J . Phys. Chem. 1984,88, 6259-6263
6259
Kinetic Study of the Reactions of Acetonitrile with CI and OH Radicals G . Poulet, G . Laverdet, J. Li Jourdain, and G . Le Bras* Centre de Recherches sur la Chimie de la Combustion et des Hautes TempZratures, 45045 Orleans Cedex, France (Received: March 14, 1984)
Reactions of OH and C1 radicals with CH3CN have been studied, at pressures around 1 torr, in discharge flow reactors associated with EPR and mass-spectrometrictechniques. For the reaction OH + CH3CN (l), the rate constant found at rmm temperature, kl = (2.1 f 0.3) X cm3molecule-' s-', is in agreement with several flash photolysis-resonance fluorescence determinations obtained at higher pressures (7-300 torr). For the reaction C1+ CH3CN (2), the rate constant measured in the range 295-723 K shows an Arrhenius behavior in the range 478-723 K, with k2 = (3.46 f 0.70) X lo-'' expl(-2785 f 115)fq cm3molecule-' s-I. At 295 K, the extrapolated value is lower than the experimental one: k2 = (8.89 f 1.24) X These results are discussed and compared with other very recent data. The atmospheric application of these data is discussed, showing that reaction 2 is a negligible atmospheric sink for both CH3CN molecules and C1 atoms.
Introduction Acetonitrile has been found to be present in the lower troposphere at ppbv levels,' whereas mixing ratios in the range of pptv in the stratosphere are estimated from mass-spectrometric measurements.2 These observations have suggested that there is a ground source of CH3CN and atmospheric sinks. Physical processes such as washout and reactions with OH and C1 radicals have been considered as possible sinks for CH3CN and their effect has been recently m ~ d e l e d . For ~ reaction 1, four determinations
OH
+ CH3CN
4
products
(1)
of the rate constant have already been published using the flash photolysis resonance fluorescence method.e7 The good agreement between the data of ref 5-7, obtained at room temperature and at pressures of 7, 100-300, and 20-50 torr, respectively, means that reaction 1 is pressure independent, or, if not, the high-pressure limit of kl is achieved at pressures lower than 7 torr. However, in ref 6, data have been also obtained at pressures down to 7 torr, giving for k , a value which is a factor of 2 lower than this high-pressure value. Thus, it appeared to be useful to reinvestigate this reaction at low pressure to see if kl is pressure dependent or not. For reaction 2 the rate constant has been recently measured CI
+ CH3CN
4
products
(2)
by a competitive method at 370 and 413 K8and in another study cm3 molecule-' s-' has been found at an upper limit of 2 X room temperature by the flash photolysis method.' Although these data show that reaction 2 is negligible in the atmospheric chemistry of CH3CN, it was interesting to determine more precisely the temperature dependence of k2 by considering a larger temperature range than that of ref 8. Such data could be used to interpret the unexpected low reactivity observed between C1 and CH3CN. The present study of O H and C1 radicals with CH3CN is the first carried out by the discharge flow method. Experimental Section Reactions of C1 and OH with CH3CN were studied in two different discharge flow experiments: discharge flow-EPR for (1) Becker, K. H.; Ionescu, A. Geophys. Res. Lett. 1982, 9, 1349. (2) Arijs, E.; Nevejans, D.; Ingels, J. Nature (London) 1983, 303, 314 and
references reported in this paper. (3) Brasseur, G.; Arijs, E.; De Rudder, A.; Nevejans, D. Geophys. Res. Lett. 1983, 10, 125. (4) Harris, G. W.; Kleindienst, T. E.; Pitts, J. N., Jr. Chem. Phys. Lett.
