J . Phys. Chem. 1991, 95, 3218-3224
3218
Reaction Rate Determinations of Vinyl Radical Reactions with Vinyl, Methyl, and Hydrogen Atoms A. Fahr,* A. Laufer; R. Klein, and W. Braun Chemical Kinetics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Received:September 4 , 1990)
Laser photolysis-kinetic spectroscopy, end-product analysis, and detailed modeling were used to investigate three reaction systems in detail. Included were vinyl-vinyl, vinyl-methyl, and vinyl-methyl-hydrogen atoms. Product ratios, as a function of the rate constants, could be approximated by using simple expressions. This greatly simplified the precise numerical modeling of these complex systems and also permitted a realistic error analysis. Reactions and rate constants (obtained at 25 OC, 100 Torr of He) in units of cm3 (molecule s)-I are summarized as follows: CH3 + CHI C2H6, (0.52 f 0.05) X C2H3 + C2H3 C4H6, (1.2 f 0.2) X C2H3 + C2H3 C2H2 + C2H4, (0.24 f 0.05) X CH3 + C2H3 C&, CH3 + C2H3 CHI + C2H2,(0.34 f 0.07) X C2H3+ H CzH4,(2.0 f 0.8) X (1.2 f 0.3) X The cross-combination rate constant obtained for vinyl-methyl is not twice the geometric mean of the vinyl-vinyl and methyl-methyl rate constants. This observation is explained on the basis that the vinyl-vinyl rate constant is faster than predicted by simple correlation arguments. The effect of bound low-lying triplet states of the product on the vinyl combination kinetics is discussed.
-
+
+
Introduction Central to understanding the chemistry of planetary atmospheres as well as combustion processes1is an accurate assessment of the kinetics of free-radical reactions. The small hydrocarbons through C2are especially important. In the systems of interest such radicals are produced by either the thermal or vacuum-ultraviolet photochemical dissociation of stable precursor compounds or through an appropriate chemical reaction such as addition of an H atom to a stable olefin. Here we focus on the vinyl radical because of its intrinsic interest and its possible role in planetary atmospheres and combustion chemistry. Very few of the spectral and chemical properties of vinyl radicals have been well characterized. Two electronic absorption systems have been observed, a weak system in the visible region2 and an intense absorption in the vacuum-ultraviolet regione3 Absolute rate constants as well as product yields for several reactions of the vinyl radical have been measured at room temperature. These HC1,5s6H, and 0 atoms,' and there include reactions with 02.s5 is an estimate for the vinyl-vinyl bromide reaction.s By use of the intense absorption of the vinyl radical in the vacuum ultraviolet region3 as a probe, the rate constant and combination/disproportionation ratio for the self-reaction have been recently determined? At elevated temperatures, in the region of combustion interest, reactions with C2H2,C2H4,and benzene, using the VLPP technique, were evaluated.I0 No direct (real time) rate measurements of vinyl reacting with other simple molecular radicals have been made, although several such reaction rates have been estimated.' The objective of this work is to determine the room temperature reaction kinetics of vinyl with methyl and vinyl with H atoms and to reinvestigate vinyl with vinyl. The strong absorption of 1,3-butadiene, the product of vinyl radical combination, in the spectral region above 200 nm can be used as a measure of the butadiene concentration and hence as a temporal monitor of vinyl. Measurements of end products such as ethylene, acetylene, and butadiene serve to define the overall chemistry. In the mixed vinyl-methyl system, direct absorption measurements of methyl radicals and of vinyl radicals indirectly by way of observations of the butadiene formed define the temporal profiles. A criterion for the success of the method is that the reaction sequence model should be consistent with the experimental measurements. Experimental Section The measurements were made using a laser photolysis-kinetic absorption spectroscopy apparatus. Features include the following. Author to whom correspondence should be addressed. 'Chemical Sciences Division, Office of Basic Energy Sciences, US.Department of Energy, Washington, DC 20545.
-
-
+
(1) A Lambda Physik Model EMG 201 MSC" excimer laser was used as the photolysis source. (2) A CW deuterium or Xe light source was used to provide near-continuum radiation for optical detection. The continuum radiation was made parallel through the photolysis cell and then focused onto the entrance slit of a 0.25-m Czerny-Turner vacuum-UV monochromator. The combination of the grating dispersion and slit width allowed measurements to be made at wavelengths shorter than 200 nm with a band-pass of 0.5 nm. The dispersed light was monitored by using one of several Hamamatsu solar blind photomultiplierdI and the signal digitized, collected, and analyzed by computer. (3) A self-enclosed gas circulating pump12 was used to flow the gas mixture through the reaction cell so that the cell contents are replaced several times each second. To minimize product photolysis, the laser pulse repetition rate was chosen not to exceed the sample replacement rate. (4) A total system volume of about 1000 times that of the photolysis cell was used. Because of the 1OOafold product dilution, product photolysis is unimportant even though the dissociation of the parent compound can be as high as 10% per pulse. Independently, 1,3-butadiene was photolyzed under conditions similar to those expected during the experiment. Less than 1% of the butadiene was photodissociated. Up to 100 laser pulses were averaged in any single kinetic determination. (5) Provision for sampling into an on-line chromatograph for product analysis was made. If necessary, the sample was concentrated through trapping in a liquid nitrogen cooled collection coil and the nonvolatile products were analyzed. To avoid the need for constant volume injections a nonreactive tracer gas was added in known amounts to the gas mixtures. In this way the tracer, relative to each product (normalized to the number of laser ( I ) Tsang, W.; Hampson, R.F. J. Phys. Chem. ReJ Daro 1986,15, 1087. (2) Hunziker, H.; Kneppe, H.; McLean, A. D.; Siegbahn, P.; Wendt, H. R. Con. J . Chem. 1983,61, 993. (3) Fahr, A.; Laufer, A. H. J. fhys. Chem. 1988,92, 7229. (4) Slagle, I. R.;Park, J. Y.;Heaven, M. C.; Gutman, D. J . Am. Chem. Soc. 1984-106, 4356. (5) Krueger, H.; Weitz, E. J. Chem. Phys. 1988,88, 1608. (6) Russell. J. J.; Senkan, S.M.;Seetula, J. A.; Gutman. E. J. Phvs. Chem. 1989,. 93, 5184. (7) Heinemann, P.; Hofmann-Sievert, R.; Hoyermann, K. Symp (fnr.) Combusr., [Proc.],21 1986. 865. (8) Kanamori, H.; Endo, Y.;Hirota, E.J. Chem. fhys. 1990, 92, 197. (9) Fahr, A.; Laufer, A. H. J. fhys. Chem. 1990, 94,726. (IO) Fahr,.A.; Stein, S. Symp. (fnr.) Combusr. [froc.],22, 1988, 1023. ( I I ) Certain commercial instruments and materials are identified in this paper to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by NIST,nor dots it imply that the instruments or materials identified are necessarily the beat available for this purpose. (12) Watson, J. S. Can. J . Techno/. 1956, 34, 343.
