite properly measuring or calculating the correct non-Arrhenius behavior of k,.
VI. Summary The laser pyrolysis/laser fluorescence method has been investigated in detail. These studies include a new direct determination of the time dependence of the density by means of OH collisional quenching together with simultaneous temperature measurements, establishment that rotational and vibrational degrees of freedom are thermally equilibrated on microsecond time scales, and the observation of the rate of conductive cooling. The understanding of the heating dynamics afforded by these results leads to selection of conditions at carefully controlled spatial locations over known reaction time periods and furnishes a quantitative measure of uncertainties introduced, in particular, by temperature and density gradients in the cell. As a result, we feel that laser pyrolysis/laser fluorescence can now produce rate constants of 20% accuracy or better in the 800-1440 K range. (This temperature range can be extended down to 300 K by using a third laser as a photolytic radical source.) An illustration of the improvement gained as the technique became better understood is given in Figure 7, where the 30-40% scatter is associated with our earliest measurementsS whereas more recent runs have typically 10-20% uncertainties (see Figure 6). This can also be seen in the CzH2study4 as well as the scatter in the C3H6and C3Hsresults (Table I). In addition, there is potential for further improvement by automated sorting of data by laser power (IR and UV) on a shot-by-shot basis; although recognized earlier: the present studies indicate how this can be realistically implemented. We conclude that, with its limitations understood and controlled, laser pyrolysis/laser fluorescence forms a useful addition to the limited number of methods for high-temperature reaction rate measurements. It is, in particular, a rapid heating technique which can avoid complicating side and surface reactions. Its utility has been demonstrated earlier4 for OH + C2H2and here for OH + C3H8and C3H6. In each case the experimental results have led to a proper theoretical understanding of these reactions at high temperature, which had not been previously established. There are many candidate reactions for future study where the technique holds promise for similar results. Acknowledgment. We thank David Golden for many useful discussions throughout these studies, Roger Patrick for the use of his unimolecular reaction rate programs, Mala Weissman for helpful comments on the propylene results, and Lynn Seaman for running the PUFF8 calculations. This research was supported by the Office of Basic Energy Sciences of the Department of Energy. Registry NO. HzOz, 7722-84-1; OH, 3352-57-6; CH,, 74-82-8; C3H8, 74-98-6; C3H6,115-07-1. ~
~
~
~~~~
(37) R. A. Perry, J . Chem. Phys., 80, 153 (1984).
