J. Phys. Chem. 1995,99, 14377-14387
14377
Chemical Kinetics of Methyl Oxidation by Molecular Oxygen C.-L. Yu, C. Wang, and M. Frenklach* Fuel Science Program, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802-2303 Received: May 16, 1995; In Final Form: July 13, 1 9 9 9
Four fuel-lean mixtures of methane and oxygen diluted in argon were studied behind reflected shock waves at temperatures from 1550 to 2200 K. The reaction progress was determined in situ by state-selective laser absorption of OH radicals and CO molecules. The rate coefficients of the CH3 0 2 reactions were determined via detailed computer modeling with the GRI-Mech 1.2 reaction mechanism and theoretical calculations using the RRKM master equation formalism. The derived rate coefficient expressions, in units of cm3 mol-' s,-I are 2.87 x 10'3e-15340'T for the reaction CH3 0 2 CH3O 0 and 1.85 x 10'2e-'0224'Tfor the reaction CH20 OH. The experimental rate coefficient of the CH30 0 channel was found to be in CH3 0 2 good agreement with the canonical variational transition state theory. The potential energy barriers relative to CH3 0 2 were found to be 15.4 kcal/mol for the CH2O OH channel and 0.9 kcal/mol for the entrance barrier, the latter indicating a tight transition state. The derived reaction model for the high-temperature oxidation of methyl by molecular oxygen is shown to be self-consistent, in harmony with theory, and in agreement with essentially all experimental data available on this reaction system.
+
-
+
+
+
-
+
+
+
Introduction Oxidation of methyl radicals by molecular oxygen plays a key role in atmospheric chemistry,' low-temperature combustion,*,, and high-temperature ignition of methane4 and hence has been the subject of numerous experimental and theoretical investigation^.^,^ It is known that the reaction between CH3 and 0 2 may proceed through three channels CH,
+
+ 0, - CH,O,
-
+0 CH,O + OH CH30
At low temperatures the reaction proceeds channel l a and rate measurements at such conditions6 show general consensus, although there is a disagreement of a factor of 2 between Cobos et al.' and Pilling et on the highpressure-limit rate coefficient at 300 K. At elevated temperatures, reactions l b and IC play a major role in the consumption of CH3 during methane oxidation, especially under radical-poor conditions. The literature datag-'* for the rate coefficient of reaction l b show reasonable agreement with the spread of about a factor of 3. On the other hand, for the rate coefficient of reaction IC,the scatter among the literature data10-14,16,19-28 reaches more than an order of magnitude, spanning the range from being dominant to negligible. For instance, at 1200 K the rate coefficient of Saito et al.I3 is more than 20 times the upper limit reported by Baldwin and Golden." At the same time, recent quantum-chemical calculation^^^-^^ show that the potential energy barrier of reaction IC is considerably higher than that reported by Zellner and Ewig,I4 who employed RRKh4 calculations to fit the data of Saito et al. While a recent study by F r a a t ~reports ~ ~ a lower rate coefficient for reaction IC, closer to the result of Baldwin and Golden, there is still no clear picture for this reaction system.
* To whom correspondence should be addressed at the Department of Mechanical Engineering, University of California, Berkeley, CA 94720. Abstract published in Advance ACS Abstracts, September 1, 1995. @
0022-3654/95/2099- 14377$09.00/0
It is apparent therefore that reexamination of methyl oxidation by molecular oxygen at high temperatures is warranted. We report here the results of a new experimental and modeling study using a series of lean CH4-02-Ar shock-heated mixtures where the concentrations of CO and OH were monitored in situ by quantitative laser absorption. The rate coefficient expressions were determined via detailed chemical kinetic modeling of the experimental shock tube data and RRKM master equation calculations describing temperature and pressure dependencies for this reaction system.
Experimental Section Shock Tube Apparatus. The experiments were performed in a conventional shock tube, made of a constant-diameter stainless steel tube with an inner diameter of 8.26 cm and a wall thickness of 3.2 mm. The end plate of the shock tube was made of aluminum. The driver and driven sections were 1.5 and 4.9 m long, respectively. A double-diaphragm burst technique was used to initiate the shock waves. The diaphragms were made of Mylar film. Prior to each experiment, the driven section of the shock tube was evacuated to at least 1 x Torr by an oil diffusion pump equipped with water- and liquid nitrogen-coupled traps. The shock tube was tested for leaks by a Varian PortaTest leak detector and was cleaned after every experimental run. The test mixtures were prepared manometrically, with the maximum uncertainty in the final reactant concentrations of about 3%, and allowed to mix in a stainless steel tank for 24 h prior to experimental runs. The stated purity of gases used in preparation of these mixtures were as follows: C b ,99.99%; 02,99.999%; Ar,99.9999%; CO, 99.99%. The driver gas was helium of 99.998%. All the gases were used as purchased, without further purification. The postshock conditions were calculated from the incident shock velocity in the usual manner,33assuming no chemical reaction and full vibrational relaxation. The incident shock velocity was determined by four PCB Model 482A piezoelectric pressure transducers mounted 25.4 cm apart with the last one being located 12.7 mm from the end plate. All pressure 0 1995 American Chemical Society
Yu et al.