This article not subject to US.Copyright. Published 1991 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3219
Rates of Vinyl Radical Reactions 3mll
1
I1
n
I
E
c
a
CH3
+ CH3
YtkylbodW
C2H3
+ C2H3
kl
kIK
C2H6 C4H6
""
(1)
(IIC) (IIIC)
The simple relationship [C3H61m2 [C2H61m[C4H61m Figure 1. Absorption coefficients for divinylmercury and methyl iodide.
I
b
---(klIlc)2 kIkIIC
(1)
applies to steady-state (CW) experiments, but for pulsed experiments as described here the situation is more complex and can be addressed through a solution of the following:
A (3)
Figure 2. Absorption coefficients for butadiene and vinyl iodide.
pulses), provided absolute product yields. The active volume of the photolysis cell, constructed of Suprasil," was 3 cm3, The total cell length, 11 cm, was restricted by a mask to a photolysis length of about 4 cm. The path length in the direction of the photolyzing laser beam was about 1 cm. The laser energy deposition was determined by chemical actinometry using methyl radical formation and yield of ethane from the photolysis of methyl iodide at 248 nm and either azomethane or acetone at 193 nm. Fluences were 10 mJ/cm2 per pulse or less. Since the analysis of the experimental results requires absorption measurements of both precursors and products, the absorption spectra of all stable species were determined separatelyI3and are shown in Figures 1 and 2. The vinyl radical combination product, 1,3-butadiene, was monitored at 210 nm and the CH3 radical in its well-characterized B-X transition at 216 nm. In earlier work from this laborat~ry,".~ (C2H3),Hg and (C2H3),Sn were used as photolytic sources of vinyl radicals. In the present experiments, using different photolysis wavelengths, the most suitable source was (C2H3)2Hgphotolyzed at 248 nm. At 193 nm, the divinylmercury (DVM) produces significant quantities of hydrogen atoms that complicate the reaction chemistry. Several other sources investigated were divinyl ketone, divinyl sulfone, and vinyl iodide and bromide and were found to have lower quantum yields for vinyl radical production. The vinyl and methyl radical sources were obtained commercially and used without further purification. In a typical experiment appropriate parent molecules were mixed with exhelium and uniformly distributed throughout the system. The laser was preset to trigger a fixed number of shots.
Results and Analysis A. Methodology. End-product measurements on mixed radical systems, such as vinyl and methyl, can lead to the evaluation of rate constants for cross-radical reactions assuming the rate constants for the two like pairings are known and that final products occur only via radical-radical intera~ti0ns.I~The combination reactions of this mixed system are given by (13) Klein, R.;Braun, W.;Fahr, A.; Mele, A.; Okabe., H.J . Res. Nut/. Imt. Stand. Tech. 1990, 95. 331. (14) An additional proviso is that vinyl and methyl radicals are not reformed through other reactions.
An exact analytical solution is not feasible. However, if the concentrations of the radicals CH3 and C2H3 are approximated by an exponential decay, the approximate relationship is obtained [C3H61m2 [c2H61*[c4H61m
N
(2k111c)2
(k1 + klic)'
(7)
The numerical comparison of this simple expression with that derived from the ACUCHEMI~program, which solves eq 2-6 numerically, shows that eq 7 is quite adequate for the range of values of kI, kllc, and klIIcand concentrations encountered in this work. The ability of either eq 1 or 7 to describe adequately the numerical solutions to the differential eqs 2-7 is examined in more detail in the Appendix. B. Photolysis of CH31at 248 nm, the Methyl-Methyl Reaction. Methyl iodide was photolyzed at 248 nm and the temporal history of CH3 was followed through measurement of its absorption at 216.4 nm. If the rate constant measured for CH3 + CH3 differed from the accepted value it could indicate the presence of interfering reactions, such as methyl with I or H atoms. Since the end product CH4, determined chromatographically, was found to be very small compared with the only significant product, C2H6, it may be concluded that H atoms are not important in this system. Figure 3 shows the CH3 absorption signal decay in the photolysis of mixtures containing 2 Torr of CH31 in 100 Torr of He buffer gas. The initial CH3 concentration, [CH,],, was obtained from the CH3 absorption signal immediately following the laser pulse by using an absorption coefficient for methyl of loo0 (cm atm)-'. Azomethane and acetone photolysis at 193 nm, with optical CH3 detection and chromatographic analysis of ethane, leads to an absorption coefficient of lo00 (cm atm)-' for CH3, in accord with previously reported values.16J7 However, the initial methyl radical absorption signal is low because CHI radicals are formed vibrationally e x ~ i t e d ~and ~ , ' ~absorb very weakly at 216.4 nm. (15) Braun, W.;Hcrron, J. T.; Kahaner, D. K. Int. J . Chem. Kinet. 1988, 20, 51. (16) Macpherson, M.T.; Pilling, M. J.; Smith, M.J. C. J . Phys. Chem. 1985, 89, 2268. (17) Arthur, N. L. J . Chem. Soc., Faraday Tram. 2 1986,82. 331. (18) Callear, A. B.; Van Den Bergh, H. E. Chem. Phys. Lcrr. 1970,5,23.