+
OH CH3CN and discharge flow-mass spectrometry for C1+ CH3CN. The following conditions were used: large excess of CH3CN over OH and large excess of CI over CH3CN. These two techniques have been described p r e v i o u ~ l y . ~ * ' ~ In the EPR experiment, the reactor made of quartz was of 22-mm i.d. and 1 mm thick. It was coated with boric acid to reduce the wall combination of OH radicals. Reactants were flowed through two sliding injectors kept in constant relative position. The pressure in the reactor was 1.2 torr and the gas flow velocity was around 12 m s-l. O H were produced by the H NOz reaction by using an excess of NO2 over H atoms. H atoms were generated from Ha, highly diluted in helium, through a miciowave discharge. CH3CN (Merck, 899.7%) was outgassed before storage in a flask, in the gas phase. Its flow rate was calculated from the pressure drop in the flask. NOz flowed through the external tube of the injector and CH3CN through the internal one, 9 cm downstream, so that the H NOz reaction could be completed before the introduction of CH3CN. O H concentrations were measured by EPR, and their absolute value could be obtained by using N O as a reference." In the mass-spectrometric experiment, the reactor, also made of quartz, was of 24-mm i.d. Ranges for pressure and gas flow velocity in the reactor were 0.47-2.06 torr and 5.6-51 m s-', respectively. The reactor was heated in the range 295-723 K by means of an electrical fiirnace. The temperature profile along the flow tube was measured and found uniform along the section used for kinetic measurements ( f 2 K at 295 K, f 4 K at 723 K). C1 atoms were generated from ClZ,highly diluted in helium, which was dissociated in a microwave discharge. C1 atom concentrations were measured by means of the mass spectrometer, which was equipped with modulated molecular beam sampling.1° Three titration methods were used: (i) measurement of Clz dissociated in the discharge by monitoring the C12+ peak at m l e 70 with discharge on/off; (ii) titration of C1 by the C1 + NOCl NO + Clz reaction, from measuring the consumption of NOCl used in excess at the peak m l e 49 (NCl'); (iii) titration of C1 by the reaction Cl C2H3Br C2H3C1 Br by measuring the consumption of CzH3Br,used in excess, at m l e 108 (C2H3Br+). This reaction was recently found to be stoichiometric and fast enough ( k = (1.43 f 0.29) X a t 298 K) to be suitable for C1 titration.I2 These three methods led to C1 atom concentrations in good agreement. Typical fractions of Clz dissociated of about 0.50 were obtained with frequent coatings of the discharge tube by H3P04. The main tube of the reactor was also periodically cleaned and coated with H3P04when wall recombination of C1 atoms was observed not to be negligible. Since the C1 atom
+
+
+
-
-
+
1981, 80, 479. ( 5 ) Fritz, B.; Lorenz, K.; Steinert, W.; Zellner, R. 'Proceedings of the 2nd
European Symposium on Physico-Chemical Behaviour of Atmospheric Pollutants, Varese, Italy, 1981"; Reidel: Dordrecht, Netherlands, 1981; p 192. (6) Zetzsch, C. Bunsekolloquium, Battelle Institut, Frankfurt, 1983. (7) Kurylo, M. J.; Knable, G. L. J . Phys. Chem. 1984, 88, 3305. (8) Olbregts, J.; Brasseur, G.; Arijs, E. J . Photochem. 1984, 24, 315.
0022-365418412088-6259$01.50/0
(9) Jourdain, J. L.; Le Bras, G.; Combourieu, J. J. Phys. Chem. 1981,85, 655. (10) Poulet, G.; Le Bras, G.; Combourieu, J. J. Chem. Phys. 1978,69,767. (11) Westengerg, A. A. Prog. React. Kinet. 1973, 7, 24. Slagle, I. R.; Gutman, D. J . Phys. Chem. 1983,87, 1812. (12) Park, J. Y.;
0 1984 American Chemical Society
6260 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
Poulet et al.
wq 478 K
[CH3 I
I
4
8
Figure 1. Reaction OH
+ CH$N
12
(1): least-squares plot of the apparent first-order rate constant vs. [CH3CNIoat room temperature. kl = (2.1 A 0.3) X cm3 molecule-' s-l. concentration measurement appears to be the main source of error in k2 determination, the C1 titration was made for each C12flow rate before and/or after each series of kinetic runs. CH3CN flowed into the reactor through a movable central tube after being purified and stored under similar conditions as for EPR experiments. Its concentration was monitored by mass spectrometry at its parent peak, m / e 41. NOCl or C2H3Bralso flowed through the central tube, in order to be able to titrate C1 atoms in different zones in the reactor. The gases used had the following purity: He, 99.9995%; Cl,, 99.9% min; NOCl, 99.2% min; C2H3Br, 99.5% min. CH3CN (99.7%) was further purified by vacuum distillation.