14378 J. Phys. Chem., Vol. 99, No. 39, 1995 transducers and optical windows were mounted flush with the inside surface of the shock tube to minimize the distortion to the gas flow. The velocity of the incident shock was extrapolated to the end plate, and this extrapolated velocity was then used in the calculations of the temperature, T5, pressure, P5, and total density, Cs, of the gas behind the reflected shock waves. The observed shock wave attenuation was less than 1.5%/m. The maximum uncertainty in the time measurements was estimated to be f 0 . 5 ps, which corresponded to f0.35% and f0.09% uncertainties in the computed values of T5 and C5, re~pectively.~~ Optical Detection Systems. The concentration of OH radicals was measured by an actively stabilized Coherent CR699-21 ring-dye laser pumped by a continuous-wave Coherent Innova 100-15 argon ion laser.34 The resulted beam was frequency-doubled and carefully tuned to the center of the OH spectral Pl(5) line, (0,O) band of the A2C+-X2lI transition (310.123 nm). The argon ion laser was operated under singleline output (514.5 nm) and current regulation modes to assure a constant temperature in the laser cavity so that a constant output beam path could be maintained. A Coherent Model 7500 frequency doubler (LiIO3 crystal) and a Coherent etalon assembly (ICA) were installed in the cavity of the ring-dye laser. Kiton red dye was used in this work. The dye solution was circulated by a Coherent 5920 dye circulator with pressure maintained at 40 psi and cooled by water as well as a Neslab CFT-25 refrigerated recirculator to maintain a constant temperature of 10 “C to achieve maximum conversion efficiency. The wavelength of the primary laser beam (620.246 nm) was monitored by a Burleigh WA-10 wave meter, which has an accuracy of fO.OO1 nm. The generated single-frequency secondary beam was centered at 310.123 nm with a line width of 2 MHz. A continuous-wave CO laser was used to monitor the concentration of CO molecules. The CO laser had an active cavity length of 1.7 m sealed by a pair of BaF2 Brewster windows.I2 The cavity was cooled by liquid nitrogen. An output coupler having a reflectance of 97.5% was mounted on a piezoelectric transducer. A grating with 300 groovestmm blazed at 4 mm and a spectral resolution of 1.4 cm-’ was used as a wavelength selector. A lock-in stabilizer (Lansing Research Corp., Model 80.125) was employed to stabilize the laser output strength. The laser was observed at the 2 1 P( 10) transition using a gas mixture of He (4 Torr), N2 (1.4 Torr), CO (0.01 Torr), and 0 2 (0.1 Torr). Both ring-dye and CO laser probe beams were coaxially passing through the shock tube, 12.7 mm away from the end plate. Shock tube windows were made of CaF2. The intensities of these beams were measured by a THORN EM1 9924B photomultiplier tube, which has a specified rise time of 15 ns, for the ring-dye beam and by a l/4 m monochromator (Oriel Model 77200) in conjunction with a liquid nitrogen-cooled InSb photovoltaic detector (Judson Model J-1OD) for the CO laser beam. The monochromator was used not only to identify the laser transition frequency but also to filter out radiation emitted by the shock-heated gas. The electronic signals generated by the CO laser beam were amplified by a preamplifier (Judson Model PA-9-50) with a frequency response of 920 W z . Both signals along with the signals generated by pressure transducers at the observation section were recorded by two Nicolet 2070 dual-channel digital oscilloscopes. The overall time constants of the OH and CO light detection systems were both 0.6 ps, as determined experimentally by using a strobe light source. The
-
lasers and associated optical instruments were set on an airfloated NRC KL-A optical table to reduce vibrational disturbances. Absolute concentrations of OH and CO were determined through the Beer-Lambert law