3220
The Journal of Physical Chemistry, Vol. 95, No. 8, I991
Fahr et al.
i a
z 4
I
0 I
0
20
Time,
m.
80
100
Figure 3. Temporal absorption obtained at 216.4 nm for CH3 radicals (248-nm photolysis of 2.0 Torr of CHJ in 100 Torr of He). Solid line modeled by using parameters in Tables 111 and IV.
Therefore, the correct [CH,], was obtained by extrapolating the methyl absorption to t = 0. The best fit to the data is shown as the solid curve obtained by modeling
(19) Baggott, J. E.; Brouard, M.; Coles, M.A.; Davis, A.; Lightfoot, P. D.; Macpherson, M. T.; Pilling. M.J. J . Phys. Chcm. 1987, 91, 317. (20) Slagle. 1. R.;Gutman, D.; Davies, J. W.; Pilling, M.J. J. Phys. Chem. 1988, 92, 2455. (21) Wagner, A. F.; Wardlaw, D. M. J . Phys. Chem. 1988, 92, 2462. (22) Braun, W.; Wallington, T.J.: CvetanoviE, R. J. J. Phorochem. Phorophys. 1988, 42, 207.
me.
80
100
Figure 4. Temporal absorption obtained at 210.0 nm for C,Hs ,(from 248-nm photolysis of 500 mTorr of DVM in 100 Torr of He). Solid line modeled by using parameters in Tables 111 and IV.
TABLE I: Photolysis of DVM at 248 nm at Variable Laser Intensity'
DVW
mTorr 600 500
500
Reaction IV contributes little to the methyl radical decay but including i t in the model improves the fit at longer times. The value for klv is not known; the simple model gives an approximate value of 8.0 X cm3 (molecule s)-I. The effect of diffusion of methyl radicals out of the detection zone was calculated and found to be negligible under our experimental conditions. The rate constant obtained from reaction I is 5.2 X 1O-Il cm3 (molecule s)-l at 100 Torr of helium. This value is in good agreement with data of previous work16-i7*M-21 obtained at lower helium pressures taking account of the pressure falloff. For reference, it can be compared directly with the value kl = 5.7 X lo-" cm3 (molecule s)-I obtained by using argon as the bath gas at 100 Torr.I9 The photodecomposition at 193 nm of a number of CH3 precursor sources, azomethane, acetone, and trimethylarsenic, yielded virtually identical results. Noticeable in Figure 3, and in some subsequent figures, are modulations in the absorption data caused by small pressure oscillations. These are not random but are due to slight thermal heating, with concomitant propagation of pressure waves a t the medium sound velocity. These have been identified and explained before.22 The interpretation of the present data is not affected by the modulation. C. Photolysis of DVM at 248 nm, Vinyl-Vinyl Reaction. Mixtures of DVM in helium were photolyzed at 248 nm (KrF laser line) and the time history of butadiene buildup was monitored a t various wavelengths above 200 nm where the absorption is strong (see Figure 2). A typical display is shown in Figure 4 and values for [C4H6]- were obtained. The final yield of butadiene from the optical measurement was in accord with the value obtained from chromatography. The only reactions involving vinyl are assumed to be combination and disproportionation:
Time,
20
1000 500 500 1000
C2H3, mTorr
kil, cm3 molecule s-I 1.3 x 10-'0 1.3 x 10-'0
8.5 31 17 31 15.5 7.8 31
av
1.5 1.2 1.2 1.4 1.1 (1.3
X
x 10-'0 x 10-10 X
x 10-10
A, nm
laser pulses
210.0 216.4 216.4 215.0 215.0 2 10.0 215.0
75 100 50 50 50 50 25
f 0.14) X 10-1°
'The rate constants for all vinyl radical reactions are obtained from the temporal history of butadiene absorption at several wavelengths. The ratio k]ID/kl]C was previously found9 to be 0.21. This value is used to calculate the initial vinyl radical concentration, [C3H3],, from the experimental values for [C4H6], by
The data of Figure 4 were modeled with the ACUCHEM program by using the sequence of reactions IIC and IID and [C2H3], = 17 mTorr obtained from eq 8, with k I l D / k I ] c = 0.21. The best fit was obtained with kIIc = 1.2 X lo-*, cm3 (molecule s)-I. In a similar way, the rate constants klfD+ kllC = kII(Table I) were obtained under different conditions of initial vinyl and DVM concentrations. It is shown in Table I that, if the laser intensity and the pressure of DVM are varied and the initial concentration of vinyl is kept approximately constant, the measured rate constant for vinyl radical decay does not vary. This shows that pseudo first-order reactions such as C2H3 + (C2H3)2Hg
kv
+
products
(VI