410 K
..
(1014cm-3)
N1,
5 3 295K
A
1
I
15 [Ci], (1014~n-3)
10
5
Figure 2. Reaction C1+ CH$N (2): least-squares plots of the apparent first-order rate constant vs. [CI],, in the range 295-723 K.
Results and Discussion
Reaction OH + C H 3 C N - Products ( I ) . The reaction OH + CH3CN was studied under pseudo-first-order conditions by
using a large excess of CH3CN over OH. The concentrations of OH and CH3CN were in the range (3-4) X 10" and 2.5 X 1014-1.36 X IOi5 ~ m - respectively. ~, The decay rate of OH radicals is given by the expression -(d In [OH]/dt) = kl[CH3CN], k,, where k, is the wall combination rate of OH radicals in the presence of CH3CN. The wall combination rate of OH was measured in the absence of CH3CN by moving the sliding injector, before and after the kinetics experiments on the OH CH3CN reaction, and the values obtained, kw(o),were in good agreement. However, some variability in kwco)was observed from one series of kinetic runs to another and k,!,) ranged from 2.6 to 10.6 s-l. Since this variation was not negligible compared to the OH decay rate in the presence of CH3CN, (- d In [OH]/dt) = 9.4-47.4 s-'), this decay rate was corrected for kw(,)measured during the same experiment. Then kl is given by the slope of the straight line -(d In [OH]/dt) - kwco)=fl[CH3CN],) (Figure 1). The least-squares analysis of the data led to the following value of k l :
+
+
kl = (2.1 f 0.3)
X
cm3 molecule-'
s-l
at 295 K
The error is two standard deviations. The intercept of the straight line is 0.22 f 3 s-', Le., near zero. This result indicates that k, = kwco);the wall combination rate of OH is the same in the presence and in the absence of CH3CN. That means that the method used to determine kl is correct and also that heterogeneous reactions of O H in the presence of CI13CN appears to be negligible at 295 K. This k l determination can be compared with existing values."' Except for the value of ref 4, which is about 2 times higher,13there is good agreement between our determination and that of the other (13) Measurements made at 393 K led to kl = (8.6 A 1) X
cm3
molecule-' s-', which is in agreement with the data of ref 4, but a factor of
2 higher than the value of ref 7. (14) Hirschfelder, J. 0.; Curtiss, C.F.; Bird, R.B. "Molecular Theory of Gases and Liquids"; Wiley: New York, 1967.
N
\
Y
\
C
, \
--34
I
f' 2
1
3
1 0 0 0 I T (K-') Figure 3. Reaction C1 CH&N (2); Arrhenius plot of kz values: ( 0 ) this work (f2o); (A) ref 8; t upper limit of ref 7 .