ln(Z/Zo) = -ECZ where I and IO are the transmitted and incident intensities, respectively, 1 is the effective length of the absorbing medium (the internal diameter of the shock tube), C is the concentration, and E is the absorption coefficient. The absorption coefficients for both OH and CO were determined by performing a series of calibration experiments. The calibration for OH absorption followed the procedure described by Yuan et al.34 The OH absorption coefficient, €OH, was derived from a series of shockheated H2-02-Ar and H2-02-C02-AI mixtures by matching the peak OH concentration. Combining the data obtained in the present study with those of Yuan et al.,34 the following expression was developed
cOH= (1.65 f 0.17) x lo-’’ - (1.00 f 0.35) x 10-14/T where Tis the gas temperature in kelvin and EOH is in units of cm2 molecule-’. The above expression is about 60% higher than the previous results of Yuan et al.34and within 10% from those of Shin et al.35 The calibration of CO absorption was performed by using known CO concentrations. The absorption coefficient of CO, ECO (cm2 molecule-’), can be expressed by the gain equation for a P-branch transition from (v”,J”) to (v” 1, J” - 1),36-38
+
E
-Y 8 2 IR,I2 S’g(w0) e-AEo”’IkeT (Butte-B,~J’(J“+l)hclkeT co - 3kBT Qco
where k~ is the Boltzmann constant, Tis the temperature, Y O is the frequency of the transition, B,,, and B,,,+I are CO molecular 1, rotational constants for vibrational states v” and v” respectively, QCO is the vibration partition function of CO molecules, AE: is the energy difference between the ground state and vibrational state v”, and AI?$+’is the energy difference between vibrational states v” and v” 1. Rt denotes the transition moment including the vibrational and rovibrational matrix elements calculated by analytical formulas derived by B o ~ a n i c h and , ~ ~g(w0) is the value of the Voigt profile38at the line center Y O which was calculated as
+
+
where
AwD = w0 4 2 In 2 kBT/mc2
In the above expressions, AYDis the Doppler half-width, m is the mass of CO, AwCis the collision broadening half-width, P is the pressure, and y is the collision broadening half-width at reference pressure, 1 atm, and reference temperature, Tref,298 K. The temperature-dependent parameter II was estimated by
Methyl Oxidation by Molecular Oxygen
J. Phys. Chem., Vol. 99, No. 39, 1995 14379
linearly interpolating the data reported by Bonamy et ale4 The CO calibration was accomplished by fitting parameter y. The calibration experiments were carried out with 0.1-0.5% CO in argon mixtures over the temperature and pressure ranges of 1450-2370 K and 1.3-2.6 atm, respectively. Vibrational relaxation times of about 80-450 ps4I were observed under these conditions. Parameter y was found to be (4.8f 0.4)x atm-’ cm-I, a value which is straddled by 5.2 x atm-’ cm-’ of Hsu et al.37 and 4.3 x atm-’ cm-’ of Varghese and H a n ~ o n . ~ ~
i ? ....*.....
Theoretical Approach
CH,O + OH
Kinetic Modeling and Reaction Mechanism. The kinetic simulations were performed using a recent methane oxidation Reaction coordinate mechanism, GRI-Mech 1.2,42 composed of 177 elementary Figure 1. A potential energy diagram of the CH3 0 2 reaction system. reactions and 32 chemical species. All reactions were assumed The potential energy barriers are referenced to the ground level of the to obey the principle of detailed balancing. The thermodynamic stabilized adduct, CH30#A”). data used for the calculation of equilibrium constants were those study of Teitelboim et al.,I6 the QRRK analysis of Dean and of GRI-Mech 1.2, except that the data for CH30 were updated and the empirical estimation of Benson.2 We with newly reported A&9,43 and vibrational f r e q u e n c i e ~ . ~ . ~ ~We~tmoreland,~~ follow this assumption in the present study as well. The use of the newer CH3O data did not affect measurably the A potential energy diagram for the reaction system is depicted predictions of GIU-Mech 1.2 but made it consistent with the in Figure 1. The barriers listed for channels de and c were present theoretical analysis. The kinetic behavior was computed obtained by fitting the experimental data, as described in the using an LSODE integrator?6 The experimentally determined next section. The value of 58.7 kcal/mol shown for channel b time constants for the measurements of CO and OH were is the difference in the heat of formation between CH30249.50 included in the kinetic simulations as described p r e v i o u ~ l y . ~ ~ and that of 20.9 kcal/mol shown for the and CH30 0,43,51 Unimolecular Reactions and Chemical Activation Proground level of CH20 OH is from a recent e v a l ~ a t i o n . ~ ~ cesses. In theoretical analysis of the CH3 0 2 system we Pressure and temperature dependencies of the rate coefficient followed the reaction scheme suggested in previous studfor reaction CH3 -I- 0 2 CH3O2, kla, were modeled by ies2,14,24,27 employing the solutions of master equation^.^^.^^ Thus, kl, was expressed through its reverse, k-la,