are not occurring. D. Photolysis of Mixtures of CH31and DVM at 248 nm. Product measurements from the mixed system (CH31and DVM) are given in Table 11. Ethylene is not included because it shows significant scatter. Mixtures containing DVM show slow steady decomposition of DVM with evolution of ethylene. The "dark" reaction results from the surface decomposition of DVM, strongly dependent on the presence of metals, aluminum in particular. In an all-aluminum cell a steady but rapid loss of DVM occurs with proportional evolution of ethylene. In an all-glass system the dark reaction is slow and photolysis of DVM mixtures after a short residence time in the cell results in the production of ethylene comparable to acetylene. After cessation of the photolysis, ethylene increases steadily relative to acetylene. It is emphasized that the products listed in Table I1 are not formed in the dark reaction. Acetylene, a major product, is formed mainly by direct photolysis of DVM, but also in part from the disproportionation
The Journal of Physical Chemistry, Vol. 95, NO. 8, 1991 3221
Rates of Vinyl Radical Reactions
TABLE 11: End-Product Measurements of the Methyl and Vinyl Radical System: 248-nm Photolysis of DVM reactants. mTorr Droducts. mTorr 2000 2000 800 800 800 1000 1000 1000 2000
400 400 150 150 150 125 125 250 400
4.87 5.01 2.47 1.89 1.92 1.29 2.57 3.49 7.17
1.1
0.3 0.7 2.0 I .5
6.20 6.24 4.45 3.65 3.71 3.20 4.75 8.64 9.35
4.03 3.99 1.92 2.42 1.68 1.18 1.85 7.2 5.70
1.37 1.23 0.44 0.66 0.65 0.21 0.43 3.2 2.00
+ CHJ svstem constantsa 1.92 2.07 1.89 2.43 1.21 2.09 1.66 1.87 1.74
3.76
3.85 2.61 3.60 3.80 3.5 & 0.6
av 1.88 & 0.4 Dimensionless. TABLE III: Reactions and Rate Constants from Modeling the CHI and CzHl Systems rate const, reactions cm3 (molecule s)-' CH, + CHI C2H6 ki = 0.52 X 1O-Io C2H3 + C2H3 C4H6 kjjc = 1.2 x 10-10 kiiD = 0.24 X C2H3 + C2H3 4 C2H2 + C2H4 CH, C2H3 C3H6 KIllC = 1.2 x 10-'0 CH, + C2H3 CH4 + C2H2 k i i l D = 0.34 X klv = 0.08 X CH3 + I CHiI C2H3+ H C;H4 C2H3 + H C2H2 + H2 CHI CH, H ... CH;N2CHI + H 'LCHI + N 2 + CHI k I x = 3.40 X
-
4
+
--
4
+
+
4
From ref 24.
From ref 19.
I
80
0
reaction of vinyl. The direct photolysis can take place by way of
+
(C2H3)2Hg2 C2H2 C2H4 + Hg
(VI)
Methane can be formed in the mixed system via H atom reactions with methyl radicals. Hydrogen atom reactions are absent in the 248 nm photolysis of DVM and CH31 mixtures, as will be shown, and hence CH4 monitors only the disproportionation reaction of methyl and vinyl CH3 CH3
- +
+ C2H3
+ C2H3
&IUD
kllK
C3H6
CH4
CZH,
Tlm,pec.
240
320
Figure 5. Temporal absorption at 216.4 nm for CH3 plus C4H6 (248-nm photolysis of a mixture of 2.0 Torr of CHJ, 500 mTorr of DVM in 100 Torr of He). Solid line modeled by using parameters in Tables 111 and IV. 10r
(IIIC) (IIID)
The ratio of combination to disproportionation, kIIIC/kIIIl)r obtained from the C3H6/CH4ratio is 3.5 (Table 11). The value of [C3H6]m2/[C2H6]m[C4H6]m is found to be a constant, independent of the CH,I/DVM ratio. As noted, the rate constant for the cross-radical reaction, kIIIc,can be calculated from eq 7, and kIllDcan be derived from the measured klIIc/kIIID ratio. Values of 1.2 X and 3.4 X IO-" cm3 (molecule s)-I were obtained for klllc and kIIID,respectively. It is useful to compare observations on the photolysis of the mixed system DVM-CH31 with those obtained from the separate systems at the same partial pressures of DVM and CH31. Results on the single-component system are shown in Figures 3 and 4. Figure 5 shows the absorption at 216.4 nm from a mixed system in which both CH3 and butadiene contribute. To monitor butadiene without interference from methyl, the absorption at 210 nm is used (Figure 6). Thus both [CH,], and [C4H6], concentrations
0
10
Time, psec.
40
50
Figure 6. Temporal absorption at 210.0 nm for C4H6 from the 248-nm photolysis of the mixture of Figure 5. Solid line modeled by using parameters in Tables I11 and IV.
can be evaluated. The initial concentration of methyl is found to be the same whether it is generated in the mixed, Figure 5 , or in the separate CH31system, Figure 3. The calculation of [C2H310 follows from [ C Z H ~ I=O 2[C4HaIm
+ [C3H6]m + [CHJm
TABLE I V Comparison of Major Products in Mixed CH3 and CzH3 Systems Observed Experimentally and Obtained from Modeling concentration, mTorr [CHilo [ C ~ H ~ I O[HI0 [ C h I [c2H6l[ C I H ~ I - [C4H61reactions model 27.0 17.0 0.0 2.1 8.8 7.3 3.2 I, IIC, IID, IIlC, HID ndc nd 0.0 2.0 8.6 7.2 3.2 expt (DVM + CHII)O model 153.0 11.0 12.0 13.0 69.5 7.1 0.36 I, IIC, IID, IIIC, IIID, VII, VIII, IX expt (VI + A Z M ) ~ nd nd nd 12.0 69.5 6.7 0.35 "DVM, 250 mTorr; CHJ, 1000 mTorr. bVI, 200 mTorr; AzM = azomethane, 500 mTorr. CNotdetermined.