+
studies, which are (2.4 f 0.3) X at 7 torr,5 (1.8 f 0.1) X at 100-300 torr: and (1.94 f 0.37) X at 20-50 torr.7 Thus, our data obtained at 1.2 torr would indicate that reaction 1 is pressure independent, which confirms the combined data of ref 5 and 7, rather than those of ref 6, which showed a decrease of kl with decreasing pressure down to about 0.8 X at 7 torr. Our additional data showing the independence of k , with pressure confirm the assumption that reaction 1 proceeds via and H atom transfer: O H + CH3CN H20 CH2CN
-
+
Reaction C1-k CH3CN- Products ( 2 ) . Reaction 2 was studied under pseudo-first-order conditions with an excess of C1 atoms over CH,CN. The ratio of initial concentrations [Cl],/ [CH3CN], ranged from 10 to 100. k2 was obtained at each temperature from the slope of the straight line -(d/dt)(ln [CH,CN]) = f([Cl]O). The results are summarized in Table I, where k2 was corrected for axial diffusion. This correction was negligible in the experiments carried out at the two lowest temperatures and did not exceed 5% at 723 K. The least-squares straight lines -(d/dt)(ln [CH3CN]) = f([Cl],) obtained at 295, 356,410, 478, 583, and
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6261
Reactions of CH3CN with C1 and OH Radicals
TABLE I: Summary of Experimental Conditions and Results for the Kinetic Study of the Reaction CI
P,torr
u, cm s-'
T = 295 f 2 K, 0.47 1.71 1.I7 0.46 1.73 1.77 1.53 1.53 1.41 1.78 1.52 1.56 1.59 1.52 1.59 1.85
2094 610 560 2212 610 560 710 710 774 600 690 702 688 690 688 599
10-'4[Cl]o, molecules cm-3 k2 = (8.89 f 1.24) X molecule-) s-I 2.63 2.82 4.24 5.35 5.71 5.73 6.21 7.15 7.52 8.36 8.64 9.81 10.26 10.80 12.30 16.66
T = 356 f 2 K, k2 = (2.11 f 0.30)
X
k,', s-'
2.50 2.93 3.77 5.67 5.90 5.33 5.95 6.28 6.29 8.06 9.66 8.77 9.00 11.20 13.10 13.87 cm3
1.01 0.59 1.56 0.59 1.01 0.59 0.97 1.58 0.60 1.60 1.04 1.05 1.62 1.05 1.01 1.OS
1555 1549 2969 1235 1302 1235 1225 1533 1225 1537 1524 1224
T = 410 f 2 K, k2 = (4.95 molecule-' 1523 2766 99 1 2683 1532 2766 1550 988 2710 977 1506 1498 976 1508 1759 1484
2.02 6.69 7.98 9.20 9.47 9.90 11.27 11.77 16.28 17.90 20.40 20.85 f 0.50) X
6.0 19.3 17.5 19.6 19.5 20.8 29.4 28.7 30.6 42.2 44.2 47.7
0.66 1.02 0.98 1.30 1.03 2.05 0.66 1.05 0.99 2.06 1.06 1.oo 1.03
10-~4[CI]o, molecules k, = (10.08 i 1.04) X molecule-' s-1 1.91 2.03 2.10 2.94 2.98 3.57 5.44 5.75 5.84 5.99 6.62 8.43 11.60
k,',
s-l
cm3 21.6 21.7 20.3 31.6 28.4 29.3 48.3 54.0 69.7 55.5 65.3 90.1 114.8
0.63 0.63 0.92 0.63 0.60 0.64 0.65 0.65 0.61 0.65 0.94 1.19 0.65 1.20 0.93
1.07 0.70 1.03 1.07 0.99 0.71 1.07 0.93 0.94 0.95 1.09 0.73 0.95
T = 723 f 4 K, k2 = (7.25 f 0.50) X lo-" cm3 molecule-' s-] 3096 1.11 88.2 5207 1.56 126.7 3299 2.00 130.6 3117 2.26 160.8 3645 2.38 174.7 5218 2.93 226.2 3130 2.94 201.5 3907 3.46 257.6 3877 3.82 288.4 3826 3.96 282.7 3096 4.06 287.3 5144 4.09 288.8 3866 5.36 400.2
cm3 13.1 13.3 20.0 21.6 18.9 18.5 25.0 34.2 31.4 38.9 38.1 34.9 55.4 55.8 59.9 69.6
3187 1761 2316 1605 1755 1033 321 1 1738 2329 1035 1724 2330 2290
Products (2)"
T = 583 f 3 K, k2 = (2.98 f 0.30) X lo-" cm3 molecule-' s-I 4516 0.47 19.7 4546 1.27 54.8 3245 1.78 69.9 4568 2.26 65.2 3676 2.45 85.8 4541 2.83 99.5 4487 3.40 104.4 4504 3.80 116.3 3676 4.05 140.2 4527 4.19 125.8 3233 4.36 142.0 2434 4.55 157.0 4563 4.96 125.8 2425 5.07 170.9 3293 5.41 164.9
s-I 2.42 2.60 3.78 3.84 3.85 3.95 4.52 6.48 6.79 7.26 7.45 8.62 10.50 10.53 10.87 14.60
u, cm s-'
T = 478 f 3 K,
cm3
molecule-I s-' 0.95 0.97 0.46 1.08 1.04 1.08 1.10 1.oo 1.10 1.02 1.04 1.11
P,torr
-
+ CH,CN
+
a Errors in k2 are twice the standard deviation. k,' was corrected from the axial diffusion following k,' = kZmess (1 k,mcasD/v2)where kzmcasis the measured first-order rate constant, u the flow velocitv, and D the binary diffusion coefficient; D(CH3CN-He) was taken equal to the given value of D(Ar-He): I 4 D(Ar-He) = 0.108T'.5P' cm2 s-' (P in torr).