+
+
+
+
-
-
and the value of k-la, the rate coefficient of the unimolecular decomposition CH3O2 CH3 0 2 , was determined by
CH302
where CH30: is the energized intermediate; kad(E), kde(E), kb(E), and k,(E) are the energy-dependent rate coefficients of the elementary reaction steps; B is the collision efficiency; and w is the collision frequency of bath gas. Ab initio quantum chemical calculation^^^,^^ showed that combination of ground state 02(3Zi) and CH3(2A”) leads to the formation of ground state CH302(2A”). Dissociation of this adduct to the CH30(2E) O(3P), channel b, takes place on the same potential energy surface, I?A“. On the other hand, its dissociationthrough channel c requires a 1,3-hydrogen migration, through a fourmembered-ring transition state, { CH200H}*, to form CH200H, which rapidly decomposes to CH~O(’AI) OH(21-I). This migration can occur only via the first excited potential energy surface CH302(2A’), produced by the addition of CH3(2A”) to the first excited state of molecular oxygen, 0,(3A,). The CH302(2A’) is about 20 kcal/mol above the ground state CH302(2A”).14,29.47In addition, to exit through channel c from the ground state CH~OZ(~A”), hopping from 2A” to 2A‘ surface is required.29 That is, an additional energy is needed to break the symmetry. Clearly, channel c is not favored by the energetics. However, Zellner and c o - w o r k e r ~argued ~ ~ ~ ~ that ~ at high energies CH302(2A’) might be also populated, and thus both surfaces are strongly mixed. This increases the probability of reaction IC. In their RRKM study, Zellner and co-workers assumed that both reactions l b and IC proceed adiabatically on the ground surface CH302(2A”) and neglected the restriction of surface crossing. The same assumption was employed in the RRKM
+
Here Kes is the equilibrium constant of CH3 is the nonequilibrium factor defined as
+0 2
CH3O2,
fne
+
+
g(E) is the state population calculated by solving the master equations for the unimolecular CH3O2 decomposition, Q is the partition function, and B(E) is the Boltzmann distribution. The rate coefficients for chemically activated reactions l b and IC were obtained following Larson, Stewart, and Golden,54 who suggested a simplified, steady state treatment for chemical activation reactions,
(4) where ktot(a= ~,-I~(E‘) k b ( a -k &(E) is the total rate coefficient for the three decomposition channels of CH3O2. A more rigorous formula, based on the solution of master equations for chemical activation and recombination, is given by Gilbert and c o - ~ o r k e r s ?which ~ ~ ~ ~leads to
14380 J. Phys. Chem., Vol. 99, No. 39, 1995
Yu et al. TABLE 1: Parameters Used in RRKM Calculations transition states adduct CH302a {CH3**a*}'b (CH30. * {CHzOOH)**
where ki is the rate coefficient for unimolecular dissociation of CH3O2 via the ith exit channel (b or c in this case), given by
and v(E) is the distribution function for the CH3O2 reaction system at steady state, determined from the following equation WJ[p(E,E')
W') - P(E",E) V(Q1 e' - kt,t(E) r(E)= -kde(E)
B(E)
vibrational frequencies (cm-])
2983 2968 2891 1453 1440 1414 1183 1118 1112 902 492 inactive rotational 0.341 (1,2) constants (cm-')d active rotational 1.65 ( 1.1) constants 6.80 (3,l) (cm-l)d A@& (kcal/mol) 2.7' potential energy barrier (kcal/mol) Lennard-Jones 4.V diameter (A) Lennard-Jones 34Of well depth (K)
3247 3159 2922 1418 1366 1022 466 233 191 130
2840 2774 2774 1487 1487 1362 1047 653 653
0.165 (1,2)
3196 3077 1777 1473 1141 1090 1070 1009 685 532 406 0.396 (1,2)
1.50 (1,l)
1.12 (1,l)