(9)
3222 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 TABLE V End-Product Measurements of the Methyl and Vinyl Radical System: 193-nm Photolysis of Vinyl Iodide + Azomethane
500
0.0 0.0 210 500 200 500 200 550 200 550 200
4.9 0.0 19.0 17.0 12.6 12.0
35.5
0.0
92.0 0.0
38.3 36.0 22.0
91.2
21.7
94.8 71.8 69.5
0.0 0.0 9.55 9.42 6.63
0.0
6.67
0.35
4.6 0.54
Fahr et al. lor
1.78 1.71 1.80
0.57 0.34
1.83 av 1.78 i 0.1
a Dimensionless.
and was found to be independent of the presence of CH31. The rate constants derived are shown in Table 111. The sensitivity of the model to changes of the cross-radical rate constants, kIllc + kIIID= kill, was assessed by increasing the values given in Table I11 by 17% and 33%. The two dashed end points in Figure 5 represent these increases and show poorer tits to the experimental data. For clarity, intermediate points were not plotted. End products for the mixed systems were modeled by using ACUCHEM and compared with the experimental values shown in Table IV. The agreement is good and corroborates previous conclusions that all of the radicals in the mixed system have been accounted for and that their reactions are in accord with the proposed mechanism. E. Photolysis of Azomethane and Vinyl Iodide at 193 nm. From the reactions in a methyl-vinyl mixture (from a CH3I-(C2H3)2Hg Source) the ratio [C3H6]’/([c&] [C&]) was found to be =2. This ratio can be affected by extraneous reactions that might produce propylene, ethane, or butadiene. To confirm the results an azomethane-vinyl iodide system was used as the source for methyl and vinyl. In addition to vinyl, vinyl iodide produces acetylene, HI, iodine, and hydrogen atoms. The measured products23in the pure and mixed systems are listed in Table V. The value of [C3H6]2/([C2H6][C4H6])(Table V) is approximately 2, the same as from (C2H3)*Hg-CH31. Azomethane and vinyl iodide were individually photolyzed at 193 nm and the time history of CH3 was followed optically at 216.4 nm. The rate constant for methyl recombination was found to be in accord with previous measurements. The methane was found to be about 5% of C2H6, indicating that, in the azomethane photolysis, there is about 5% production of hydrogen atoms. This level does not significantly affect the methyl radical decay rate. Methane production by the abstraction of an H atom from parent is considered to be negligible since it is a high activation energy process. Figure 7 shows the data for the temporal history of butadiene obtained from the 193-nm photolysis of vinyl iodide. Analysis of the data results in a vinyl decay which is a factor of 1.8 times faster than that obtained in the DVM system. This is due to the reaction of vinyl with hydrogen atoms (present in this system) according to C2H3 + H C2H3 + H
-% ~
kWlD __+
2
C2H2 + H2
~
4
(VIIC) (VIID)
Reaction VIID is the dominant reaction channel at very low pressure^.^ A final butadiene pressure of 2.8 mTorr was obtained from the data in Figure 7. The solid curve was modeled by using kIIc = 1.2 X k1ID = 0.24 x lo-’’, and + kvIiD) = kvlr = 2.0 X cm3 (molecule s)-I. This produces the best fit when [HI, (23) Ethylene is not listed in Table IV. It is small in the mixed radical experiment, but a significant product in the photolysis of pure vinyl iodide where it increases relative to acetylene with increasing number of laser pulses. Modeling shows that not all of the hydrogen atoms react with vinyl in this system. The ‘left-over” H atoms can react with acetylene, the major primary product, and form ethylene.
Time, psec.
10
0
40
50
Figure 7. Temporal absorption at 210 nm for C4H6from 193-nm photolysis of 200 mTorr of CzHJ in 100 Torr of He. Solid line modeled assuming [HIo = [C2H310= 15.6 mTorr, and kvlr = 2.0 X cm3 (molecule s)-I.