723 K are plotted in Figure 2. The Arrhenius plot of k2 is represented in Figure 3 . A linear dependence is observed in the higher temperature range whereas a curvature appears at the lower temperatures. Then, the data obtained can be given under the a t 295 K and k2 = following form: k2 = (8.89 f 1.24) X (3.46 f 0.70) X lo-" expl(-2785 f 115)lq in the range 478-723 K (errors are twice the standard deviation). Another expression, strictly empirical, k2 = 1.0 X 1O-l3(T/478),jcan reproduce all the experimental rate constants to within 10%. A qualitative study of the overall mechanism was also carried out by mass spectrometry. The different chlorosubstitutedspecies CH2C1CN,CHC12CN,and CC13CNwere observed at their parent peaks or at their fragment peaks. The CH2CN radical was also detected at its parent peak ( m l e 40), where the contribution of the fragment peak of CH3CN was decreased by using a low ionization energy (- 20 eV). Under these conditions an increase of the ratio of peak intensities ( m / e 4 0 ) / ( m / e41) was observed. The following mechanism can be proposed for the conditions of
our experiments in which C12 was present, due to the only partial dissociation of C12 in the microwave discharge: C1+ CH3CN CH2CN HCl
--
--+
Cl2
+ CHzCN
C1 + CHzClCN
+ CHClCN + CHClzCN C12 + CC12CN
C12 C1
+
+ C1 CHClCN + HC1 CHC1,CN + C1 CClZCN + HC1 CC1,CN + C1
CH2ClCN
--+
In our experiments, reaction of C1 atoms with CH,CN, CHClCN, and CCl,CN, which probably need a third body, were found to be negligible at the low pressures used compared to reactions of C12 molecules with these radicals. This has been established by observing that the introduction of additional C12 into the reactor, under conditions of moderate excess of C1 atoms
6262 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 over CH3CN, led to a consumption of this additional chlorine by the intermediate radicals and to an increase of the concentrations of the chlorosubstituted products. Furthermore, this addition of C12did not change the CH3CN decay rate, which agrees with the proposed secondary reactions whereby the C1 concentration is stationary. This also makes valid, a posteriori, the pseudofirst-ordei assumption in the measurements of k2,even with the lowest [Cl],/[CH,CN], ratios used. Our k2 determinations can be discussed by comparison with the two very recent results from ref 7 and 8. Olbregts et aL8 measured k2 at 370 and 413 K by a competitive method, using the reaction of C1 atoms with CHC13 as reference and analyzing the final products, CH2ClCN and C C 4 , by gas chromatography. These products resulted from reactions of C12 with CHzCN and CC13 initially produced in reaction 2 and in the reference reaction. Olbregts et al. obtained for k2 the values 2.2 X and 5.1 X at 370 and 413 K, respectively. Although these values are given without uncertainty range, they agree well with our deand 4.9 X at the same terminations, which are 2.55 X temperatures. At room temperature, another comparison can be made with the study of Kurylo and Knable,’ who determined for k2 an upper using the flash photolysis-resonance fluorescence limit of 2 X method. This discrepancy could be due to an underestimation of k2 in the study of Kurylo, but there is no apparent explanation for this in their experimental conditions. This discrepancy may also be due to an overestimation of our value of k2 at 295 K. This could not be due to secondary reactions or gas-phase reactions of CH3CN with impurities under the conditions used (excess of C1 atoms over CH,CN, high purity of C12,and He flowing through the discharge). A heterogeneous reaction between C1 and CH3CN at the wall of the reactor could yield an overestimation of k2. If CH3CN was partly adsorbed at the reactor wall, addition of C1 atoms into the