6.67 (3,l) where P(E,E') is the probability of molecular energy transfer from level E' to E. This equation was solved by Gaussian e l i m i n a t i ~ n ,employing ~~ the exponential-down for 3 1.70 46.20 P(E,E'). In the low-pressure limit, when o 0, eq 5 is reduced to eq 4. For the conditions of the present experimental study, the calculations showed that the differeice between eqs 4 and 5 is below 1%. On the basis of these results, and because the a Vibrational frequencies are from Ase et ~ 1and. rotational ~ constants computer evaluation of eq 4 takes much less CPU time than from W a l ~ h . From ~ ~ W a l ~ h . Vibrational ~~ frequencies are those of that of eq 5 , we chose to use eq 4 in the numerical analysis of CH3O radical measured by Foster et uLM Quantities in parentheses the collected experimental data. are symmetry number and dimension, in that order. e From Slagle and The calculations of the rate coefficient for the loose transition G ~ t m a nf. From ~ ~ Patrick and Golden.79 g Given in Table 4. state of the exit channel b followed a two-dimensional hinderedrotor model with the Pacey type potential energy f u n c t i o r ~ . ~ ~ . ~energy ~ increment was set to 10 cm-' instead of 100 cm-I, a An analytical solution for the density of states for this model Gauss elimination subroutine was added to the master equation was recently derived by Hase and Zhu5* We extended their program, the convergence criterion for iteration of master results to include the convolution of a two-dimensional hindered equation solutions was set to l V 4 or lower, a subroutine was rotor with m two-dimensional and n one-dimensional active free added for calculation of eqs 6a and 6b, and integration of tworotors, for which case the density of states @ ( E )and the sum of dimensional angular momentum was carried out employing states W(E) were derived as follows, convergence criteria not only for high-pressure-limit unimolecular processes, as in the original code, but also for lowpressure-limit chemical activation. The convergence criteria in both cases were set to 5 x
-
(-b1
E
Results and Discussion
m+n/2
fsdR sin R( 1 - VO sin2 0)
(6a)
2ffhhBhr
where 0,and B, are the symmetry number and the rotational constant, respectively, of a jth (one- or two-dimensional) free rotor; 0 h r and Bhr are the symmetry number and rotational constant, respectively, of the two-dimensional hindered rotor; VOis the potential energy barrier for the hindered rotation; 8 is the rotational angle of the hindered rotor; and 8, is the maximum angle the fragment can rotate. The effect of steric hindrance between two fragments on the maximum rotational angle 8, was calculated using the hard-sphere hindrance treatment of Jordan et al.59 The numerical integration of eqs 6a and 6b was carried out only for the domain of 8 that satisfies E 2 VOsin2 8 as suggested by Hase and Z ~ U . ~ ~ The RRKM and master equation calculations were performed using the UNIMOL code53 with several modifications: the
+
-
Reaction CH3 0 2 CH3O2. As mentioned in the previous section, the rate coefficient of this reaction, kl,, was calculated by eq 3 with the conservation of two-dimensional angular momentum. The parameters used in the calculations are listed in Table 1. The value of for CH3O2 was taken from Slagle and G ~ t m a n ?which ~ is in good agreement with that of Khachatryan et aL5* The vibrational frequencies of CH302 were those of Ase et a1.60 A torsional vibration of CH3 and 0 2 groups about the C - 0 axis was treated as a free rotor. The reduced moment of inertia for this free rotor, Z,, was calculated by the method of Pitzer and Gwinn,6'S6* cos2 a,
r'
= 'CH[l
- C' H{
l=x,y,z
Ti]
where ZCH~is the moment of inertia of CH3, Zl is the lth principal moment of inertia of CH3O2, and a/is the angle between the internal rotational and the lth principal axes. Using a value63 of 35.11 kcal/mol for A S 9 , of CH3, the equilibrium constant of reaction CH3 0 2 CH3O2 was fitted against temperature, which resulted in
+
-
Methyl Oxidation by Molecular Oxygen
J. Phys. Chem., Vol. 99, No. 39, 1995 14381 (a)
10-1
100
101
102
103
I,
105
104
I