is set equal to [C2H3], a condition dictated by modeling the mixed system (see below). The value for the rate constant for reaction VI1 may be compared with the previously measured value7of kvrrD = 0.5 X 1O-Io cm3 (molecule s)-I, at low pressure (mTorr) where reaction VIIC would be negligible. The photolysis at 193 nm of the mixed system, vinyl iodide and azomethane, was modeled and a comparison with experimental results is shown in Table IV. The reaction sequences and rate constants (Table 111) used were the same as those for the CHJ-DVM system. Reactions VI1 and the two additional reactions were also included CH3 + H
+
kWll
CH4
CH3N2CH3 H -% CH,
+ N2 + CH3
(VIII)
(IX)
cm3 (molecule s)-I and using the valuez4 of kVIIl= 6.4 X the valueIg of k I x = 3.4 X cm3 (molecule s)-I. The initial concentrations [CH,],, [C2H310,and [HIo used in modeling were obtained from the end products, e.g., [CH310 = [CH,], 2[C2H6], [C3H6],. Slight adjustment to [HIo and [C2H3IOwas made to achieve the best fit to the final product distribution (Table IV). This is required because some H atoms do not react entirely with the other radicals present in the system. Also, some vinyl radicals react with hydrogen atoms, and hence butadiene and propylene are not an exclusive measure of the initial vinyl concentration. However, this is a small perturbation. From these determinations, the photolysis of vinyl iodide at 193 nm yields 51% acetylene (and HI), 25.5% vinyl radicals, and 23.5% hydrogen atoms. The ratio [HIO/[C2H3], so obtained was used in the modeling of reaction VI1 (described above). Other experiments were performed using the 193-nm photolysis of DVM and vinyl bromide and again evidence was found for large amounts of H atom production. F. Evaluation of Rate Constant Uncertainties. The value for the rate constant for the combination plus disproportionation of vinyl radicals is klI = ( 1.3 f 0.14) X 1@lo cm3 (molecule s)-I from Table I, where the standard deviation is obtained from repetitive runs. However, even at 248 nm, radicals other than vinyl, mainly H atoms, may be present to a small extent. Based upon endproduct measurements, determinations of [C2H3]o agree to better than 10% in both the pure and the mixed systems. Therefore, hydrogen (and other radicals) can be no more than 10% of the initial vinyl concentration. The appropriate correction for the measured rate constants, k ~ lis, a decrease by as much as 20%. This represents a potential “systematic” error and hence kIIcan be in the range between 1.0 and 1.4 (X1O-Io) cm3 (molecule s)-I. In the mixed system of vinyl-methyl the error in the crosscombination rate constant, k~llc,is calculated from the propagation
+
+
(24) Brouard, M.; Macpherson, M. T.; Pilling, M. J. J . Phys. Chcm. 1989,
93, 4047.
The Journal of Physical Chemistry, Vola95, No. 8, 1991 3223
Rates of Vinyl Radical Reactions
of errors applied to eq 7 and kllIc = (1.2 f 0.24) (molecule s)-I is obtained.
X
cm3
An approximate propagation of errors formula applicable to the vinyl-H atom system (modeled in Figure 7) is given by25 [.(kVll)12
--
[kV11I2 b(4/2)I2 [u(C2H3)0l2 [.(klI)l2 [.(.)I2 9+9 -+,4+ (10) [tl,212 [c2H310z [knl [.I2 In this expression u represents one standard deviation, tl12 is the time when [C4H6]= [C4H,],/2 and represents the precision with which the model corresponds to the experimental results. The estimate for ~ ( t ~ / ~ =) 0.1. / t ~ In/ ~eq 10 a is the ratio [HIo/ [C2H310,with u ( a ) / a = 0.15, U ( [ C ~ H ~ ] ~ ) / [ C = ~0.07, H ~and ]~ u(kll)/kll = 0.1. These values lead to u(kVll)/kVII= 0.40.
Discussion The rate constant for vinyl combination, kllc = (1.2 f 0.2) X cm3 (molecule s)-l agrees with the earlier result9 kllc = (0.85 f 0.25) X cm3 (molecule s)-l from the broad-band vacuum-UV flash photolysis of DVM. There the wavelengths for dissociation were maximized in the 165-nm region and involved only single photon absorption, and dissociation occurred in different electronic bands than in the present work. The good agreement with the present experiments suggests that multiple photon dissociation is not occurring. Further, radicals produced in both experiments are either electronically and/or vibrationally excited in the same way or, more likely, are produced electronically and vibrationally cold. The ratio [C3H6I2/([C&] [C&]) represented by (k111~)~/ (klkllc) was found to be =2. If klllc were twice the geometric mean of kl and kllc, as has been found for most of the crosscombination rate constants investigated,2629a value of 4 would be expected. It is useful to compare the rate constants for methyl-methyl, methyl-vinyl, and vinyl-vinyl with collision theory. The methyl-methyl rate constant represents one reaction per four collisions, and the collision efficiency for methyl-vinyl is also one in four. For vinyl-vinyl it is about one reaction in two collisions. A value of one in four is usually explained on the basis that a collision between two doublet species leads to three dissociative triplet states and one bound singlet state. This may not be the case for the vinyl-vinyl reaction because of the presence of accessible triplet product states. Using standard heats of formation30 we find the combination reaction of two doublet vinyl radicals to be exothermic by 112 kcal/mol. At an energy less than the reaction exothermicity there is a low-lying triplet state of 1,3-butadiene,the 3Bluat 3.2 eV (73.8 kcal/mol) above the ground state.” The presence of the low-lying bound triplet state is energetically and spin accessible through the reaction of two doublets. Therefore, the vinyl combination reaction may be significantly different from those of the alkyl radicals where the lowest lying electronically excited states of the alkane product are bound singlets and are not energetically accessible. If the butadiene product is formed on the bound triplet (25) By assuming that [HI is proportional to [C,H,] an analytical expression can be derived for the time-dependent vinyl radical decay. Compared with the result from exact numerical modeling, it is good to 15% in evaluating kVIand thus is adequate for use in error analysis. (26) Kerr, J. A.; Trotman-Dickenson, A. F. In Progress in Reaction Kinetics; Porter, G.,Stevens, B., Eds.; Pergamon: New York, New York, 1961; Vol. I , p 107. (27) Gibian, M. J.; Corley, R. C. Chem. Rev. 1973, 73, 441. (28) Terry, J. 0.;Futrell, J. H. Can. J. Chem. 1967, 45, 2327. (29) Garland, L. J.: Bayes, K. E. J . Phys. Chem. 1990, 94, 4941. (30) AHp29~used (in units of kcal/mol) are CH, 33.2, C2H3= 69.0, C,H2 = 54.2, and C2H, = 12.5. obtained from: Wagman, D. D.: Evans, W. H.; Parker, V. B.; Halow, 1.; Bailey, S.M.; Schumm, R. H. Natl. Bur. Stand., NBS Tech. Note 270-3; 1,3-butadiene = 26.33, 1,5-hexadiene = 20.0 from: Stull. D. R.;Westrum, Jr., E.F.; Sinke, G. C. The Chemical Thermodynamics of Orgunic Compounds; Wiley: New York. 1960; allyl = 40.0, C,H6 = 4.8 from: Tsang, W. Chemical Kinetic Data Base for Combustion Chemistry V-Propene; J . Phys. Chem. Ref.Data, in press. (31) Mosher, 0. A.; Flicker, W. M.; Kuppermann, A. Chem. Phys. Lett. 1973, 19, 332.