reactor and reaction with adsorbed CH3CN would decrease the gas-phase concentration of CH3CN, if we assume that the equilibrium between gas-phase and adsorbed CH3CN was unchanged by addition of C1 atoms. The curvature of the Arrhenius plot could be explained by such a heterogeneous process, which would become negligible at the highest temperatures of this study. If we consider the good linearity observed for the Arrhenius plot in the range 478-723 K, the extrapolation at 298 K gives for instead of the experimental value of 8.9 k2 a value of 3.0 X X This extrapolated value is not very different from the upper limit of 2 X estimated by Kurylo. The occurrence of a heterogeneous reaction in our reactor between C1 atoms and CH3CN is possible since CH3CN is known to adsorb at silica surfaces, with formation of a hydrogen bond between the Si-OH group and the nitrogen atom of CH3CN.15 In order to reduce such effects, some measurements of k2 were carried out at room temperature in a quartz reactor coated with halocarbon wax (Halocarbon Products Corp. wax 12.00). A value was found for k2, which is the same as that of (9 f 1) X obtained without this coating. Therefore, if a wall reaction occurs, this reaction would have the same rate on the quartz and on the halocarbon wax coated wall. Besides, a wall contribution to the C1+ CH3CN gas-phase reaction may not be excluded in a recent discharge flow study16 where a rapid stoichiometric conversion of C1 to CH3CN was observed with initial CH3CN concentration of 5 X 1014~ m - ~In , this study, the reactor was made of Pyrex coated with phosphoric acid. Since the wurrence of a wall reaction has not been definitively proved, an alternative explanation of the discrepancy between our determination and the flash photolysis result’ would be that, a t room temperature, reaction 2 could Occur via the addition C1+ CH3CN
-+
CH3CNCl
The adduct would be very unstable and would decompose rapidly, leading to the equilibrium (15) Kiselev, A. V.; Lygin, V. I. “InfraredSpectra of Surface Compounds”; Wiley: New York, 1975; p 204. (16) Park, J. Y.; Gutman, D. J . Phys. Chem. 1983,87, 1844.
Poulet et al.
C1
+ CH3CN * CH3CNCl
And at the higher pressures of the flash photolysis study, the equilibrium would be reached more rapidly than at the low pressures of the discharge flow technique, and so no reaction would be observed in the flash photolysis experiments. A similar argument has been suggested to explain the discrepancy observed in rate constant measurements for the N H 2 + O2 reaction in a flow reactorI7 and by the flash photolysis methodI8. However, the occurrence of an addition step for reaction 2 remains speculative since no experimental evidence was found from massspectrometric analysis of the products. Specifically, no peak was observed at mass 76 corresponding to the adduct ion CH3CNCl+. In any case, the rates measured at room temperature are very low compared to those measured in the higher temperature range. Consequently, the possible contribution of the room-temperature process can be neglected at these higher temperatures, and the strictly linear Arrhenius plot observed leads to kinetic parameters which correspond to the gas-phase metathesis reaction. The reactivity observed between C1 and CH3CN is much lower than expected from comparison with similar reactions of C1 atoms with the methyl-containing molecules: CH4, CH,Cl, and CH3OH.19 The preexponential factor of the rate constants are similar but the activation energy of reaction 2 is noticeably higher. The activation energy of reaction 2 cannot be related to the C-H bond energy of CH3CN as it has been done for reactions of C1 and CH4, CH3Cl, and CH30H. Such a consideration would give for reaction 2 a near-zero activation energy as for the C1+ C H 3 0 H