Pressure (torr) Figure 2. Comparison of the present theoretical predictions (solid lines) CH302 with for the rate coefficient of reaction CH3 + 0 2 experimental literature data (symbols) at 300 K and bath gas Ar or He. Symbols: x, Cobos et al.;7 0, Kaiser;68A, Pilling and Smith;* 0, Plumb and Ryan;65 0, Selzer and Bayes.% The symbols in the inset at (A) 334, (0)382, (+) designate experimental data of Keiffer et
-
IS
and kl, Keq
(AEdown)
T(K) (cm3mol-’) (cm-I) 300 334 382 420 474 530 583
1.93 x 8.39 x 1.99 x 4.38 x 5.53 x 1.52 x 9.53 x
lo2’ lOI7 10l6 lOI4 lo‘* 10” lo9
300 275 250 240 230 220 220
k7a
p
(cm6mol-2 s-]) (cm3mol-’ s-l) 0.365 1.47 x lOI7 1.16 x 10l2 0.314 0.256 0.222 0.184 0.151 0.129
1.19 8.75 6.93 4.97 3.50 2.59
x lOI7 x 10l6 x 10l6 x 10l6 x 10I6 x loL6
1.54 x 2.16 x 2.73 x 3.66 x 4.80 x 6.04 x
10l2 lo’* 10l2 10l2 10l2 1OI2
Figure 3. Comparison of the present theoretical predictions (solid lines) for the low-pressure (a) and high-pressure (b) limits of the rate coefficient of reaction CH3 02 CH302 with literature data obtained for bath gas Ar or He: e, Hochanadel et al.;77 + Kaiser? A, Laufer ; ~ Patrick ~ and Golden;790, Pilling and Smith;8 et al.;760, P a r k e ~ 0, W, Plumb and Ryan;65 x, Selzer and Bayes;@ A, Van Den Bergh and Callear;75 dotted line, Cobos et al.;7 three-dot-dashed line, Kaiser;68 dot-dashed line Keiffer et al.;67long-dashed line, Forst and C a r a l ~ ; ~ ~ short-dashed line, Pratt and Wood.8o
+
for a temperature range from 300 to 1000 K, and 8 1.785 17570/T
Keq= 1.07 x 10- T
e
30
1 0 4 ~(-1K )
420, (0)474, ( x ) 530, and (0)582 K.
TABLE 2: Summary of Calculated Weak-Collision Data
25
20
-
0.12 Q)
0
e5
0.50
8
e
z
for a temperature range from 1000 to 2500 K, all in the 2 0.0s concentration units of moYcm3. The molecular geometry and 4 4 T vibrational frequencies for the CH3* - 0 2 transition state were 0.25 0 taken from ab initio quantum-chemical calculations of W a l ~ h . ~ ~ 0.04 The vibrational frequencies were scaled by a factor of 0.943 as The near-zero vibrational frequency suggested by Pople et was treated as a free rotor whose reduced moment was 0.00 0.00 calculated using the Pitzer and Gwinn method as described 0 100 200 300 above. Time (p) The potential energy b e e r for the decomposition channel, Figure 4. Typical CO and OH absorption profiles obtained in a 0.4% &e, and the average downward energy transferred per collision, CH4-5.0% OZ-Ar mixture at T5 = 1821 K and P5 = 1.55 atm. (&??down), were used as adjustable parameters in fitting eq 3 to low-temperature falloff literature data.7.8%65-69 The best-quality stantially lower than 900 cm-’ and agree with those reported fit is demonstrated in Figure 2; it was obtained with E d e = 3 1.7 by Whyte and Gilbert73and Forst and C a r a l ~ .The ~ ~ value of kcal/mol, which translates into an entrance barrier of 0.9 kcal/ fne calculated at 300 K is equal exactly to 1, in agreement with mol relative to the CH3 0 2 energy level. The obtained values the~ry.~~,~~ of the average energy transfer (&??down), the corresponding Figure 3 compares the obtained kya and kTa with literature calculated collision efficiency B, and the low- and high-pressure data. The prediction for the low-pressure limit, demonstrated limits of kl, are listed in Table 2. in Figure 3a, was found to be in good agreement with the data Inspection of Figure 2 indicates that the present theoretical of Kaiser,68Pilling and Smith,8 and Selzer and Bayes.66 The prediction fits both the experimental data of Cobos et aL7 and theoretical prediction for the high-pressure limit is compared Pilling and Smith.8 Employing the Troe factorization meth0d,7O-~~ to the literature data7,8,65-68,74-80 in Figure 3b. As can be seen, Pilling and Smith obtained about 2-fold lower kya than did the present values of kya have a stronger temperature dependence and are larger than those of Keiffer et al.,67 and Cobos et al. Fitting kya of Pilling and Smith at 300 K results in E a d = 1.22 kcal/mol and ( m d o w n ) = 900 cm-I. The latter is Cobos et al.,7 all using the Troe factorization method. The stronger temperature dependence in our case results mainly from too high for the Ar or He bath gases. The present results for the potential energy barrier of 0.9 kcaYmol being slightly higher (&?down), showing a weak temperature dependence, are sub-
s
+
Yu et al.