-
1 1
1 1
1 1
2 4
1 1
4.00 16.0
4.00 16.0
4.00 16.0
1 1 1
1 2 4
1 1 1
1 1 1
2 2 2
0.47 0.43 0.37
0.44 0.44 0.44
0.50
2 4
1 1
1 1
1 1
2 2
0.50 0.50
0.44 0.44
0.50 0.50
1
1 2 4
1 1 1
2 2 2
2 2 2
1.84 1.73 1.60
1.78 1.78 1.78
2.00 2.00 2.00
2 4 20
1
1 1
1 1 1
2 2 2
2 2 2
1.92 1.96 2.00
1.78 1.78 1.78
2.00 2.00 2.00
1
1 1
1 2 4
1 1 1
4 4 4
2 2 2
7.00 7.54 7.86
7.10 7.10
7.10
8.00 8.00 8.00
2 4
1 1
1 1
4 4
2 2
6.52 6.26
7.10 7.10
8.00
1 1
0.50 0.50
8.00
surface then spin-induced quenching to the ground singlet by collision in a time short compared to possible unimolecular decay might be expected. Reaction IIIC, the combination of CH3 with C2H3, may be similar in that its exothermicity (97.3 kcal/mol) could provide the necessary energy to reach the bound low-lying T1(3A) of C3H6, (97.5 k c a l / m ~ l ~ ~ ) . Alternatively, the slower combination reaction of allyl radicals which produce 1S-hexadiene (6.95 X lo-’* cm3 (molecule s)-I) is exothermic by about 60 kcal/m01.~~The energy of the lowest triplet of 1,s-hexadiene is not known. Although there is some interaction between the two nonconjugated double bonds,34the relative position of the T1 is not expected to be shifted significantly. Therefore, 1,5-hexadiene is considered as a substituted ethylene for which the energetics of a series of triplets has been rep~rted.’~ The suggestion of Ni et al. that the triplet resembles a 1,2 biradial predicts that the relaxed triplet is about 65 kcal/mol above the ground state in agreement with the triplet energy levels of other simple olefins. However, the lowest triplet of 1,5-hexadiene is twisted while allyl radicals are planar. The lowest lying planar triplet will be still higher in energy and an additional several kcal/mol is necessary to provide for the twisting motion required to produce the lowest triplet 1,S-he~adiene.’~This suggests that the allyl combination reaction takes place only on an excited singlet surface. Vinyl combination reactions, capable of accessing both singlet and triplet surfaces, will be faster than combination reactions which take place only on a single potential surface. Acknowledgment. We acknowledge the financial support of the Planetary Atmospheres Program of NASA and the Army Research Office under Grant No. MIPR 119-89. Conversations with R. Caldwell (University of Texas, Dallas) were most helpful in consideration of the thermochemical and spectroscopic aspects of this work.
Appendix Equation 1 applies to steady-state experiments in which the two radical species CH3 and C2H3 are continuously injected into the reacting system. In the present experiments these species are introduced at t = 0 in a single pulse. Only relative concentrations and rate constants need be considered. Table V I represents a (32) Johnson, K. E.; Johnston, D. B.; Lipky, S . J . Chem. Phys. 1979,70, 3844. (33) Tullcch, J. M.; MacPherson, M. T.; Morgan, C. A.; filling, M. J. J. Phys. Chem. 1982,86, 3812. (34) Robin, M. B. Higher Excited States ojPolyatomic Molecules; Academic Press: New York, 1975; Vol. 2. (35) Ni, T.; Caldwell, R.A.; Melton, L. A. J . Am. Chem. Soc. 1989,111, 457. (36) Caldwell, R. A. Private communication.
J. Phys. Chem. 1991,95, 3224-3229
3224
"matrix" that includes relative concentrations of [CHJO and [C2H310and kl, kllc, and klllc covering a reasonable (though not extensive) range of values normally encountered in such experiments. The quantity R = [C3H6]m2/( [C2H6],[C,H6],) is usually taken to be a "system constant". In Table VI this quantity is calculated by using the ACUCHEM program and it is compared with the approximations, eq 1 and 7 in the text. It can be seen that, if k l / k l l c = 1, the pulsed system behaves as though it were in a quasi-steady state. For other ratios the above product ratios vary depending upon the relative rate constants and upon the initial concentration ratios. For the present experiments where kl:kll&lc = 1:2:2 the ratio R is approximately constant (within
experimental error) and either eq 1 or 7 represents a reasonable approximation. The matrix shown in Table VI shows the limitations of taking R as a constant and the accuracy of using either eq 1 or 7. In the final analysis, numerical integrations should be used to establish best fits to the real time data and the product ratios. Taking R to be constant and employing either eq 1 or 7 as an approximation simply serves to minimize the number of iterations when fitting many runs under different initial conditions. Similar conclusions were drawn p r e v i o ~ s l y . ~ ~ Registry No. CH3, 2229-07-4; C2H3. 2669-89-8; H, 12385-13-6.