reaction, since the C-H bond energies are about the same in CH3CN and C H 3 0 H (94 and 93 kcal/mol, respectively). Other arguments such as the large dipole moment of the CH3CN molecule, coupled with the strong electron affinity of C1 atom, should be considered to try to explain the low reactivity between C1 and CH3CN. Atmospheric Application. These data also have applications in relation to the chemical behavior of CH3CN in the atmosphere. For the reaction of O H and CH3CN, the rate constant obtained contributes to establishing the data to be used in atmospheric modeling, especially in the upper stratosphere, where pressure and temperature are comparable to those considered in this study. It confirms that this reaction is not sufficiently fast to explain the discrepancy between ground and stratospheric concentrations of CH3CN.3 For the reaction of C1 with CH3CN, our data show that CH3CN does not constitute an additional sink for chlorine atoms. At 35-km altitude, for instance, the rate of C1 and CH3CN is times the rate of C1 CH4 if we take approximately 1.5 X k(C1 CH4) = 3.15 X at 236 KI9 and k2 from our expression, k2 = 3.46 X lo-” exp(-2785/T), and use typical values for [CH3CN] and [CH,] at 35 km.3320 Even if k2 is calculated from the extrapolated value of our low-temperature measurements k2 4 X lo-’$ at 236 K, the rate of C1 CH3CN is still 2 X time the rate of C1 + CH4. In addition, our data indicate that reaction 2 is a negligible atmospheric sink for CH3CN compared to the O H CH3CN reaction. For instance, at 35 !an, the rate ratio for reactions of CH$N with C1 and OH is approximately 6 X 10“ with kz = 3.46 X lo-’’ exp(-2785/T), and considering for k2 the extrapolated value from the low9X and 2 X temperature data. At 45 km, these ratios are 3 X respectively. Finally, the reaction of C1 with CH3CN is negligible in the earth’s atmosphere at the CH3CN concentrations recently measured.
+
+
+
+
Conclusion The present study provides additional kinetic data for the reactions of potential atmospheric interest between acetonitrile and C1 and O H radicals. For the O H + CH3CN reaction, the de(17) Hack, W.; Horie, 0.; Wagner, H. Gg. J . Phys. Chem. 1982,86,765. (18) Lesclaux, R.; Demissy, M. N o w . J. Chim. 1977, 1 , 443. (19) DeMore, W. B.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. JPL Pub. 1982, NO. 82-57. (20) Brasseur, G.; “Physique et Chimie de I’AtmosphEre Moyenne”; Masson: Paris, 1982.
J. Phys. Chem. 1984,88, 6263-6266
6263
be definitively explained. However, the rate parameters of this reaction were obtained from the strictly linear Arrhenius plot observed at the higher temperatures of this study.
termination of the rate constant, at pressure near 1 torr, indicates that this rate constant is pressure independent, which supports an H atom transfer mechanism and not an addition one. For the C1 CH,CN, the temperature dependence of the rate constant has been determined on a rather extended temperature range, showing an unexpected temperature dependence which could not
+
Registry No. CH,CN, 75-05-8; OH radical, 3352-57-6;CI2,7782-
50-5.
Representation of Multistage Mechanisms In Detailed Computer Modeling of Polymerlzatlon Kinetics M. Frenklach* Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803
and W. C. Gardiner, Jr. Department of Chemistry, University of Texas, Austin, Texas 78712 (Received: March 12, 1984)
A method for condensing the differential equations describing homogeneous polymer growth kinetics is described. It permits accounting for polymer mass growth in detailed kinetic modeling by adding a single set of kinetic equations for the elementary reactions augmenting polymer size. Flexibility for adjusting rates to change with concentration or time is retained. Growth
of nascent soot polymer is discussed as an example.