14382 J. Phys. Chem., Vol. 99,No. 39, 1995 TABLE 3: Experimental Conditions and Results
1651 1711 1717 1732 1759 1763 1803 1944 2002 2089 2192
10.99 10.37 15.84 10.76 10.54 10.97 15.82 10.68 10.84 10.62 10.39
1.49 1.46 2.23 1.50 1.52 1.59 2.34 1.70 1.78 1.82 1.87
285.3 194.4 128.2 140.9 139.2 125.1 78.3 52.7 38.5 27.8 16.6
Series A: 0.4% CH4-20.0% O2-Ar 304.1 308.6 320.2 202.2 211.6 202.7 145.3 135.9 135.9 171.6 163.3 172.4 154.7 161.7 150.6 142.5 141.2 149.4 82.0 85.6 94.1 58.3 49.1 55.2 39.6 42.5 46.7 29.6 34.8 27.8 17.1 18.7 21.8
326.8 217.3 145.5 187.4 164.9 153.0 89.0 53.9 43.8 29.8 19.4
358.8 301.6 160.1 253.2 223.4 170.6 95.7 58.0 47.8 32.8 21.6
3.2 x 4.5 4.6 x 5.9 x 6.1 x 6.4 6.6 x 1.3 x 1.5 x 1.8 x 2.5 x
109 109 109 109 109 109 lo9 1O'O 1OIo 1OIo 1Olo
1538 1555 1568 1628 1630 1635 1636 1676 1726 1743 1752 1756 1769 1843 1852
16.03 15.78 11.17 10.85 16.11 10.99 15.48 15.80 16.18 10.54 10.48 10.86 15.82 10.55 15.92
2.02 2.01 1.44 1.45 2.15 1.47 2.08 2.17 2.29 1.51 1.51 1.57 2.30 1.60 2.42
632.7 554.3 663.0 461.1 329.0 463.0 301.6 216.5 163.8 202.0 171.5 168.0 110.4 113.5 76.7
Series B: 0.5% C&-lO.O% 651.1 678.5 627.7 678.0 696.8 722.0 480.7 500.4 343.5 355.2 496.1 521.9 33 1.6 355.2 236.3 256.2 175.3 201.3 226.5 213.5 185.9 199.6 181.0 205.1 122.2 128.5 127.7 140.3 81.9 87.1
O*-Ar 681.2 712.5 713.5 487.0 367.1 506.3 359.7 259.7 187.2 221.7 202.9 225.5 127.6 131.2 80.3
704.3 730.3 735.0 525.5 378.5 522.6 371.1 274.2 195.0 230.2 212.5 235.0 134.1 136.9 83.8
741.4 756.7 774.6 564.1 401.3 537.3 394.0 301.7 201.8 241.4 224.4 243.3 149.7 144.8 87.1
1.6 x 1.4 x 2.0 x 2.3 x 2.2 2.0 x 2.3 2.9 3.2 4.8 x 5.5 x 5.1 x 5.7 x 6.2 6.7
109 109 109 109 109 109 109 109 109 109 109 109 109 109 109
1687 1699 1718 1821 1826 1829 1929 2012
15.75 10.68 15.59 10.37 10.71 15.73 15.78 10.51
2.18 1.45 2.20 1.55 1.60 2.36 2.50 1.75
317.7 425.3 240.5 174.8 172.1 117.2 65.7 58.6
Series C: 0.4% CH4-5.0% 02-Ar 346.7 363.3 367.3 498.3 471.1 460.1 295.3 268.6 295.5 190.9 207.7 203.2 201.5 187.1 196.2 128.7 137.0 137.6 71.0 75.4 65.4 65.5 69.2 62.9
381.5 500.6 308.2 213.4 198.1 147.0 69.8 67.5
396.0 523.9 318.7 227.6 209.3 154.1 73.6 71.6
2.9 2.8 3.5 6.5 5.8 6.1 1.1 1.5
x x x
109 109 109 109 109 109 1010 1Olo
1680 1707 1723 1762 1826 1856
15.84 10.86 10.69 15.94 10.69 15.78
2.18 2.18 1.51 2.31 1.60 2.40
644.8 684.3 571.3 289.4 264.5 155.6
Series D: 1.0% CI&-3.0% 02-Ar 723.6 730.7 689.5 728.3 753.5 752.7 633.8 652.1 660.0 362.3 369.4 334.0 288.7 297.1 303.6 166.0 173.4 171.1
750.4 771.0 676.5 375.8 316.7 181.9
772.5 785.0 686.0 381.7 330.2 188.8
2.3 2.7 3.0 3.5 5.1 5.8
x x x x
109 109 109 109 109 109
than those of Keiffer et al. (0.45 kcdmol) and Cobos et al. (0.26 kcdmol). Nonetheless, all three studies-those of Keiffer et al., Cobos et al., and ours-suggest a transition state which is a tightly bound complex. Forst and C a r a l ~on , ~ the ~ other hand, favored a loose transition state but were still able to fit the experimental data, except those of Cobos et aL7 However, recent ab initio quantum-mechanical calculations performed by Melius81 and Jafri and Phillips82 support a tight transition structure. Reactions CH3 0 2 CH3O 0 and CH3 0 2 CH2O OH. Four series of experiments with different initial compositions were used in the course of the present study. The mixture composition, experimental conditions, and obtained characteristic times for the CO and OH profiles are listed in Table 3. Typical absorption profiles are shown in Figure 4. Extraction of kinetic information from the experimental data collected in this study was performed by matching the initial parts of the CO and OH profiles: from the onset of reaction up to the maximum in the profiles.34 For this purpose, each profile was represented by three points, those corresponding to l14, '12, and 3/4 of the maximum concentration. The rate coefficient determination was then performed by matching the correspond-