Spatlotemporal Temperature Patterns on an Electrlcally Heated Catalytic Ribbon Ceorgios Philippou, Fred Schultz, and Dan Luss* Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792 (Received: September 21, 1990)
Oscillatory and chaotic variations in the overall reaction rate were observed during the oxidation of propylene in air on a thin platinum ribbon, the average temperature (resistance) of which was kept at a preset value via electrical heating. A thermal image showed that back and forth movement of a high-temperature wave on the ribbon and the dynamic change in the length and temperature of the ignited zone were the cause of the variation in the overall reaction rate. The overall reaction rate in the chaotic region oscillates at a much higher frequency than the local temperature. The corresponding power spectrum of the reaction rate decays exponentially, while that of the local temperature decays as a power law.
Introduction Many chemical and electrochemical reacting systems exhibit periodic, quasiperiodic, and chaotic behavior.'" The discovery of the Belousov-Zhabotinski reaction6generated significant interest in spatial and spatiotemporal patterns, and waves in chemically reacting homogeneous systems. Theoretical studies7-I0 predict that propagating waves and dissipative structures exist also on heterogeneous catalytic surfaces. Experimental studies' revealed spatiotemporal temperature patterns on Pt and Ni surfaces on which catalytic oxidation reactions were carried out. As yet there exist no understanding of the cause of these patterns, the conditions and reactions for which they occur, and their impact. This work is an experimental study of the oscillatory and chaotic behavior of an electrically heated catalytic Pt ribbon on which the oxidation of propylene in air was carried out in order to characterize the local temperature oscillations and the overall reaction rate, and the relation between them.
Kodak IRTRAN 2 infrared transparent window in the reactor wall. The infrared image was magnified by a telescopic lens which allowed viewing of 1 cm segment of the ribbon. The imager measures 25 times per second the infrared radiation emitted from a two-dimensional grid of 64 X 128 points. The ribbon images were stored on a computer at the rate of 25 images/s when only 8 center lines of each image of the ribbon were recorded and up to 12.5 images/s when all grid points were recorded. The spatial resolution of the thermal imager was 0.1mm and the temperature resolution was between 1 and 2 OC depending on the temperature and thermal range setting. The infrared camera was mounted on a motorized table and driven parallel to the ribbon. The thermal imager was used to carry out two types of measurements: (a) Temperature profiles of the ribbon were obtained by juxtaposing a series of consecutive infrared images, recorded as the camera was driven parallel to the platinum ribbon. (b) Local temperature images of 1 cm segment of the ribbon were recorded
Experimentnl System
The reaction was carried out on a 14.7 cm long, 0.05 cm wide by 0.0025 cm thick pure platinum ribbon (Johnson Mathey Inc.) placed in a rectangular duct with a cross section of 0.93 cm X 22.9 cm and a height of 27 cm. The platinum ribbon was maintained at a constant total resistance (and therefore constant average temperature) by a constant temperature anemometer (TSI IFA-100). The ribbon was suspended in the center of the reactor channel with the gaseous reacting mixture (linear velocity of 2.9 cm/s) flowing perpendicular to its length. The gases, extra dry grade oxygen, prepurified nitrogen, and propylene (99.0% minimum purity), were controlled by a mass flow controller, purified, dried, and mixed before they entered the reactor at room temperature (22 "C). The catalyst was activated by heating to lo00 OC in air for 1 h before 1% propylene was introduced to the air stream for about 14 h. The infrared radiation from the ribbon was measured by a thermal imager (AGEMA Thermovision 780) placed next to a To whom correspondence should be addressed.
0022-3654/91/2095-3224$02.50/0
( 1 ) Field, R. J.; Burger, M. Oscillatiotu and Trawling Waves in Chemical Systems; Wiley: New York, 1985. (2) Razbn, L. F.; Chang, S.M.; Schmitz, R. A. Chem. Eng. Sci. 1986,41,
1561. (3) Lev, 0.; Wolffberg, A.; Pismen, L. M.; Sheintuch, M. J. Phys. Chem. 1989, 93, 1663. (4) Lev, 0.;Sheintuch, M.; Yarnitzky, C.; Pismen, L. M. Chem. Eng. Sci. 1990.45, 839. ( 5 ) Bassett, M. R.; Hudson, J. L. J. Phys. Chem. 1989, 93, 2731. (6) Zaikin, A. N.; Zhabotinski, A. M. Nature 1970, 255, 535. (7) Pismen, L. Chem. Eng. Sci. 1980, 35, 1950. (8) Sheintuch, M.; Pismen, L. Chem. Eng. Sci. 1981, 36, 893. (9) Schmitz, R.; Tsotsis, T. Chem. Eng. Sci. 1983, 38, 1421. (10) Bykov, V.; Gorban, A.; Kamenshehikov, L.; Yabloskii, G. Kinef. Catal. 1983, 24, 520. (11) Imbihl, R.; Cox, M. P.; Ertl. G. J . Chem. Phys. 1986. 84, 3518. (12) Imbihl, R.; Ladas, S.; Ertl, G. Surf. Sci. 1989. 215, L307. (13) Pawlicki, P. C.; Schmitz. R. A. Chem. Eng. frog. 1987, 83, 40. (14) Lobban, L.; Philippou, G.; Luss, D. J . Phys. Chem. 1989, 93, 733. (15) Lobban, L.; Luss, D. J . Phys. Chem. 1989, 93, 6530. (16) Kellow, J. C.; Wolf, E. Chem. Eng. Sci. 1990, 45, 2597. (17) Cordonier, G. A.; Schmidt, L. D. Chem. Eng. Sci. 1989, 44, 1983.
Q 1991 American Chemical Society