Introduction Modeling of complex homogeneous chemical processes by numerical integration of the kinetic equations for assumed reaction mechanisms has become a standard technique for gaining insight into the fluxes of chemical change and for deriving elementary reaction rate In its most fundamental form, such modeling requires one differential equation for each species concentration, each equation expressing a concentration derivative as a sum of mass-action terms for each of the elementary reactions producing or consuming that species. The number of species considered can be quite large if sophisticated numerical integration techniques are Nonetheless, in modeling polymerization kinetics15 it sooner or later becomes impractical to continue considering each stage of polymerization as a new species. We describe here a method of combining polymerization stages such that explicit account can be taken of all pathways for increasing the degree of polymerization. In place of the concentration growth of different size polymers, the total amount of polymer growth appears as the essential measure of reaction progress. (1) Symposium on Reaction Mechanisms, Models, and Computers, J . Phys. Chem. 81, 2309-2586 (1977). (2) W. C. Gardiner, Jr., J . Phys. Chem., 83, 37 (1979). (3) "Modeling of Chemical Reaction Systems", K. H. Ebert, P. Deuflhard, and W. Jager, Eds., Springer-Verlag,New York, 1981. (4) E. S . Oran and J. P. Boris, Prog. Energy Combust. Sei., 7, 1 (1981). (5) C. K. Westbrook and F. Dryer, Symp. (Int.) Combust., [Proc.],Z8th, 749 (1981). (6) F. Kaufman, Symp. (In?.) Combust., [Proc.],Z9th, 1 (1982). (7) K. H. Ebert, H. J. Ederer, and U. Stabel, Ber. Bumenges. Phys. Chem., 87, 1036 (1983). (8) M. Frenklach in "Combustion Chemistry", W. C. Gardiner, Jr., Ed., Springer-Verlag, New York, 1984, Chapter 7. (9) C. W. Gear, "Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hall, Englewood Cliffs, NJ, 1971. (10) A. C. Hindmarsh, 10th World IMACS Congress on Systems Simulation and Scientific Computation, Montreal, Canada, 1982; also Lawrence Livermore Laboratory Report UCRL-87465, 1982. (1 1) T. R. Young and J. P. Boris in ref 1, p 2424. (12) P. Deuflhard, G.Bader, and U. Nowak in ref 3, p 38. (13) G. Bader, U. Nowak, and P. Deuflhard, International Conference on Stiff Computation, Park City, Utah, 1982. (14) D. T. Pratt, Spring Technical Meeting of the Combustion Institute (Western States Section), Pasadena, CA, 1983. (15) W. H. Ray in ref 3, p 337.
0022-365418412088-6263$01.50/0
Analysis We denote a polymeric species as P,, where the first index indicates degree of polymerization and the second refers to the specific chemical form of the s p i e s . The degree of polymerization i could be the number of monomer units incorporated, or some linear function thereof, as may be appropriate for a specific model. The choice of defining i is arbitrary and has no effect upon the results given below. For completeness of the mathematical formalism it will be assumed that each species may be formed from nonpolymeric species or decompose to these species at rates rij in irreversible elementary reactions. The value of each rij is assumed to be recomputed from the prevailing species concentrations at each stage of the numerical integration. Let the number of different species at each stage of polymerization be n. Then the rate law for the P, takes the form
-d[Pijl - dt
or combining the summations
j'#j
Since in computer modeling it is usually convenient to compute reaction rates separately, our further development is therefore based upon the multiple summations of eq 1. We use the notation &#l. hereafter to denote summation over j ' = 1 to j' = n omitting j' = J . In these equations the coefficients xjjt contain as factors the rate coefficientscharacterizing the process of converting species Pij to species Pv,. Similarly, the yjy contain as factors the rate coefficients for the processes that increase the degree of polymerization by one. In addition, the x's and y's may (and presumably do) contain functions of the nonpolymeric species concentrations (see Discussion). These are assumed to remain the same for all i, however, thus requiring that the rates of all j j'conversions are independent of the size of the polymer molecules. The last j' terms for the two summations in eq 1 contain j ' - j and j
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0 1984 American Chemical Society