+
+
-
+
+
-
x x
ing characteristic times: 21/4, 2112, and 23/4. The criteria used for the mixture selection, as before,34were based on the sensitivity with respect to the rate coefficients in question, the absorption strength of CO and OH laser beams, and minimization of experimental uncertainties. A sensitivity analysis showed that for fuel-lean mixtures 21/2 of CO and OH is mainly affected by the CH3 0 2 reactions (Figure 5 ) , while for fuel-rich and stoichiometric mixtures 21/2 was mostly sensitive to other reactions, like H 0 2 OH 0, CH3 CH3 products, etc. The principal difficulty underlying the study of the CH3 0 2 reaction at high temperatures is due to the fact that the two reaction channels, (lb) and (IC), cannot be determined simultaneously or differentiated between each other based solely on experimental observations at such conditions. This is exemplified in Figure 6, which shows a large scatter in literature reports for klc.lO.l 1,13,14,16.19-26,28,32,83 These determinations of klc can be categorized into high- and low-value groups: the high-value group contains all those results which were obtained when reaction IC was assumed to be the dominant one, and the lowvalue group consists of those when reaction Ib was presumed to dominate.
+
-
+
-
+
+
+
Methyl Oxidation by Molecular Oxygen
J. Phys. Chem., Vol. 99, No. 39, 1995 14383
CH3 + O2 -+ CHzO + OH
+ CH, + O H .......... H + O2 + OH + 0 ...... ....
O + C H .,
.
CH3 + H CH4 + H OH
............
>
+ CH4
.......
+ CH3 + H2
+ CH3 + lCHz + H 2 0
H 0 2 + CH3 + O2 + CH, H 0 2 + CH3 + OH
+ CH30
_"
.....
...
...
..
...... ........
.....
............ .....
..........
_
....... ...
.
.^
HCO + M
+H + CO+ M
...............
..............I. .
. -.
".
...........................
HCO + 0 2-+ H 0 2 + C 0
-0.3
-0.4
-0.5
-0.1
-0.2
0.0
0.1
0.2
Sensitivity Figure 5. Logarithmic response sensitivity of t l / 2 for CO and OH absorption profiles with respect to influential reactions computed for mixture series B at T5 = 1600 K and C5 = 1.0 x mol/cm3. Dean & Ki~tiakowsky~~
Assuming, on the other hand, that the kl, expression of Saito et al. is too high implies that the barrier height of 38.2 kcal/ mol suggested by Zellner and EwigI4 for channel c is too low. Indeed, the results of recent quantum ab initio calculations for this barrier range from 42 to 57 kcal/m01,*~-~~ all being higher than that of Zellner and Ewig. The barrier determined in the present study, as described below, is 46.2 kcdmol, which is about the average of those reported in the above-cited ab initio studies. On the basis of these considerations, we analyzed the experimental data collected in the present study as follows. First, we determined kl, through the described above theoretical calculations and using the barrier height of the exit channel c as an adjustable parameter while numerically fitting an average of experimental kl, values at 1200 K of Baldwin and Golden24 and Grela et al.,28the only two direct determinations at the lower end of the high-temperature range. The RRKM calculations were performed utilizing the transition state parameters listed in Table 1. The vibrational frequencies and rotational constants were those of W a l ~ h Again, . ~ ~ the vibrational frequencies were scaled by 0.943. The result of these calculations, expressed in the Arrhenius form over a temperature range of 1000-2500 K, is
Olson & G a r d i ~ ~ e r ~ ~
k,, = 1.85 Zellncr & Ewig14
2 1 \h
,$ \.-
Teitelboim et d.I6 ,
